abp i.M. 'Mi iCtbrarij 
 
 North CEaraltna *talp (CoUnje 
 
 NA3310 
 L3 
 
 Arch, lib, 
 
 ^Y 
 
Digitized by the Internet Archive 
 
 in 2009 with funding from 
 
 NCSU Libraries 
 
 http://www.archive.org/details/citycountrybuildOOIang 
 
The City and C o u n t r y 
 
 BUILDERS and IVORK MAN'S 
 TREASURY of DESIGNS: 
 
 Or the ART of 
 
 DRAWING and WORKING 
 
 The Ornamental PARTS of 
 
 ARCHITECrUREy 
 
 lUuftrated by upwards of Four Hundred grand Defigns, neatly engraved on 
 One Hundred and Eighty-ftx COPPER PLATES, for 
 
 PierSy 
 
 Pavements^ 
 
 Pedejlals, for 
 
 Gates, 
 
 Frets, 
 
 Sun-Dials, 
 
 Doors, 
 
 Gulochi's, 
 
 Bufto's, and 
 
 Windowsy 
 
 Pulpits^ 
 
 Stone Tables, 
 
 Niches, 
 
 Types, 
 
 Book-Cafes, 
 
 Buffets, 
 
 Altar Pieces, 
 
 Cielifigs, and 
 
 Cifterns, 
 
 Monuments, 
 
 Iron PForks^ 
 
 Chimney Pieces, 
 
 Fonts, 
 
 
 Tabernacle Frames^ 
 
 Obelifques, 
 
 
 Proportioned by A L I QJJ O T PARTS. 
 
 With an AFP E ND IX of Fourteen P L A T E S of "Trujes for Girders and Beams, different 
 
 Sorts of Rafters, and a Variety of Roofs, &c. 
 
 To which are prefix'd, 
 
 The Five Orders of Columns, according to Andrea Palladioj wliofe Members arc 
 proportioned by Aliquot Parts, in a more eafy Manner, than has yet been done. 
 
 The WHOLE interfperfed 
 
 With fure RULES for working all the Varieties of Raking Members in Pediments, Modilions, &c. 
 The like, for the immediate Ufe of W O R K M E N, never publifhed before, in any Language. 
 
 By B. L. Surveyor. 
 
 LONDON, Printed for and Sold by S. Harding on the Pavement in St. Martin's Lam. 1741. 
 
INTRODUCTION. 
 
 H E great Pleafure that Builders and Workmen of all Kinds have of late Years taken 
 in the Study of Architedlure ; and the great Advantages that have accrued to thofe, 
 for whom they have been employed ; by having their Works executed in a much 
 neater and more magnificent Manner than was ever done in this Kingdom before ; has 
 been the real Motive that induced me, to the compiling of this Work, for their further 
 Improvement. 
 
 Befides, as the Study of Architefture is really delightful in all its Procefs ; its Praftice is evidently 
 of the greateft Importance to Artificers in general ; and its Rules fo eafy, as to be acquired at leifure 
 Times, when the Bufinefs of Days is over, by Way of Diverfion : 'Tis a Matter of very great Sur- 
 prize to me i how any Perfon dare prefume to difcourage others from the Study thereof, and there- 
 by render them very often lefs ferviceable to the Publick than fo many Brutes. 
 
 But to prevent this Infeftion from diffufing its poifonous Effluvia's any further ; and in Confidera- 
 tion that amongft all Sorts of People, there are fome, in whom Nature has implanted that noble 
 Faculty of the Soul, called Reason, whereby we judge of Things : I have therefore, at a very great 
 Expence, compiled this Work for the common Good of all Af<f« of Reajotiy whofe Bufinefles require 
 the Knowledge of this Art, and who defire to become Proficients therein. 
 
 The firft Work to be done in order thereto, is perfeftly to.underftand the Five Orders of Columns, 
 which here I have placed precedent to the Defigns for that Purpofe ; and which I peremptorily admo- 
 nifh, be well underftood, before any Proceeding be made to attempt the Art of Defigning. 
 
 The Five Orders of Columns have their Members fo eafily adjufted, that the Reader, after having 
 once read their Explanations, need never read them a fecond Time. Nor will their general Pro- 
 portions efcape his Memory, after having praAifed them about half a Dozen Times. 
 
 The Defigns contained herein, and the Orders preceding them, are in general adjufted by Aliquot 
 Parts-, fo that when the. Height of any Work to be made, is known, (which in all Cafes muft firft be 
 given) and divided into fome certain Number of equal Parts, as affix'd to every Defign ; the Heights 
 and Projedtions of its Members are thereby determined. And, that young Students may not be at a 
 I.ofs herein, I have, for their further Inftruftions, ftiewn their particular Members, with their Mea- 
 fures at large -, which the Defigns of Inigo Jones, and all other Mafters to this Time, are defedive 
 in, and confequently are of no more Ufe to Workmen, than fo many Pictures to gaze at •, not fo 
 many Rules, or Examples to work by, or after ; unlefs to fuch, who underftand the Architedure 
 thereof, as well as their Authors, who defign'd them. 
 
 I ftiall now proceed to explain the Orders in the moft familiar Manner ; which will render the Un- 
 derftandiiig of all the following Defigns confpicuous to every Capacity. 
 
 B. LANGLE T. 
 CONTENTS 
 
 Of the Fourteen Plates of R O O F S, ^c. which are added to the IFcrk. 
 
 Plate I. Thefp'iceing or lengthening of Beams explained ; a 
 Beam Camber, with an Inch and quarter Spring, to 25 Feet 
 extent; diffeient Trufies for Girders and Beams, different Scarf- 
 ings for Wall-plates, Raifings, is'c. Plate II. Requifites for 
 fquare Roofs explained. Plate 1 1 1. A fecond Method for fpliceing 
 and lengthen ng of Beams. ThcLengthsandAnglcs of the Backs 
 of Hip-Rafters in irregular Roofs explained. The Lengths 
 and Angles of the Backs of Hip-Rafters in polygonal Roofs 
 explained. Plate IV. Circular, Elliptical, l^c. Hip-Rafters to 
 oflangular and (pheroidical Roofs explained. Plate V. To lay 
 out a Iquare Roof in l.cdgraent. Plate VI. A fquare double 
 Roof (commonly called an M J?»«/j in Ledgmenl. Plate VII. 
 An oblong double Roof (returned with fingle liipi at one End, 
 
 with an open Gutter, and double hip'd at the other End) in 
 Ledgement. Plate Vlll. A hip'd Roof in Ledgment having, 
 one End fquare, and the other End bevel with a cambred 
 Flat for a Balcony on its Top. Plate IX. An irregular 
 double Roof in Ledgment. Plate X. Two Vareties of framing 
 irregular fingle Roofs which are hip'd atone End, and gabled 
 at tlie other. Plate XL Two Examples of irregular Roofs in 
 Ledgement. Plate XII. Eight Examples of TrufTes for prin- 
 cipal Rafters true pitch. Plate XI IL Ten Examples for iruf- 
 fed Roofs. Plate XIV. Seftions of truffed Roofs, with the 
 Roofs of the Chmchti ol^K. Paul CnentGardat, and Grcen- 
 ivkh, with Remaiks. 
 
THE 
 
 AKT o£ DESIGNING ^nd WORKING 
 
 THE ) 
 
 ORNAMENTAL PARTS of BUILDINGS. 
 
 CHAP. I. 
 
 Of the Manner of Proportioning the Five Orders of Columns in Archite6lure 
 
 by Aliquot Parts. 
 
 I, Of the TUSCAN ORDER. 
 
 PR O B. I. To prof or Hon the Heights of the princi- 
 pal Parts of TvSq&w Order, Fig. I. Plate I. 
 
 RACriCE. Divide ^ a given 
 Height into 5 equal Parts, the low- 
 er I Part ko IS, the Height of the 
 Pedeftal. Divide a k the remain- 
 ing 4 Parts into 5 equal Parts, the 
 upper I Part ad, is the Height of 
 
 the Entablature, and d k, the lower 4, of the 
 
 Column, 
 
 P R O B. II. to proportion the Heights of the prin- 
 cipal Parts of the Tufcan Pedeftal, Fig. II. 
 
 Divide v w, a given Height into 4 Parts, the 
 
 lower I, is the Height of the Plinth, \ of the 
 next I, of the Mouldings on the Plinth, and half 
 the upper i of the Cornice. 
 
 P R O B. III. To proportion the Heights of the Mem- 
 bers on the Plinth ; and of the Cornice of the 
 Tufcan Pedeflal. 
 
 If the Mouldings on the Plinth be an Inverted 
 Cjma refta between two Fillets, divide the Height 
 in 6, give i to each Filler, and 4 to the Cima -, 
 but if the Mouldings are a Caveto on a Filler, 
 give 4 to the Caveto and z to the Fillet. Di- 
 vide the Height of the Cornice in 6, give the 
 upper I to theRegula E, the next 3 todieFaf- 
 cia F, and the remaining a to a Cima reverla, or 
 a Caveto with its Fillet, whofe Height is half 
 one Part. 
 
 C PROS. 
 
 D. H. HILL LIBRARY 
 North Carolina State Coileg* 
 
 139103 
 
Of the TUSCAN ORDER. 
 
 PR OB. IV. ^0 determine the PrejeHions of the 
 Dado, Bafi and Cornice of the Tufcan Pedejial^ 
 Fig. II. Plate I. 
 
 • (i.) Divide QJsf, equal to the Height of the 
 Bale in 5 Parts, and the upper i in 7 Parts ; 
 Make z O the Projeftion of the Dado, equal to 
 4 Barts and ^ (2.) The Projedion of the 
 Plinth {qp) is equal to {r q) the Height of the 
 Mouldings on the Plinth, as alfo is the Projeaion 
 of the Cornice, from the Upright of the Dado, 
 in every Order. Draw *■ jy at Pleafure, at any 
 Part againfl: the Dado, which divide in 6 P.uts, 
 and terminate the Members in the Bafe and Cor- 
 nice, as is exprefTcd by the dotted Lines proceed- 
 inor upward and downward from them. 
 
 'pig. G. exhibits the Manner of defcribing a 
 Cima reverfa at large, whofe Projedtion is 5 of 
 its Height. 
 
 PR O B. V. To proportion the Heights of the prin- 
 cipal Parts of the Tufcan Column, Fig. I. PI. II. 
 
 (1.) Divide the given Height in 7 equal Parts, 
 and take i for the Diameter of the Column at its 
 Bafe •, therefore note, that the Height of the Co- 
 lumn is 7 Diameters. (2.) The Height of the 
 B.ill', and of the Capital, are each half a Dia- 
 meter. 
 
 P ROB. VI. To proportion the Heights of the 
 Ahmbers of the Bafe of the Tufcan Column. 
 
 Divide s t the Height of the Bafe in t Parts, as 
 the B.ife on the Pedcltal Fig. II. Plate I. the low- 
 cr 1 is the Height of the Plinth D, and the upper 
 I of its Torus C, with the Cindlure B, which is 
 a fourth Part thereof. 
 
 PR OB. VII. To proportion the Heights of the 
 Members of the Tufcan Capital. 
 
 Divide, the Height of the Capital M R, into 3 
 Parts, as in Fig. II. Plate II. give the upper i to its 
 Abacus M N, the Middle 1 to the Ovolo O with 
 its Fillet P, which is a fixth Part, and the lower 
 1 to CLthe Neck of the Capital. The Height 
 of the AiVrjgal R S, is equal to Half the Height 
 of the Neck, which divide in 3 : Give 1 to the 
 Aflragal R, and i to the Fillet S. Note, The 
 Aftragal in every Order is a Part of the Shaft, 
 not of the Capital. 
 
 PROB. VIII. To diminifh the Shaft of the Tufcan, 
 or any other Colwnn, Fig. I. Plate II. 
 
 (i.; Divide the given Height of the Shaft be- 
 tween the Cmdlure B, and An:ragal A, into 3 
 equal Parts, and draw the Line nxy, though 
 the firft Part, parallel to the Cinfture 4, 5 ; make 
 B 4, B 5, and x n, x y, each equal to Half a 
 Diameter, and draw the Lines 4W, Sj' ^'^^^ 
 A b, and A c, each ■equal to i or t of n x, ac- 
 cording to what Quantity you have a Mind to di- 
 minifh the Shaft ; fome making the Diminution 
 i or t, as in this Example. (2.) On « defcribe 
 the Semicircle nr i y, and dn\w the Lines b r, 
 and c f. from the Points be, parallel to the cen- 
 tral Line A B. Divide the Arches n r and i y, 
 each into any Number of like equal Parts, fup- 
 pofe four, as at p q, and 2, 3,2, and dr.iw the 
 Ordinates q r, p 2-, ^^nd %. i^.) Divide A a; 
 into the fame Number of equal Parts as in « r, 
 or 1 y, as at / /?> d, and draw the Lines, e f equal 
 to ^ 2 ; ^ / equal to p 3, and k m equal to z. 
 (4.) From w, through the Points k g e, draw the 
 curved Line « )^_g-^ /J-, and from y through the 
 Points m i f, the curved Line y m if, which com- 
 pletes the Diminution of the Shaft as required. 
 
 PROB. IX. To determine the ProjeSlions of the 
 Members in the Bafe of the Tufcan Coluran^ 
 Fig. I. Plate I. 
 
 (i.) Divide the Semldi.. viviter in 3 P.;rrs, and 
 turn I Part out for the Projecflion of the Plinth, 
 v.hich in every Order, Itands exactly over the 
 r^do of the Pcdcftal. (1.) The Proieftica of 
 tho Torus is always the f.iiv.e as of th ; Plinth. 
 (3.) Divide the Projefbioa of the Plinth bcforo the 
 Uprif t - of the Shaft into 4 Parts, and the third 
 Part rito 4, then the firft i Part terminates the 
 Prqjeftion of the Cinfture B. 
 
 PROB. X. To determine the ProjeSlions of the 
 Members in the Tufcan Capital, Fig. II. PI. II. 
 
 Divide the Semidiameter of the Shaft continued 
 to the Abacus into a Parts, as at /, and make 
 the Projeftion of the Abacus, equal to x of thofe 
 Parts, when the Abacus is finifhed with a Fillet, 
 and to 1^ of I Part, when without a Fillet. The 
 Proieftion of the Fillet under the Aftragal, is e- 
 qual to twice its own Height, and the Fillet un- 
 der the Ovolo, to its Height. 
 
 PROB. 
 
 f 
 
Of ths DORICK ORDER. 
 
 P R O B. XI. to proportion the Heights of the prin- 
 cipal Parts of the- Tulcan Entablature, Fig. II. 
 Plate II. 
 
 Divide A M the given Height, into 7 equal 
 Parts ; give ^ to the Architrave, 2 to the Freeze, 
 and 3 to the Cornice. 
 
 PROS. XII. To proportion the Heights of the 
 Members of the Tulcan Architrave. 
 
 If the Architrave is to conilil: but of i Fafcia, 
 divide its Height in 7 Parts, and give i and , to 
 the Height of the Tenia I, and the Remainder to 
 the Fafcia K; but if of two Fafcia'^, give the low- 
 er % to the fmall Fafcia, tlic wtxx. 4 to the great 
 Fafcia, and the upper i to tiie Tenia. 
 
 PROB. XIII. To proportion the Heights of the 
 Members of the Tulcan Cornice. 
 
 The Height of the Cornice confifting of 3 Parts 
 divide the upper 1 Part, in 4, and when this En- 
 tablature is finiih'd with aCima rcCLa, give the up- 
 per 1 to its Fillet ; but when with an Ovolo, give 
 the lower i to its Afliragal. The middle i Tart 
 of the Cornice being divided in 6 Parts, give the 
 upper 1 to the Fiilet C, and tlie other 5 to the Co- 
 rona D. The lower i Pai t of the Cornice, di- 
 vided in a Pa.T% give the uppfr i to the Ovolo 
 E, and the other i to .ls Caveto G, and Fillet E, 
 which is \ Part iliereol. 
 
 PROB. XIV. "To determine the ProjeSures of the 
 Ahmbcrs in the Tufcan Architrave and Cornice.. 
 Fig. II. Plate II. 
 
 (i.) The Projeftion of the lower Fafcia of the 
 Architrave, and of the Freeze, in every Order, is 
 always the fame from the central Line of the Co- 
 lumn as the Upright of the Column, at its Allra- 
 gal •, and therefore are all diredlly over each o- 
 ther. It is from the upright Line of the Face of 
 the Freeze, that the Projeftions of all the Mem- 
 bers in every Architrave and Cornice of each Or- 
 der, is accounted. (2.) The Projeftion of the 
 Tenia I is equal to its Height, and the upper 
 Fafcia, when the Architrave has two, projefts \ 
 thereof. (3.) The Projedtion of the Cornice, is 
 (as 'tis in all the other Orders, the Dorick only ex- 
 cepted) equal to its own Height. Draw b c, e- 
 qual to the whole Projeftion, which divide in 3 
 
 equal Parts -, then I the firft Part, terminates the 
 Fillet F, of the Caveto G. The firft Part termi- 
 nates the Ovolo E, the fecond Part the Corona D, 
 and the firft fixth Part of the laft Part, the Fillet 
 C. And thus this Order is compleated, and 
 which being prafticed about half a dozen Times, 
 will render the underftanding of this and the fol- 
 lowing Order, eafy and delightful. 
 
 II. 0/ the DORICK ORDER. 
 
 PROB. I. To proportion the Heights of the prin- 
 cipal Parts of the Dorick Order, Fig. I. PI. III. 
 
 Practice. Divide <z ^ a given Height, in- 
 to 5 Parts Cas before in the Tufcan) the lower i 
 Part i k, is the Height of the Pedeftal. Divide 
 a i the remaining 4 Parts in 5 Parts, the upper 
 1 Part af is the Entablature, and//, the lower 
 4 Parts, of the Column. Here you fee that thje 
 Manner of proportioning the principal Parts of 
 the Tufcan and Dorick Orders, is the fame. 
 
 PROB. II. To proportion the Heights of the pritu 
 cipal Parts of theDonck Pedejiat. Fig. II. PI. III. 
 
 Divide the Height in 4 Parts, give i and J t5> 
 the Bafe ; y the upper i to the Cornice, and the 
 Remains to the Dado. 
 
 PROB. III. To proportion the Heights of the 
 Members on the Plinth, and of the Cornice of the- 
 Dorick PedeflaU Fig. II. Plate III.. 
 
 (i.) Divide ti the Height of the Mouldings 
 on the Plinth, in S Parts, give the lower 1 Part to 
 theFilletK,the next 4 to the Cimal,and the upper 
 3, to an Aftragal H, and Fillet G; or to a Fillet 
 and Caveto. (2.) Divide the Height of the 
 Cornice in 2 Parts, i of the upper i,. is the 
 Height of the Regula A and the Remainder, of 
 the Fafcia B. The upper Half, of the lower i, is 
 the Height of the Ovolo C, and the lower Half 
 divided in 3, give the upper i to the Fillet D, and 
 lower 2 to a Cima Inverfa,. or Caveto E. 
 
 PROB. IV. To determine the ProjeSIions cf t he- 
 Dado, Baje, and Cornice of the Dorick Pedefial, 
 Fig. II. Plate III. 
 Make u w the Pro)e£l:ion of the Dado, equal 
 
 to A,- J, which is the Height of the Plinth divided 
 
 ini 
 
Of ihc DORICK ORDER. 
 
 in 5 Parts, and j of the upper Part divided in 3, 
 turned up. Tlie Projeftion of the PJiiuh and 
 Cornice before the Upright of the Dado, is (as 
 before obfcrvcd in the 'Tw^va;; Order) always equal 
 to the Height of the Mouldings on the Plinth, 
 which here at m «, being divided in 4 Parts, the 
 Projedlions of the Members in the Cor:iice, and 
 Bafe are determined, as exhibited by the perpen- 
 dicular dotted Lines. 
 
 PROB. V. "To proportion the Heights of the prin- 
 cipal Parts of the Dorick Coli!!n»,¥\^. I. PI. III. 
 
 (I.) Divide ft the Height of the Column in- 
 to 8 Parts, and take 1 Part, for the Diameter of 
 the Column at its Bafe : Therefore note, chat the 
 Height of the Dorick Column is 8 Diameters. 
 (I.) The Height of the Dorick Bafe and Capital 
 are each Half a Diameter, as thofe of the Tujcan. 
 
 PROB. VI. To proportion the Heights of the Bafe 
 of the Dorick Column. 
 
 Divide fh. Fig. II. Plate III. In 3 Parts, the 
 lower I Part is the Height of the Plinth T, and 
 I of the Middle i, of the lower Torus S. Half 
 the upper i Part, is the Height of the upper To- 
 rus O, and the Remains between the two Torus's 
 being divided in 6 Parts, give the upper and low- 
 er, to the two Fillets P and R, and the Middle 4 
 to the Scotia Q^ The Height of the Cinfture N 
 is half of the Height of the upper Torus. 
 
 PROB. VII. To proportion the Heights of the 
 Dorick Capital. 
 
 Divide a h the Height of the Capital, Fig. II. 
 Plate III, into 3 Parts, and v the upper i, into 
 3 -, give the upper i to the Fillet A, the other 2 
 to the Cima reverfa B, and the other ^ Part to 
 the Abacus C. Divide the Middle Part in 3, give 
 the upper ^ to the Ovolo D, and the other i to 
 an Aftragal and Fillet, or Fillet and Caveto, or 
 Cima reverfa, or to three Annulets, at Pleafure. 
 The Height of the Hypotrachclium G, or Neck 
 of the Capital, is the lower i Part, and the Height 
 of the Aftragal \ thereof, as before in the Tufcan. 
 The Shaft of this Column is diminifhed v at its 
 Aftragal in Manner aforefaid. 
 
 PROB. Vlir. To determine the ProjeElions of the 
 Members of the Bafe of the Dorick Column. 
 
 (I.) Divide the Semldiameter ? 3, in 3 Parts, 
 and turn out i Part from / to k, for the Projeftion 
 of the Plinth, before the Upright of the Column. 
 (1.) Divide the Projeftion >(• r, in 4 Parts, the firft: 
 one and a half, terminates the Projeftion of the 
 Fillet R ; and a Parts and half, the Centre of the 
 upper Torus O, and Cincture M. 
 
 PROB. IX. To defer ibe the Scotia Q^at large, 
 as at g ; Plate III. 
 
 Divide its Height in 3 Parts, and fct one Parr, 
 from the fecond Part towards the Right Hand ; 
 then the Points * * are the Centers on which the 
 Scotia may be defcribcd as required. 
 
 PROB.X. To determine the Proje£lions of the Mem- 
 bers of the Dorick Capital. Fig. II. Plate III. 
 
 Divide the Semldiameter of the Column at its 
 Aftragal on its Abacus, into 2 Parts, and turn 
 out I Part for the Projeftion of the Abacus v 
 which divide in 4 Parts,- and terminate the Pro- 
 jeftions of the Members, as exhibited by the 
 dotted perpendicular Lines. The Projeftion of 
 the Aftragal H I, is determined the fame, as that 
 of the Tufcan Order. 
 
 PROB. XI. To proportion the Heights of the 
 principal Parts of the Dorick Entablature^ Plate 
 IV. 
 
 Divide a b, the given Height into 8 equal 
 Parts, give 2 to the Architrave M N O P, 3 to 
 the Freeze L, and 3 to the Cornice. 
 
 PROB. XII. To proportion the Heights of the 
 Members of the Dorick Architrave. 
 
 Divide the upper one Part of the Architrave in 
 3, the upper i, is the Height of the Tenia M, 
 and the lower a Parts, divided in 3 Parts, the 
 upper I Part is the Height of the Fillet N, and 
 the next 3 Parts of the Gutta's or Drops O. 
 
 PROB. XIII. To proportion the Heights of the 
 Members of the Dorick Cornice. 
 
 Divide the two upper Parts of the Height of 
 the Cornice into 3 Parts, and the upper i, in 4 
 Parts ; give the upper i to the Regula A, and 
 the other 3 to the Caveto or Cima refta B, Di- 
 vide 
 
Of thg DORICK ORDER. 
 
 vide the next Part in 3, give half the upper i to 
 the Fillet C, and the Remains to the Corona D. 
 Divide the third Part in 3, and the upper i thereof, 
 in 3 ; of which, give the upper 1 to the Fillet E, 
 the other i to the Cima reverfa F •, and the Re- 
 fidue of this Part to G, the Fafcia of the Mutule 
 E F G. Divide the lower third Part of the Height 
 of the whole Cornice into 3 Parts, and give the 
 lower I to K, the Capping of the Triglyphs ; di- 
 vide the next 2, each into 3 ; give the lower i to 
 the Fillet I, and the next 4, to the Ovolo H, or 
 to an Ovolo, with its Aliragal on the Fillet I. 
 The Height of the Freeze being in 3, divide the 
 upper I in 3, and the fecond will terminate the 
 Heights of the Channels in the Triglyphs ; as half 
 the middle 1, doth, that of the Coffer or hollow 
 Pannel, in the Metope Q^ 
 
 P R O B. XIV. To determine the Proj enures of the 
 Members, in the Dorick. EiUablattire. Plate IV. 
 
 (1.) As the Projedlion of the Cornice is equal 
 to half the Height of the whole Entablature, 
 therefore draw a Line from any Part of the Freeze, 
 as c d, equal thereto, which divide in 4 Parts, and 
 the firfl:,. third, and laft, each into 3 Parts, from 
 whence determine the Projei5lion of every Mem- 
 ber, as exprefs'd by the perpendicular dotted Lines 
 which pals through them from the Profile to the 
 Plan. 
 
 PR OB. XV. 
 
 To proportion a Triglyph, 
 Metope. 
 
 and 
 
 The Breadth of each Triglyph is always equal 
 to half the Diameter of the Column at its Bafc; and 
 the Metope or Dillance between them, fhould al- 
 ways be equal to the Height of the Freeze. The 
 Breadth of each Triglyph being divided into 12 
 Parts, and Lines drav/n, as the dotted Lines 1, 
 2, 3, £5?^. will form the Limits of the Channel- 
 lings, and fix Gutta's, or Drops, under them. As 
 by the Mutule S, 'tis evident, that the Frojeftion 
 is very confiderable, I have therefore added the 
 Plan of the Planceer of the Cornice,wherein V V V 
 reprefent, the under Surface of the Mutules, as 
 they are generally enriched with their 36 Drops, 
 commonly called Bells, and X X are hollow 
 Pannels, or Coffers, enriched with Rofes. By the 
 perpendicular dotted Lines, 'tis evident, that the 
 Diftances of the Members in the Plan, are equal 
 to their refpedive Projedions in the Profile. 
 
 Fig. W exhibits two Methods for fluting the 
 Shafts of Dorick Columns •, that on the Right 
 Hand has no Fillets, as was anciently pradticed, 
 and which contain 20 in Number ; the Flutings 
 on the Left, are after the modern Manner, and 
 contain 24 in Number. 
 
 PROB. XVL To divide the Flutes of the Dorick 
 Shaft, after the antient Manner. 
 
 Divide the Circumference of the Column into 
 20 equal Parts, and draw the Chord Line of 
 each Part, on every of which, complete an equi- 
 lateral Triangle ; then on the Out-Angle of 
 every Triangle, with the Radius of one Side, de- 
 fcribe the Curve of each Flute. 
 
 PROB. XVII. To divide the Flutes and Fillets of 
 the Dorick Shaft, after the modem Alanner. 
 
 (i.) Divide the Circumference of the Column 
 into 10, but by fome 'tis divided into 24 Parts. 
 (z.) Divide any one Part into 6 Parts, and with 
 a Radius of 3 of thofe Parts, on every of the ao, 
 or 14 Points defcribe the Flutes, which will leave 
 between them, the Fillets required. 
 
 nr> Of the lO^lCK ORDER. 
 
 PROB. I. To proportion the Heights of the princi- 
 pal Parts cf the lonick Order, Fig. I. Plate V. 
 
 Pro AT ICE. ( I.) Divide « /, a given Height^, 
 into 5 Parts, and give the lower i to the Pede- 
 ftal, as in the preceding Orders. (2.) Divide ag 
 the Remainder, into 6 Parts, the upper i Part^^ 
 is the Height of the Entablature, .ind dg the low- 
 er 5 Parts, of the Column.. 
 
 PROB. II. To proportion the Heights of the princi- 
 pal Parts of the lonick PedeJ^al, Fig. II. PI. V. 
 
 Divide the given Height in 4 equal Part:«, give 
 the lower i to the Plinth N ; one third ot the 
 next to the Mouldings on the Plinth, including 
 the Hollow on the Aftraga!, when ufed inftead of 
 a Caveto, (as is fometimes done )•, hali the upper 
 I to the Cornice y a, arid the Remains to the 
 Dado a b. 
 
 D 
 
 PROB. 
 
Of the 10NICK ^ORDER. 
 
 V R () B. III. To propcrlion the Heights of ike 
 Members on the Plinth ; crdof the Cernice of the 
 lonick Pedefia\ Fig. II. Plate V. 
 
 (i.) Divide the Height of the Mouldings on 
 the Bale i.nto 8 Parts ; give the lower i to the Fillet 
 M, the next 4 to the Cima rcfta L ; the next i 
 and a half, to the Aitragal K-, half the next i to the 
 Fillet I, and the remaining i and a half to a Cave- 
 to, or Hollow, as H. (i.) Divide y <t, the Height 
 of the Cornice into 3 Parts, and each Part into 4 
 Parts, then the Whole is in 12 Parts -, give the 
 upper I to the Regiila A ; the next 2 t6 the Ca- 
 vcto, orCima re^'c^fa B •, the next 3 Parts to the 
 Fafcia or Platband C ; the next 3 to the Cima 
 refta D,. (which is oft.;n made an Ovolo,) ; the 
 next 1 tothe Aftragal E, and the remaining 2 to 
 a Caveto, or Cima reverfa, as F. 
 
 ■PTIOB. IV. To deter mive the Proje^ ions cf the 
 ■ Dado, Bafe emd Cornice of the lonick Pedefial, 
 •Fig. II. Plate V. 
 
 (i.) Divide the Height of the Plinth into three 
 Parts, the upper i into 9, and the upper i ot 
 the p into 3 -, fiom the firfl: of which draw the 
 Line /f, cutting the central Line in c ; makex^^ 
 the Ptojeftion of the Dado, equal to c z. (2.) 
 Make ^/equal to one third of the Plinth's Height, 
 for the Projedtion of the Plinth and Cornice before 
 tire Dado. (3.) In any Place againil the Dado, 
 as at s, draw the Line r .?, equal to f g -, which 
 ■divide -in 4 Parts -, fubdivide them again as by 
 Infpeclion is flvjwn, and terminate every Mem- 
 ber as eyprelTed by the perpendicular dotted Lines 
 •proceeding from tlience. 
 
 P R O B. V. To proportion the Heights of the prin- 
 cipal Parts of the lonick Column. 
 
 Divide d g., Fi*. I. Plate V. into 9 Parts, and 
 take I Part for the Diameter of the Column at its 
 "Bafc. The Height of the Bafe is half a Diame- 
 'ter, as alio is the Height of the Capital, including 
 the Height of its Volute. 
 
 PR OB. VI. To proportion the Heights of the 
 Members of the Bafe of the lonick Column. 
 
 Divide 0/), the given Height (Fig. II. PI. V.) 
 in 3 Parts i the lower i, is the Height of the 
 
 Plinth S. Divide the upper 2 Parts in 9, the 
 firft 3 Parts is the Height of the lower Torus R 5 
 two thirds of the next Part, of the Fillet Q ; 
 fhc uppermoll two and half, of the upper Torus 
 N ; which is made with a Bead under-it, the half 
 Part is given to the Bead, and but a to the To- 
 rus. The remaining half Part is given to the Fil- 
 let O. The Height of the Aftragal with its Fil- 
 let, when ufcd on tlie upperTorus, is equal to half 
 the Height of the upper Torus, but when a Cinc- 
 ture only is placed there, its Height is two fifths 
 of the upper Torus. 
 
 PR OB. VII. To proportion the Heights of the 
 Members of tU lonick Capital., Fig. II. PI. V. 
 
 ('r.) Divide v %\ the given Height into three 
 Parts, and half the upper i into 4 Parts, then the 
 upper 3 Parts, is the Height of the Ovolo A, of 
 the Abacus ; and the lower i of the Fillet B. 
 (a.) Divide to to, equal to \ of vv, in 8 Parts ; 
 give the upper i and a half to the Caveto C -, 
 the next half to the Fillet D ; the next 1 to the 
 Ovolo E ; the next 1 to the Aftragal F, and die 
 next h;ilf to its Fillet G ; then the remaining two 
 halfs will be the Depth that the Volutes will de- 
 fctnd. The Shaft of this Column is diminifhed 
 at its Aftragal, one fixth of its Diameter at the 
 Bafe. 
 
 P R O B. VIII. To determine the ProjeElures of the 
 Members of the hafe of the lonick Capital, Fig. 
 II. Plate V. 
 
 (I.) Divide the Seniidiametcr i v in 3 Parts, 
 and turn out i Parr, for the Projeflion of the 
 Plinths, and Torus R. {i.) Divide the Projec- 
 tion of the Plinth before the Upright of the Co- 
 lumn into 3 Parts, the firft i terminates the Cen- 
 tre of the lower Torus, and the fecond of the 
 Cinfture L , divide the Middle Part in 4, half 
 the firft 1 terminates the Fillet Q_, and half the 
 laft, the Fillet O. The Scotia P is defcribed at 
 large, as in Fig. III. 
 
 P R O B. IX. To determine the PrcjeBures cf the 
 Members ef the lomck Capital, Fig. II. PI.VIIL 
 
 Place the Diameter of the Column at its Bafe 
 divided into 60 Minutes , as is done between 
 F and E, and continue it 15 Minutes both ■ways 
 to Y and Z. This done, fct 45 Minutes '^on 
 
 each 
 
0/ the aONICK ORDER. 
 
 each Side the central Line which terminates the 
 Ovolo A, in Plate V. Alfo let 40 Minutes on 
 each Side for the rrojeaion of the Fillet B ; 38 
 for the Projec-'lion of theCaveto C, and 35 for the 
 O/olo E. The Projcdion of the Fillet G, is its 
 own Height and two thirds thereof, over which 
 the Aliragal projeds half its own Height. The 
 next Thing in order to complete this Capital, is to 
 dcfcribe its Volutes as following. 
 
 PR OB. X. To defcribe the lomck' Volute, Pkte 
 
 VII. 
 
 (I.) Divide « X, a given Height of a Capital 
 into 3 Pans, and the upper i Part in 2 Parts at 
 f, and proceed to complete all the Members as 
 taught in the laft Problem. (2.) On p the Cen- 
 tre of the Aftragal defcribe the Circle r ox q for 
 the Eye of the Volute, through whofe Centre p, 
 draw the perpendicular Line napq^, alfo the 
 horizontal Line r p s, at right Angles thereto ; 
 and complete the Geometrical Square r xq; 
 whofe Sides divide each in two equal Parts at the 
 Points X, 1,3, 4, and draw the Diameters a, 4; 
 
 and 1,3-, (3.) Divide each Semidiameter into 3 
 equal Parts, at the Points 6, 10 •, 5, 9 ; 1 1, 7 > 
 and I^, 8 •, then the Points « 2345678910 
 11 I a, are 1 1 Centres on which the Out-line of 
 the Volute is dcfcribed •, for the Point i is the 
 Centre of the Arch n h ; the Point 1, of the Arch 
 be; the Point 3, of the Arch eg; the Point 4 
 of the Arch g h ; the Point 5, of the Arch h k, &c. 
 (3.) Divide W Z in 4 Parts •, the upper 1 equal 
 to n a, is the Breadth of the Lift ; which divide 
 in 12 Parts, of which make b c equal to 11 ; ed 
 equal to 10; ^/ equal to 9 ; hi equal to 8 ; k I 
 equal to 7, isc. ftill diminiihing i at every Quar- 
 ter. This done divide the Diftance between every 
 two Centres, as between i and 6; i and 5, ^c. 
 into 5 Parts, and the it outermoft ones will be the 
 II Centres, on which the inward Line of the Lift 
 may be defcribed, wliich from the Point a will 
 pafs through the Points c d f i I, ^c. and com- 
 plete the Volute as required. 
 
 To make the Jcnick Volute well underftood, I 
 have given the Plan of a Quarter Part of it" Ca- 
 pital, Fig. III. Plate VIII. wherein obferve ; that 
 as the Volutes are placed anglewife, or rather dia- 
 gonally -, therefore when we ftand direftly before 
 a Column, though .they are really circular, as in 
 Plate VII, yet they will appear elliptical 5 as hav- 
 
 ing their Breadths forefliorten'd by being feenin 
 an oblique View ; and therefore when we make ;i 
 Drawing of this Ca.pita!, the Volutes muft be 
 made elliptical, as in Fig. II. Plate VIII. 
 
 PR OB. XI. To divide the .Flutes and Fillets of a 
 round or fquare lonick Column, Fig. \\l. Plate 
 
 VIII. : 
 
 Firft, Of a round Column, as the Quarter Part 
 M Kli divide the Circumference of the Pillar into 
 14 equal Parts, and each Part into 8 Parts ; with 
 the Radius of 3 of thofe 8 Parts, on every of the 
 14 Parts, defcribe the Flutes, as before done in 
 the Dorick Order. 
 
 Secondly, Of a fquare Column, as the Quarter 
 Part K A L ; divide each Semidiameter, or each 
 Side of the Column, into 31 Parts, give 6 to 
 each Flute, 1 to each Fillet and .Bead at the 
 Angles, when the Semidiameters are divided 
 into 3 1 Parts •, and 3 to each Flute, and i to 
 each Fillet, and Bead, at the Angles, when a Side 
 of the Column is divided in the fame Number of 
 Parts. On the Right Hand, at the lower Angle 
 of Plate VIII, I have defcribed the Bead A at 
 large, by which the young Student may fee that 
 'tis no more, than three fourths of a Circle ia- 
 fcribed in a geometrical Square. 
 
 As the Ovolo of this Capital is generally en- 
 riched with Eggs and Darts, commonly called 
 Anchors^ I ftiall therefore fliew at large, the Man- 
 ner of delcribing them. 
 
 P R OB. X.\[. Jo defcribe-Eggs and Darts for the 
 Enrichment of an Ovolo, Fig. I, Plate VIII. 
 
 Firft, To proportion their Diflances. 
 
 Divide the Height into 9 Parts, and at the Di- 
 ftance of 7 of thofe Parts, draw the central Lines 
 of the Eggs and Darts. 
 
 Secondly, To defcribe an Egg, a^ Fig. B. 
 
 The Height of the central Line- being divided 
 in 9 Parts, with a Radius equal to 3 Parts, on tlie 
 Point 6, the third Part from the Top, defcribe 
 a Semicircle. On the Point ■ 3, the third Point 
 from the Bottom, v/ith a Radius of 2 Parts, de- 
 fcribe an entire Circle. Draw down the Lines 
 .4 a, 4^, each equal to 3 Parts, and through the 
 Point 3, draw the Lines a b and a c. On the 
 Points a a, with the Radius a b, defcribe the Side 
 Curves, which will complete the Egg, as requi- 
 red. 
 
 Thirdly, 
 
8 
 
 Of the lONICK ORDER. 
 
 Thirdly, To defcrihe the inward Curve of the 
 Hujk, Fig. C. 
 
 Draw the Lines 4 *, 4 <: as before, but make 
 each equal to 2 Parts. Through the Point d, 
 which is the Midft between the Points 3 and 4, 
 draw the Lines a b and a c oi Length at Plea- 
 fure. On d with the Radius of 3 Parts defcribe 
 the Arch be, and on the Points a a, with the 
 Radius a b, defcribe the Arches ba 4 and f « 4, 
 which completes the inward Line as required. 
 
 Fourthly, To defcribe the cutward Line of the 
 R-'A, Fig. D. 
 
 Draw '^a, I a each 1 Part in Length, and 
 through the Point b, which is the Midft between 
 the Points 4 and 5, draw the Lines a b c, and 
 abd, of Length at Pleafure. On the Point b 
 with a Radius equal to 4 Parts and an half de- 
 fcribe the Arch cd. On the Points a a, with the 
 Radius a c, defcribe the upper Side Cui-ves,which 
 completes the Out-curve as required. 
 Fifthly, To defcribe a Dart. 
 
 Divide one Part on each Side its central Line in 
 a Parts, and from the angular Point of the Dart, 
 draw the interior Lines ; let ^ Parts up from the 
 angular Point, and from that Point, draw Lines 
 to 14 Parts Diftance on the Top Line -, alio from 
 the angular Point draw Lines up to 7 Parts on 
 each Side its central Line. Then draw Lines 
 from the angular Point to i Part on each Side its 
 central Line, will complete a Dart as required. 
 P'ig. A rcprefents the Lines of all thcle i;ift Four 
 Operations, compriz'd in one. 
 
 PR OB. XIII. To proportion the Heights of the 
 principal Parts of the lonick Entablature, Plate 
 VI. 
 
 Divide the Height ae into 10 Parts, give 3 to 
 the Architrave, 3 to the Freeze, and 4 to the 
 Cornice. 
 
 PR OB. XIV. To proportion the Heights of the 
 Members of the lonick Jrchitr^ve, Plate VI. 
 
 Divide df the Height, in 4 Parts •, the firft 
 one is the Height of the lower Fafcia R, and one 
 third of the next Part of the Cima reverfa Q^; 
 divide the upper Part in 3, give the upper third 
 Part to the Tenia N, and the other a Parts to the 
 Cima reveria, or Caveto O. The remaining one 
 Part and two thirds is the Height of the upper 
 F-ifcia P. 
 
 P R O B. XV. To proportion the Heights of (he 
 Membors in the lonick Cornice, Plate VI. 
 
 (I.) The Height being in 4 Parts, divide the 
 upper I in 4, and when the Cima refta B, has no 
 Artragal under it, give the upper i to the Re- 
 gula A, and 2 and two thirds to the Cima -, but 
 if an Aftragal be introduced under the Cima, then 
 give half the upper i to the Regula A ; the next 
 2 and an half to the Cima rcfta B, and remaining 
 two thirds of 1 to the Aftragal on the Fillet C. 
 (z.) Divide the fecond 1 Part in 4 ; give the up- 
 per I to the Cima reverfa D, and the lower 3 to 
 the Corona E. C3.) Divide the third 1, from 
 the Top in 4, and the upper i thereof in 4 ; of 
 which give the upper i to the Fillet F, and the 
 other 3 to the Cima reveria G. The Depth of 
 the Face of the Modillion is two Parts and an half. 
 (4.) Divide the lower fourth Part in a Parts, and 
 give the upper i to the Ovolo I : And the lower 1 
 divided in 5, give the upper i to the Fillet K, and 
 other 4 to a Caveto or Cima reverfa, L. 
 
 P R O B. XVI. To determine the ProjeHions of the 
 Members of the lonick Architrave and Freeze. 
 
 (i.) The Projeftion of the Tenia is equal to 
 one fourth of the Height of the whole Archi- 
 trave; and the great Fafcia P, to one third there- 
 of. (1.) The Projeftion of the Freeze is equal ta 
 that of the Architrave. 
 
 P R O B. XVII. To determine the PrcjeHions of the 
 Members of the lonick Cornice. 
 
 The Projeftion of the whole Cornice is always 
 equal to its whole Height, and its particular Mem- 
 bers have their Projections determined as follows, 
 viz. draw a Line as iv x, equal to the Projedtion 
 of the whole Cornice, which divide in 4 Parts v 
 fubdivide them again, and terminate each Mem- 
 ber as exhibited by the dotted perpendicular Lines, 
 which pafs through the Divifions from the Profile 
 to the Plan, or Planceer of the Cornice. 
 
 P R O B. XVIII. To defcribe the under Curvature 
 of <j«Jonick Modillion at large. Fig, V. Plate 
 XII. 
 
 The Projeftion being found, as in the laft Pro- 
 blem, which fuppofe to be r n, or * 6 j divide it 
 
 in 
 
Of the CORINTHIAN ORDER. 
 
 in 6 Parts. On the Point w, ereft the Perpen- 
 dicular TO V, equal to i Part, and on the Point 
 2, defcribe the Aich i i;; on the Point 5, ereft 
 the Perpendicular 5 j, equal to 2 Parts and an 
 half ; make v z equal to 5 s, and draw the 
 Line s z. On the Points s and 2, with the Di- 
 ftance s 5, defcribe the compound Curve v 5, 
 which completes the Curve of its Planceer. The 
 Breadth of the Face of a Modillion, is 10 Mi- 
 nutes, or one fixth Part of the Diameter of the 
 Column at its B.ife. The Interval or Diftance 
 between them in a Cornice over Columns, is 25 
 Minutes, or ^ of a Semidiameter : But in a Cor- 
 nice over Pillaftcrs, which are not diminiflied, 
 the Interval muft be 30 Minutes or a Semidia- 
 meter, precifcly. In the Plan of the Cornice 
 Plate VI. S S, &c. reprefents the Planceers of 
 the Modillions ; and T T, ^c. the CotFers or 
 hollow Pannels enriched with Rofes in the In- 
 tervals. 
 
 of the Torus O, and one third of the next half 
 to the Fillet N J give the upper two thirds of the 
 upper half, of the upper Part, to the Caveto K, 
 and the other third Part, being divided in three 
 Parts, give i to the Fillet, and x to the Affra- 
 gal, L. {2.) Divide de the Height of the Cor- 
 nice in 3 Parts, and the upper i in 6 Parts ; of 
 which, give the upper i and one third, to the 
 Height of the Regula A ; the next two Parts 
 and two thirds to the Height of the Cima re- 
 verfa B, and the next i Part 'to the Height of 
 the Aftragal C; divide the Middle Part in 2, 
 and give the upper i to the Height of the Fafcia 
 or Platband D; and the lower i thereof divided 
 in 3, give the upper i, to the Fillet E. Di- 
 vide the lower i Part in 2 Parts, and the lower 
 I Part thereof, in 3 Parts -, of which give the up- 
 per I, to the Height of the Aftragal G •, half the 
 next Part, to its Fillet ; and the Remainder to 
 the Caveto H. 
 
 IV. Of the CORINTHIAN ORDER. 
 
 P R O B. I. To proportion the Heights of the prin- 
 cipal Parts of the Corinthian Order. Fig. I. 
 Plate IX. 
 
 Practice, (i.) Divide the given Height 
 as f /^ in 5 Parts -, and give the lower i Part ik^ 
 to the Height of thePedeftal. (x.) Divide <: /, 
 the remaining 4 Parts, in 6 Parts ; the upper i 
 c d, is the Height of the Entablature, and / i 
 the lower 5, of the Column, 
 
 PR OB. II. To proportion the Heights of the 
 principal Parts of the Corinthian Pedejlal. Fi- 
 gure II. Plate IX. 
 
 Divide '0 t the given Height in 4 Parts ; give 
 the lower i to the Height of the Plinth ; one 
 third of the next Part to the Height of the Mem- 
 bers on the Plinth; and half the upper 1, to the 
 Height of the Cornice. 
 
 P R O B. III. To proportion the Height of the 
 Members on the Plinth, and of the Cornice of 
 the Corinthian Pedeftdl. Fig. II. Plate IX. 
 
 (i.) Divide rs the Height in two Parts, and 
 the two upper halves of each, in 3 Parts ; give 
 the lower half of the firft i Part to the Height 
 
 P R O B. IV. To determine the Proje£iions of the 
 Dado, Bafe and Cornice of the Corinthian Pe- 
 dejlal. Fig. II. Plate IX. 
 
 (I.) Divide st the Height of the Plinth in 
 nine Parts, and make b a the Projeclion of 
 the Dado, equal to eight Parts. (2.) Make y w 
 the Projedlion of the Plinth, and of 'the Cornice, 
 equal to xjy the Height of the Members on the 
 Plinth ; and at any Place againft the Dado, as 
 at q, draw the Lines p q, equal to wy ; which 
 divide in 4 Parts, and fubdivide them again, in 
 thirds, as exhibited ; from whence determine the 
 Projeftions of the Members on the Plinth, and 
 of the Cornice, as by Infpedion is Ihewn, by the 
 perpendicular dotted Lines proceeding from 
 thence. 
 
 P R O B. V. To proportion the Heights of the 
 principal Parts of the Corinthian Column. Fi- 
 gure I. Plate IX. 
 
 Divide di the given Height, into 10 Parts, 
 and take i, for the Diameter of the Column at.^ 
 its Bafe. The Height of the Bafe hi, is half a' 
 Diameter; and of the Capital ^/, one Diameter 
 and one fixth. 
 
 PROB. 
 
to 
 
 Of the CORINTHIAN ORDER. 
 
 PROB. VI. To proportion tie Heights of the 
 Members of the Bafe^ of the Corinthian Column, 
 Fig. II. Plate IX. 
 
 (I.) Divide mn the given Height in three 
 Parts, the lower i is the Height of the Plinth. 
 (r.) Divide the Middle i, in 5 Parts, and the 
 fourth Part thereof, in 3 Parts j give the upper i 
 Part thereof, to the Height of the Fillet F, the 
 other two Parts, to the Aftragai G ; and the Re- 
 mains of the Middle Part, to the Height of the 
 lower Torus, H. (3.) Divide the upper i Part 
 in 5; and the fecond and third P.irts thereof, 
 each in 3 Parts i give the upper third Part, of 
 the fecond fifth Part, to the Fillet under the A- 
 ftragal D ; the next 2 Parts to the Aftragai D, 
 and the Remains upward, to the Torus C. The 
 Height of the Aftragai B and Ciniftture A, is e- 
 qual to half the Height of the upper Torus,which 
 divide in 3, and give i to the CinAure and 1 to 
 the Aftragai. The Scotia E is defcribed at large. 
 Fig. III. as follows. Divide the Height .a f in 
 7 Parts, through the third Part, drxvf d b ; make 
 7 />, equal to f g, and b c equal to b g \ and 
 from f, to the Point 7, draw the Line c "] e. On 
 the Point 7, defcribe the Arch a d c ; and on the 
 Point f, the Arch eg, which completes tjie Scotia. 
 Note, The Scotia of the lonick Bafe, is beft de- 
 fcribed by d)is Method. 
 
 PROB. VII. Te determine the Projc^ions of the 
 Ji-kvibers of the Bafe cf the Corinthian Column. 
 Fig. II. Plate IX. 
 
 (1.) Divide the Semidiatrk;ter in 3 Parts and 
 turnout I Part, for the Projeftion of the Plinth 
 and lower Torus. (^.) Divide the Proie<5tion of 
 the Plinrii before the Upright of the Shaft, into 
 5 Pirts ; then one Part and an half terminates 
 the Projedlion of the Aftragai G, and ? of the 
 next ', of the Fillet F. The 3d Part terminates the 
 Fillet undcrtheAnragalD,and the Aftragai B jand 
 3 Parts aixi an half, terminates the Cindure A. 
 
 PROB. VlII. To proportion the Heights of the 
 Members of the Corinthian Capital. Plate X. 
 
 , Divide ah, rlie given Height into 7 Parts-, 
 or 70 Mlnwtcs, ^each Part being fuppofed to be 
 divided in 10 P.i.rts, which are Minutes. Then, 
 10 the Height of the firft Range of Leaves, give 
 10 Minutes , to the fecond, 40 Minutes ; to 
 the third, 50 Minutes ; and up to the Abacus 
 
 60 Minutes. Divide the Height of the Abacus 
 in 2 Parts ; give the lower i, to the Caveto gy 
 one fixth of the upper half to the Fillet e ; 
 and the Remains is the Height of the Ovolo d. 
 The Height of the Aftragai /.; k, is 5 Minutes, 
 which divide in 3, give i to the Fillet b, and a 
 to the Aftragai a. 
 
 PROB. IX. To determine the ProjeHions of the 
 Members of the Corinthian Capital, Plate X. 
 
 The better to explain this Capital, I have gi- 
 ven a Qtiarter Part of its Plan, in two different 
 Manners ; as I have already done, of the lonick 
 Capital, viz. the one, of the fourth Part of a 
 round Column ; the other, of the like Part of a 
 fquare Column ; By which the Manner and 
 Reafons of determining the Projeftions of the 
 Members in the Profile, may the better be un- 
 deril:ood. To efFecl which, draw the Diameter 
 of the Column at its Bafe, equally on each Side 
 the central Line of the Capital ; divide it in 60 
 Minutes, and continue out the fame, 15 Minutes 
 on each Side, as before done in the lonick Order. 
 As the Shaft of this Column is diminifh'd one 
 fixth of its Diameter at its B.ife, therefore from 
 the [it"th, and fifty-lifth Minutes in the Diameter, 
 draw the Out-lines of the upper Part of the Shaft 
 next the Aftragai, and complete the Projeftion 
 of the Aftragai, which is 5 Minutes, and fts 
 Fillet two thirds thereof. On any Part of the 
 central Line as at A, with a Radius eqp.al to 
 25 Minutes, defcribe a Quadrant, which divide 
 in 4 equal Parts, and from the three inward Di- 
 vifions, dniw Lines parallel to the central Line, 
 as thole dotted Lines on the Left H.md Side, 
 which are tlie central Lines of the Leaves.. Now 
 the Diftanccs and Heights of the Leaves being 
 thus determined ; proceed next to dct.-rmine the 
 Projedion of the Abacus, as follows, viz. Make 
 the Projection of its Ovolo d, equal to 45 Minutes, 
 its Fillet e, 41 Minutes and an half, and its Ca- 
 veto/, 40 Minutes. Laftly, From the Extream 
 of the Abacus, to a the Extream of the Aftragai 
 draw a Line : as that dotted, v^hich terminates, 
 the Projeftion of the Leaves, in the Middle 
 Range ; and make the Projeftions of every o- 
 ther particular Part , as exprefTcd by the dot- 
 ted Parallels, proceeding from both Profiles, 
 through the Scale of Minutes to the two Plans ; 
 which being very plain to Infp^ftion need no fur- 
 ther Explanation. The Number of Flutes arid 
 
 Fillets 
 
Of ths CORINTHIAN ORDER. 
 
 II 
 
 FiHets in the Shaft of this Column, are the fame 
 as thofe in the lonick. 
 
 PROB. X. To proportion the Heights of the 
 principal Parts of the Corinthian Entablature . 
 Plate XI. 
 
 Divide the Height ab^ in lo Parts, give 3 to 
 the Architrave •, 3 to the Freeze ; and 4 to the 
 Cornice. 
 
 PROB. XI. I'o proportion the Heights of the 
 Members of the Corinthian Architrave, PI. XI. 
 
 Divide ef the given Height in 5 Parts, and 
 the lower i in 4 •, of which give the lower 3 to 
 the firlT: Fafcia, and the upper one, to its Bead. 
 The fecond Part of the Architrave's Height, is 
 the Height of the fecond Fafcia, and one fourth 
 of the third Part, is the Height of its Cima. 
 The remaining three fourths of the third Part, 
 and three fourths of the fourth Part, istheHeight 
 of the upper Fafcia •, and the next one fourth 
 Part of its Bead. The fifth or upper Part be- 
 ing divided in 4 Parts, and the third Part up- 
 wards thereof divided in 3, give the upper 4th 
 Parr, aiid one third of the next, to the Height 
 of tiie Tenia -, and the remaining two thirds and 
 1 Parts, to the Height of the Cima reverfa. 
 
 PROB. XII. To proportion the Heights of the 
 Members of the Corinthian Cornice. Plate XI. 
 
 ( I . ) Divide c d the given Height in 5 Parts, 
 and the upper i Part in 4, of which give the 
 upper I to the Regula ; one third of the lower i 
 to the Fillet under the Cima refta, and the Re- 
 mains, to the Cima refta. (2.) D>ide the 4th 
 Part in 4 5 give the upper i to the Cima rever- 
 fa ; and the lower 3 to the Corona. C3.) Di- 
 vide the third Part in 4, and its upper 1 in 4 ; 
 of which give the upper i to ihe Fillet, and the 
 lower 3, to the Cima reverfa, which make the 
 Capping of the Modillions, whofc Dep:h termi- 
 nates at half the firft Part. ('4.) Divide the fe- 
 cond Part in 3, and the Middle i thereof in 3 ; 
 of which give the firft Part to the Fillet over the 
 Dentules, and the remaining Part upwards to the 
 Ovolo, under the ModilUons. (5.) Give half 
 the lower \ in the fecond Part, to the Height of 
 the Fillet, on which the D.ntules are placed. 
 Laftly, The firft Part divided in 3, the upper i 
 
 terminates the Depth of the Denfules ; the next 
 one third, of the Middle third Part, the Depth 
 of the Denticulej and the remaining i Part and 
 two thirds is the Height of the Cima reverfa, of 
 the Bed Mould. 
 
 PROB. XIII. To determine the Proje^lions of 
 the Members in the Corinthian Architrave. PI. 
 XI. 
 
 The Projeftion of the Tenia, Is equal to i fifth 
 and one touith of a fifth of the Architrave's 
 whole Height. The Projeftion of the Tenia, 
 divided in 5, the firft 2, terminates the Projec- 
 tion of the upper Fafcia ; and three fourths of 
 the firft Part terminates the Projedion of the fe- 
 cond Fafcia. 
 
 PROB. XIV. To determine the ProjeElions of the 
 Members in the Corinthian Cornice. Plate XI. 
 
 The Projeftion of the entire Cornice, is equal 
 to the whole Height, as expreffed by the Arch 
 g k. At any Place againft the Freeze, as at /, 
 draw a right Line, as / m, equal to / k, the 
 whole Projeftion. Divide I m in 4 Parts, fubdi- 
 vide them again, and terminate each Member, 
 as exhibited by the dotted perpendicular Lines 
 which pafs through the Divifions from the Pro-> 
 file to the Plan, or Planceer of the Cornice. 
 
 PROB. XV. Todefcribe the Connthhn Modil- 
 lion at large. Fig. I. Plate XII. 
 
 The Breadth of a Modillion is equal to one 
 fixth of the Diameter, or 10 Minutes, and the 
 Interval or Diftance between them in a Cornice 
 over Columns is 15 Minutes •, but in a Cornice 
 over Pilafters, undiminiftied, the Interval is 30 
 Minutes : And therefore the Diftance between 
 the central Lines of Modiijions in the firft, muft 
 be ^<i Minutes, and 40 Minutes in the laft. 
 
 As the Breadth of a Modillion in Front, as 
 Fig. A. Plate XII, is thus determined -, and as 
 the Height and Projefture of its Profile, is de- 
 termined in the laft Problem, it therefore now 
 only Remains to fhew. How to proportion the 
 Parts into which they are divided, as follows : 
 
 I. To proportion the Parts in the Fro7it of a Co-"- 
 rinthian Modilion. Fig. A. 
 
 Divide the Breadth of the Front in S Parts,, 
 
 and: 
 
1 1 
 
 Of the CORINTHIAN ORDER. 
 
 and give the outer i Parts, to the Fillets as 
 CB, iJc. Divide the hit half of the fourth 
 Part, and firft half of the fifth Part, each into 
 4 Parts ; give the two outer i Parts thereof to 
 the Fillets, and the Middle 6 Parts, to the A- 
 Ilragal A. 
 
 II. To proportion the Parts in the Prcfile of the 
 Corinthian Modilion. Fig. I. Plate XII. 
 
 Divide its Height in 8 Parts, and fet feven of 
 thofe Parts from 7 to p. From the third Part 
 from p, draw the perpendicular Line c e, which 
 interfe(5l by a horizontal Line, drawn from 4 Parts 
 and an half, reckon'd upwards in the Height of 
 the Modilion ; and the Point of Interfeftion is the 
 Center of the Eye of the Volute, whofe Diame- 
 ter is equal to 1 Part. Within the Circle of the 
 Eye, infcribe a geometrical Square as in Fig. II, 
 und therein ; inkribe another, as 4, 3, i, 1, 
 whofe Diagonals divide in 4 Parts at the Points 
 8, 7, 5, 6. Then the Points i, 2, 3, 4, 5, 6, 7, 
 8, are the Centres on which the large Volute is 
 defcribed. The Height k i of the Imall Volute 
 rt, is equal to half the Height of the Modilion ; 
 •which divide in 8 Parts ; and then fetting 7 of 
 thofe Parts from k to /, proceed in every Rcfpedl; 
 to dcfcribe that Volute, as you did the other. 
 
 To join thefe Volutes, draw the Line a c ; bi- 
 •fect it in b ; and again at b and d ; on which 
 Points erect the Perpendiculars hf and d e, cut- 
 ting the Perpendiculars e f and c e \n the Points 
 / and e, which are the Centres, on which the 
 Curve a he is defciibjd. In the fame Manner 
 the -Under-curve is defcribed, whofe Centre is 
 the Point g. 
 
 Fig. III. reprefents the Planceer of the Mo- 
 dilion ; whofe Breadth is equal to that, in Front, 
 Fig. A, and Length to the Profile, Fig. I. 
 
 Divide the Side f 5, Fig. III. in 5 Parts; 
 then I Part, is the Breadth of the Margin, about 
 the Coffer Fig. IV •, and half of i Parr, equal to 
 ih. Fig. IV •, is theProjedlionof the Ovolo with 
 its Fillet, that encompaffes the Coffer. Make / m 
 equal to / /, and draw m ti, which determines 
 the Diameter of the central Enrichment -, which 
 may be, any Kind of circular Flower at Plea- 
 fure. 
 
 P R O B. XVI. 7e defer ibe the Bentules at large, 
 as in the lower left Angle of Plate XI. 
 
 Divide the Height of the Denticiile (which is 
 
 the Surfiice againft which the Dentules are fix'd, 
 when made ii^ Wood; in 8 Parts, and give i to 
 the Fillet, and 6 to the Depth of the Dentules •, 
 which lail divide in 3 Parts ; and give 2 to the 
 Breadth of a D>:ntule, and i to the Breadth of 
 an Interval. The Dep:h of the Fillet, or Eye- 
 Dencule between, is one fourth of the Depth of 
 a Dciitule. 
 
 By the feveral dotted parallel Lines, proceed- 
 ing from the Profile, to the Plan, the Conftruc- 
 tion of the Plan, is plain ; and, what has been 
 laid before, concerning the Planceer of the Mo- 
 dilion, and Coffer in Plate XII, is herein fur- 
 ther exemplified, by tke feveral Planceers, and 
 Coffers between them ; of the Modilions and 
 their Intervals in the Profile above. 
 
 V. Of the COMPOSITE ORDER. 
 
 P R O B. I. To proportion the Heights of the prin- 
 cipal Parts of the Compofite Order. Fig. I. 
 Plate XIII. 
 
 (1.) Divide b m, the given Height, in five 
 Parts, and give the lower i , h m ; to the Kl|eight 
 of the Pedeltal. 
 
 (2.) Divide b h, the remaining 4 Parts, into 
 5 Parts ; give b e the upper i, to the Height 
 of the Entablature ; and e h, the lower 4, to 
 the Height of the Column. 
 
 PROB. II. To proportion the Heights of the 
 principal Parts of the Compofite Pedejlal. Fig. 
 II. Plate XIII. 
 
 Divide the given Height r q into 4 Parts ; 
 give the lower 1, to the Height of the Plinth -, 
 o.-^e third of the fecond, to the Height of the 
 Mouldings on the Plinth ■, and half the upper i, 
 to the Height of the Cornice. 
 
 PROB. III. To proportion the Heights of the 
 Alembers on the Plinth, and of the Cornice, of 
 the Compofite Pedeftal. Fig. II, Plate XIII. 
 
 (i.; Divide e f, the Height of the Mould- 
 ings on the Bafe •, into 4 Parts : Give the low- 
 er I to the Torus N, and one third of the next, 
 to the Fillet M ; divide the upper i in 3 ; give 
 the upper 2 thereof, to the Caveto I ; and the 
 other I, to the Fillet K. The remaining one 
 
 fourth 
 
Of the COMPOSITE ORDER. 
 
 13 
 
 fourth Part and two thirds is the Height of the 
 inverted Cima refta L. 
 
 (X.) Divide cd the Height of the Cornice in 
 6 Parts -, give the lower i divided in 3, to the 
 Caveto G and Fillet F-, give the t next Parts 
 to the Cima r^jfta E and Fillet 
 Fillet one fixch of the Whole ; 
 Part and half the fifth Part, 
 Platband C -, and the remaining 
 to the Cima reverfa B, and its Fillet A, making 
 the Fillet one third of the Whole. 
 
 PROB. IV. To determine the ProjeBions of the P R O B. VIII. To proportion the Heights of the 
 Dado., Safe, and Cornice, of the CompoCnc Pe- Members of the Compofite Capital. Plate 
 de_fial. Fig. II. Plate XIII. . XIV. 
 
 D, making the 
 
 give the fourth 
 
 to the Fafcia, or 
 
 1 Part and half, 
 
 tion of the Plinth, and Torus H. (z.) Divide 
 the Projedion of the Plinth before the Upright 
 of the Column, into. 5. Parts -, the firfl: i and an 
 half i terminates the Aftragal G -, and the next 
 half, the Fillet F. (3.) The third Part terminates 
 the Fillet D, and Aftragal B ; and 3 Parts and 
 an half, the Cinfture A. 
 
 The Scotia at large, is defcribed, by the fame 
 Rule, as the Scotia of the Corinthian Bafe, in 
 Prob, VI. of the Corinthian Order. 
 
 The Projections of this Dado, Bafe. and Cor- 
 nice, are found in the fame Manner, as thofe of 
 the Corinthian Pedeftal, in Prob. IV. of the Co- 
 rinthian Order. 
 
 PROB. V. To proportion the Heights of the prin- 
 cipal Parts of the Compofite Column. 
 
 The Proportions of thefe Parts are the very 
 fame, as thofe of the Corinthian Column, in Pro- 
 blem V. of the Corinthian Order. 
 
 PROB. VI. To proportion the Heights of the 
 Members of the Bafe of the Compofite Column. 
 Fig. II. Plate XIII. 
 
 (1.) Divide np the given Height in 3 Parts ; 
 the lower i, is the Height of the Plinth I. 
 
 (a.) Divide the fecond Part in 5 ; give the 
 firft 3, to the Torus H ; the next 1, to the A- 
 ftragal G -, and half the next to its Fillet F. 
 
 C3.) Divide the upper Part in 5 ; give the up- 
 per 1 and an half, to the Torus C, and the next 
 half to the Fillet D ; and the Remains, is the 
 Scotia E. The Height of the Allragal B, and 
 Cinfture A, is i Part and an half, turned up, as 
 fignified by the dotted Semicircle, divided in 3, 
 of which, the Aftragal is ^, and the Cinc- 
 ture I. 
 
 PROB. VII. To determine the ProjeHions of the 
 Members of the Bafe of the Compofite Column. 
 Fig. II. Plate XIII. 
 
 (i.) Divide b c, the Semidiameter of the Co- 
 lumn in 3 Parts, and give 1 Part to the Projcc- 
 
 The Heights of the Aftragal, Leaves, and of 
 the Abacus, are the fame here, as before in the 
 Corinthian Capital. The Height of the Volute 
 V d, equal to ^ Parts and an half, divided in 8 v 
 give the upper half of the third Part, from v, to 
 the Fillet ; the fourth Part to the Aftragal en- 
 riched with Pearls and Beads ; and the next up- 
 per 2 to the Ovolo, enriched with Eggs and 
 D.;rts. 
 
 PROB. IX. To determine the Proje^ions of the 
 Members of the Compofite Capital. Plate 
 XIV. 
 
 The Projections of the feveral Members of this 
 Capital, are the fame, as thofe of the C(7ra//.;w« ; 
 as alfo is the Diminution of the Shaft ; and the 
 Proportion of its Flutes and Fillets. 
 
 This Capital is compofed of the lonick and 
 C<5n«/,6w« Capitals; for the Abacus, Ovolo, A- 
 ftragal. Fillet, and Volutes ; are the very Mem- 
 bers that compofe the lonick Capital -, and the 
 two Heights of Leaves, and Aftragal on whicli 
 they ftand ; are the very fame as thofe in the Co- 
 rinthian Capital. 
 
 P R O B. X. To proportion the Heights of the 
 principal Parts of the Compofite Entablature. 
 Plate XV. 
 
 Divide the Height a /, in 10 Parts ; give ,3, 
 to the Architrave i 3 to the Freeze-, and 4 to 
 the Coi~nice. 
 
14 
 
 Of theCOU?QS\TE ORDER. 
 
 PR OB. XI. To proportion the Heights of the 
 Members of the CompoiiK'/lrchitrave. Plate 
 XV. 
 
 Divide eg in 4 Parts, the lower i, is the 
 Height of the lower Fafcia ; and one third of 
 the next i, of its Cima reverfa. Divide the up- 
 per I, in 4. i give the upper i thereof, to the 
 Height of the Fillet on the Tenia-, the next 2 to 
 the Ovoloi one third of the next 1, to the Fil- 
 let ; the remaining two thirds to the Caveto, and 
 tl^ intermediate h Part and two thirds is the 
 Height of the Fafcia next under it. 
 
 PR OB. XIII. To determine the ProjeSiions of 
 the Members of the Compofite Architrave. PI. 
 XV. 
 
 The Projeftion of the Tenia, before the Up- 
 right of the Freeze, which ftands over the Up- 
 right of the upper Part of the Shaft of the Co- 
 lumn is equal to one fourth of the Height of 
 the whole Architrave. Divide op the Projec- 
 tion of the Tenia, in 3 Parts, give the firft one 
 to the Projection of the upper Fafiia ; and three 
 fourths of the next r, to the Projeftion of the 
 Fillet over the Caveto. 
 
 P R O B. XII. To proportion the Heights of the 
 Members of the Compofite Cornice. Plate 
 XV. 
 
 . (I.) Divide be the Height in 4 Parts, and 
 the upper 1 Part in 4 Parts -, of which give its 
 upper 1 to the Regula E ; the lower third Part 
 of the lower x to the Fillet, and the interme- 
 diate Space to the Cima refta, between them. 
 
 (2 J Divide the third Part in 4; give the up- 
 per I to the Cima reverfa ; and the lower 4 to 
 the Corona. 
 
 (3.) Divide the fecond Part, in 3, and its up- 
 per i in 4 j give the upper 2, to the Ovolo, 
 :ind the next i, to the Filler, which caps the 
 Modiiions. 
 
 Half the lower third Part, is the I Light of 
 the Cima reverlii, between the upper and lower 
 Modillions. 
 
 (4.) Divide the loweft fourth Part of the 
 Height, in 4 ; give the lower half to the Cima 
 reverfa C •, and the other half being divided 
 in a , give the upper i and two thirds ot 
 the nexV, to the Height of the lower Mo- 
 dilion. 
 
 The Height of the Aftragal c ^ is equal to 
 half the Height of the Cima, over them ; wliich 
 divide in 3 •, give ^ to the Aftragal, and I to 
 the Filler. 
 
 PROB. XIV. To determine the ProjeSicHS of 
 the Members of the Compofite Cornice. PI, 
 XV. 
 
 The Projedion D E of the whole Cornice, is 
 equal to D C its entire Height. Againft any 
 Part of the Freeze, as at ?«, draw a Line vi ;:, 
 equal to D E, which divide in 4 Parts ; fubdi- 
 vide them again, and terminate each Member, 
 as exhibited by dotted perper-diciiiar Linesj which 
 pafs through the Divifions from the Profile to the 
 Plan, or Planceer of the Cornice. 
 
 The Breadth of the upper Modillions is one 
 fixth of the Diameter of the Column at its Bale 
 or 10 Minutes, and the Interval between them 
 being twice^heir Breadth, or ao Minutes-, there- 
 fore the central Lines of every 1 Modillions, is 
 half a Diameter or '30 Minutes-, as the Modilli- 
 ons are, in the lonick Cornice. 
 
 "When the young Student hath pafs'd through 
 all the preceeding Operations, he v.'ill be ena- 
 bled not only to underftand every Part of an 
 Order, by InfpedlioQ, without having any Re- 
 courfe to chis explanatory Part again : But will 
 alfo, underftand the Proportions of all the fol- 
 lowing Defigns by Infpecftion, the very Jnftant 
 that he cafts his Eye on them. 
 
 CHAP. 
 
0/INTERCOLUMNATIONS. 
 
 '5 
 
 CHAP. 11. 
 
 of the Intercolumnation or proper Diftance that the Columns of every Or- 
 der, are to be placed at ; in the forming of Defigns, for Frontifpieces,, 
 Doors, Windows, ^6'. 
 
 Note, That herein I account the Dillance or Intercokimnation, from the central Line 
 of one Column, to the central Line of the other ; and not from the Outfide of the 
 one, to the Outfide of the other, as many Perfons have done. 
 
 I- inVr'i'Myfflfffffiil H £ Diflance of Tufcan Co- 
 lumns in Pairs is one Diame- 
 ter 45 Minutes -, but when fin- 
 g'e, in Fiontifpieces, 4 Dia- 
 meters •, and in Arcades, they 
 may extend from 5 to 7 Dia- 
 meters , where NeceiTity re- 
 quires it, making the Arch a Semi-Ellipfis, in- 
 ftead of a Semicircle ; but 6 Diameters is the 
 ufual and proper Dillance for an Arcade. 
 
 II. The Diftar.ce of Columns in the Dcrick 
 Order, is regulated by the Number of Triglyphs 
 that is to be between them. For as the Breadth 
 of a Triglyph is 50 Minutes and the Breadth 
 of a Metope, or Diilance between two Triglyphs 
 is 45 Minute?, and as a Triglyph is always pla- 
 ced over the central Line of every Column. 
 Therefore it follows, that to have i Triglyph 
 between thoie over tv/o Columns, the Diftance 
 muft be ^ Diameters, 30 Minutes; that is, 60 Mi- 
 nutes, or I Diameter, for the two half Triglyphs 
 over each Column, and the whole Triglyph be- 
 tween them ; and 90 Minutes or i Diameter and 
 and half, for twice 45 Minutes, the Breadths of 
 the two Metopes. So in like Manner to have 
 two Triglyphs between ; the Diftance muft be 
 3 Diameters, 45 Minutes ; to have 3 Triglyphs 
 5 Diameters, which Vitru-vii'.s calls Arasoftyle ; 
 and to have 4 Triglyphs ; 6 Diameters, 15 Mi- 
 nutes, which laft is ufed in Colonades, and Ar- 
 cade.s j and that of 5 Diameters for Doors, i£c. 
 
 III. The Diftance of Columns in the lonkk 
 Order, is regulated by the Number of Modilli- 
 ons, which are placed over Columns, the fime as 
 the Triglyphs in the Dorick Order. And as the 
 Diftance of the central Lines of lonick Modilli- 
 ons, in a Cornice over Columns has been fhewn 
 to be 30 Minutes or half a Diameter, therefore 
 the Diilance between Columns in this Order to 
 have two Modillions between, which is the leaft 
 that can be, to have the Columns clear of each 
 other -, muft be i Diameter and an half j to 
 have 3 Modillions between, 2 Diameters and an 
 half; to have 5 Modillions between, 3 Diame- 
 ters ; which laft being doubled, is ufed in Ar- 
 cades ; and that of 2 Diameters and an half 
 doubled, for Doors, ^c. 
 
 The Diftance of 7o»/V/^ Pilafters not diminifh^ 
 ed, muft be greater than of Cokim.ns, becaufe 
 the central Lines of their Modillions, are at '35 
 Minutes Diftance ; and therefore it follows, that 
 to have two Modillions between, the Diftance 
 muft be I Diameter 45 Minutes ; to have three 
 Modillions between two Diameters and ao Mi- 
 nutes ; to have four Modillions between ; two 
 Diameters 5^ Minutes ; and to have five Modil- 
 lions between, 3. Diameters 30 Minutes, i^c, 
 
 IV. The Diftance of Columns in the Ccrinthi- 
 an Order, is alio regulated by the Number of 
 Modillions between them ; and as in Prob. XV, 
 of the Corinthian Order, the Diftance of their- 
 central Lines are ^5 Minutes, which is the fams 
 
 Diftance^ 
 
1 ■-) 
 
 Of P I E R S /c?r GATES. 
 
 D.fl:.ince, as the Modillions in the lonick Cornice 
 over Pihifters •, therefore the Diftances of Corin- 
 thian Columns, muft be tlie fime, as of lonick 
 Pilaftcrs. And as the Diftance of the central 
 Lines of Corinthian Modillions, in a Cornice o- 
 ver undiminifhed Pilafteis, is alfo flicwn in Pro- 
 blem XV of the Corinthian Order, to be 40 
 Minutes -, therefore it follows ; That to have 2 
 Modillions between, the Diftance muft be two 
 Diameters ; to have three Modillions between, 
 two Diameters 40 Minutes -, to have four Mo- 
 dillions between, three Diameters, twenty Mi- 
 nutes, tff. 
 
 V. The Diftance of Compofite Modillions in a 
 Cornice over Columns, is the fame as in the lo- 
 nick Order ; therefore the Diftance of Compofite 
 Column; and Pilallers are the fame, as of lonick 
 Columns and Pilafters. 
 
 The Manner of proportioning the fcveral Or- 
 ders, and determining the proper Diftances they 
 are to be placed at, being thus explained -, I fhall 
 now proceed to give fuch Explanation of the fol- 
 lowing Plates, as will render the Bufinefs of eve- 
 ry Djlign eafy and delightful to every one, who 
 has made himfclf a Mafter of the Precedent Or- 
 ders. 
 
 Plate XVI, XVII, XVIII, XIX, XX. 
 
 0/ PIERS /«• GATES. 
 
 To make thcfe, and all other Dcfigns contain- 
 ed in this Work, cafy to the Undcrftanding ot 
 all Capacities, and to enable fuch, to work them, 
 of any Magnitude required ; I have to every Dc- 
 fign affixed Scales of x'Vliquot Parts, ("which ne- 
 ver was done before by any Mafter) whereby, 
 having only, thcPI-jight of any Work to be made 
 (which in all Cafes mufl be) given ; the Whole 
 may be performed v\idi the uimoft Exadlnefs as 
 required. 
 
 A. for Exmr.pU ; Let it be required to propor- 
 tion the Pia G, Plate XVI. to any given Height . 
 
 D'.vide the given Height (fuppofc ten Feet) 
 into four equal Parts, (as fignified by the Scale 
 • '11 its Left Side) give two thirds of the loweft i 
 ^art to the Height of the Subplinth G ; and two 
 
 thirds of the other third Part, to the Height of 
 the Plinth, Torus and Fdlet. Divide the upper 
 fourth Part, in 3 Parts ; and the upper i Part 
 thereof in 3 Parts j of which, give the upper 
 2 Parts to the Height of the Capital ; whofe 
 Members arc above defcrib'd at large by Fig. B. 
 By the dotted Arch of a Quadrant in the Sub- 
 plinth G, it is evident, that the Breadth of the 
 middle projefting Part of the Pier ; is equal to 
 the Height of the Subplinth, which Breadth di- 
 vide in 4 ; and give i to the Projeftion of each 
 Side. 
 
 The Height of the Subplinth of the Pine Ap- 
 ple on the Capital, is one Part, and one third, 
 as fignified by the dotted Semicircle : And the 
 Height of the Pine Apple and its Pedeftal, is de- 
 termined by the Interfeftion of Arches defcribed 
 on the extream Points of the Capital's Projec- 
 tion, and which being divided in 3- Parts j and 
 the lower i in j, fsfc. give to every particular 
 Member, its refpedlive Height, as exhibited. 
 The Projeflion of the Plinth to the Pedeftal of 
 the Pine Apple, is two thirds of the Projeflion 
 of the Middle Part of the Pier. 
 
 Now the young Student is to obferve, that as 
 the conftituent Parts of all the Defigns in this 
 Work, are adjufted in the very fmie Manner ; 
 as thole of the above Example ■, which it is ma- 
 nifeft are no fooner feen, but underftood ; it is 
 therefore evident •, that to fay any Thing further 
 relating thereto, is needlefs. 
 
 Thefe five Plates contain eighteen D.-figns of 
 Tiers for Gates at Enteranccs into Gardens, Ave- 
 nues, Courts, Palaces, i^c. which may be built 
 either of Stone or Brick, or of both, intermix'd, 
 at the Pleafure of thole for whom they may be 
 erefted. 
 
 Plate XXI, XXII, XXIII, XXIV, XXV. 
 
 GATES for Enterances into Palaces^ &c. 
 
 Five Defigns for Gates, of which the firft, 
 fecond, third, and fourth, are according to the 
 Tufcan^ Doriek, lonick and Corinthian Orders ; 
 whofe refpeftive Imports and Architraves of 
 their Arches are defcribed at large, and propor- 
 tioned by Aliquot Parts, at the Bottom of each 
 Defign ; as likewife is, the Impoft and Archi- 
 trave to the Gate Plate XXV. made for an Ente- 
 rance to theFIoufe of a private Gentleman, £sfr. 
 
 Plate 
 
Of Front ifpieees for Doors to Manfton Houfes. 
 
 Plate XXVI, XXVII, XXVIII, XXIX, XXX, 
 XXXI, XXXII, XXXIII» XXXIV, XXXV, 
 XXXVI. 
 
 Frontispieces /(3r Doors /i? Mansion- 
 HousEs, £rf. 
 
 Thcfc Eleven Plates contain twenty-two De- 
 figns of Frontifpieces for Doors, of which the 
 firrt two, Plate XXVI, are compofed of Cham- 
 pher'd Rufticks •, and proper for Enterances into 
 Buildings that have Porticoes before them, to 
 carry off the Rains, which themfelves cannot do. 
 The next twoDefigns, Plate XXVII, are alfo ru- 
 rticated ; the one B, as the preceding -, the other 
 with fquare Rufticks, and being both crowned 
 with Pediments are thereby made fit, to adorn 
 the Enterance of any Building without a Porti- 
 co ; As alfo, are all the Difigns with Pediments 
 in the following Plates. And when it happens, 
 for Want of a proper Height, that a Pediment 
 cannot be made •, then in all fuch Cafes the Cor- 
 nice muft break forward, and be fupported by 
 Truflls, as A, Pl.ue XXVlII, XXXI, XXXII, 
 to carry off the Rains. It alfo very often hap- 
 pens, that even when Frontifpieces may be finifh- 
 ed with Pediments, that the Piojeftion of the 
 Pediment will not be fufficient to prote(5l the En- 
 trance from the Inllilts of Rains ; therefore in 
 fuch Cafes, the Pediments muff advance for- 
 ward, and be fuftain'd either by Truffes, as ex- 
 hibited in Plate XXX, XXXI, or by Pilafters, 
 or Columns, as in Plate XXXIIl, XXXIV, 
 XXXV, XXXVI. 
 
 As I have finiftied the greateft Part of thefe 
 Defigns with Pediments of all the Varieties of 
 the Orders, I fliall in the next Place fhew 
 
 Hoiv to find the different Curvatures of Raking 
 Mouldings of Pediments^ and lilodillions, Plate 
 XXXVII. 
 
 . (i.) Let 4!, V b, be the upper Fillet or Re- 
 gula, and w c, x 0, the lower Filler, of a level 
 Cima Redla of a Cornice, alio k I, g b be the 
 Raking Regula or upper Fillet; and / c, m z the 
 lower Fillet of the Raking Cima Reifla, and let 
 a be, be the Level Cima Refta given, whofe 
 Height is a e, and Projeftion a h. Divide a c in- 
 to any Number of equal Parts, fuppofe 8, and 
 draw the Ordinates 1 p, 2 p, ^p, ^c. 
 
 17 
 
 (2.) On any Part of g b, as at tf, raife a Per- 
 pendicular as ef to the Height of the Raking 
 Cima, which divide in the fame Number of equal 
 Parts as a c, as at the Points i, 2, 3, ^c. from 
 which draw Ordinates i ^, 2/), 3^, ^c. each 
 refpedlively equal to the Ordinates in the Cima A, 
 and then tracing the Curve dp p, (£0. /, it will 
 be the true Curve of the Raking Cima, 
 
 (Z-) Suppofe the Point 9 Fig. C, to be the ut- 
 mefi Point of ProjeSHen, in the Return of the Ra- 
 king Cima, in an open Pediment. 
 
 Draw g h parallel to w c, and from h draw 
 the Perpendicular /^ ;, tvhich divide in eio-ht e- 
 qual Pai-ts at the Points i 2 3, from vvhence 
 draw the Ordinates 1 />, 2 />, 3 /), i£c. equal to 
 the Ordinates i p, 2 p, 3^, ^c. in F]o-, A. 
 From the Point g, through the Points qqq. feV. 
 trace the Curve ^ p/), &?f, /, which is die true 
 Curve of the returned Cima, as required. 
 
 Fig. D E F is a fecond Example of an Ovo- 
 lo, whsrein the three feveral Heights are all e- 
 qually divided into the fame Number of Parts, 
 and the Ordinates of every one, are refpedtively 
 equal. 
 
 Now what is here faid with Refpedl to the 
 Raking Members of a Pediment, is to be alfo 
 underftood of the Members of Raking Modilli- 
 ons. For if Fig. E, or Fig. B, be confider'd as 
 the Front Moulding, then the Figures F and D, 
 or C and A, are the Moulds or Curvatures of 
 the two returned Mouldings. 
 
 For this excellent Method I am greatly oblig- 
 ed to the Ingenious Mr. Robert Hart well, 
 at the Tower of London, Carpenter. 
 
 Plate XXXVIII. 
 
 To defcribe the Curvature of a Trufs, for the Sup- 
 port of a Cornice, &c. 
 
 (x.) Divide the given Hsight into eleven equal 
 Parts ; divide the upper three Parts in feven Parts 
 and make ;/ e the perpendicular Line of the Pro- 
 jeaioi of the upper Volute to eight of thofeParts, 
 Alio, divide the third and fourth Parts of its 
 Height in feven Parts ; and make the Projeflion 
 of the lower Volute equal to eight of thofc Parts. 
 
 (X.J This done proceed in every Particular to 
 defcribe the two Volutes, and the Curve e c g., 
 as dircfted in Seft. II. Prob. XV. of the Corin- 
 thian Order, to defciibe the Volutes or Scrolls of 
 G the 
 
i8 
 
 the CirirtlbiimModiUion. Fig. B rcprefents tlie 
 Eye of a Volute, with its Centres at large -, and 
 Fig. A, the Face or Front of a Trufs ; which 
 divide in eight Parts, give the outer ones to the 
 two Fillets i the middle one, to the Aftragal, 
 and its Fillets ; and the Remainers on each Side, 
 to the two Cima Reda's. 
 
 Plate XXXIX, XL. 
 
 Of Attick Windows, xvho/e Diameter and Heights 
 are equal, 
 
 Thefe two Plates contain ten Windows, for 
 Attick Stories, which are differently adorned, the 
 firll two having Window Stools, the one with 
 plain Brick Work, the other with an Architrave 
 exprefled at large, by Fig. G, whofe Breadth is 
 equal to one fixth of the Wfndow. The other 
 eight, are alfo adorned with Architraves, fquare 
 and knec'd, entire and broken, or interfperfed 
 with Ruftick Blocks, on Stools, fupported by 
 Truffes, of which Fig. C, D, E, F are four 
 Varieties. 
 
 Plate XLl. 
 
 X)/ Windows, whofe Heights are equal to the Dia- 
 gonal of a geometrical Square, whofe Side is equal 
 to the Diameter of the IVindctv. 
 
 This Plate contains four Defigns, viz. two 
 fquare headed, proper for an Atticic Story, alfo 
 one fcmi-circular, and fcmi-clliptical headed one. 
 Chambers next under them. 
 
 Plite XLII, XLTII, XLIV, XLV, XLVI, 
 XLVII, XLVIII, XLIX, L, LI, LII, LIU. 
 
 Of Windows for State Rooms, and their Enrich- 
 ments. 
 As thefe Sort of Windows are fometimes en- 
 riched with an Entablature, and plain Archi- 
 trave only, as thofe in Plate XLV, XLVI -, or 
 have their Architraves interfperfed with Rufticks 
 as A, Plate XLIV, ^c. I have therefore pre- 
 cedent to them, given three Varieties of Enta- 
 blatures, fit to be placed over Windows, viz. 
 Fig. A, B, Plate XLII, and B, Plate XLIII, as 
 alio for V.iricty Sake the Block Cornice A, which 
 ■when practiced, mufl: be placed on Champhered 
 
 0/ W I N D O W S. 
 
 Ruflicks, as in B, Plate XLIV. Plate XLVII 
 contains a Dorick and Tufcan Window, the firft 
 with Columns, the other with Pilailers, (whofe 
 Flutings I fliall prefently (hew. How to defcribe.) 
 Plate XLIX contains an lonick and Corinthian ; 
 and Plate L, two Compcfite Windows, which fix 
 lalt are of all others the moll magnificent that can 
 be made, except thofe which are called Venetian 
 Windows, of which I have given three Varieties, 
 viz. Tufcan, Dorick and lonick, in Plate LI, LII, 
 LIII, and which are mod proper for a grand Stair- 
 Cafe, Saloon, Library, Chancel of a Church, i^c. 
 were much Light is required ; or for a Dining 
 Room, 6fr. whence fine Views may be feen. 
 
 Plate LIV. 
 
 Of circular and elliptical Windows . 
 
 This Plate contains five Varieties of circul.ir 
 Windows, and one ovalar, differently adorntil 
 with Architraves and Rufticks ; which are pro- 
 per lor Attick Stories, or in Tympanums of Pe- 
 diments, l£c. 
 
 To defcribe an Oval Window of any Breadth and 
 Height, this is the Rule. 
 
 Draw the two Diameters at right Angles, each 
 of their affigned Length. Set half the fliorc 
 Diameter from / the End of the long Diameter 
 to k, and divide the Remains to the Centre h, in 
 tliree equal Parts, and fet one Part from k to ;'. 
 Make h g equal to h i, and complete the two 
 equilateral Triangles g a i, and g n i. On the 
 Centres g and /, with the Opening, // defcribe 
 the Arches dfm and ley, and on the Centres 
 a n with the Opening a m, defcribe the Arches 
 m 1, and "j b d, which completes the. Oval, as 
 required. 
 
 Plate XLVIII. 
 
 To defcribe the Flutes and Fillets of Pilaflers,. and 
 to reprefnt, the perfpe5live Appearances of Flutes 
 and Fillets of Columns. 
 
 Ex A M p L E I, To divide the Flutes and Fillets of 
 any Pilajler, Fig. A. 
 Draw a Line at Pleafure, as hi, and therein 
 fet 19 equal Parts of any Magnitude at Pleafure, 
 
 and 
 
0/ N I C, H E S. 
 
 and complete the. equilateral Triangle A b I, fee 
 the given Breadth of the Pilaller, fuppofe / k, 
 frorrj A, to /, and from A to k, then drawing 
 Lines from A to the Rrft one, the next three, 
 the next one, the next three, &c. in thelLine h /, 
 they will divide the Line : k into its Flutes and 
 Kllets, as required. 
 
 Exam p. II. To divide the. Flutes and Fillets ivith 
 Beads at the Angles, of any Pilajier, .as Fig. B. 
 
 Draw a Line as «»^ at Pleafure, and therein 
 fet 31 Parts as before, and then completing the 
 equilateral Triangle B m p, proceed in every Re- 
 fpjft, as in the preceeding Example. And here 
 note. That when the Lines reprefenting the Flutes 
 and-FiUets of a Pi 1 after are thus drawn, on a 
 DraugliL Board, (3'c. from thofe Lines, the Flutes 
 and Fillets of all other Pilafrers of greater Dia- 
 meter may be readily found. As for Example : 
 Suppofe the Lines /■/ and a d. Fig. B were the 
 Diameters of two other Pilafters. On any Point, in 
 any Side, fuppofe on b^ with an Opening equal to 
 b f^ defcribe the Arch g e^ cutting the Side of 
 the Filafter in/; tlicn drawing the Line b f, 
 the feveral Flutes and Fillets firft drawn, will di- 
 vide that Line in the fame Proportion ; and fo 
 the Line a d the Diameter of the leff^r Pilafter. 
 
 The I^ines r t and j 5, Fig. B, exprefs the 
 fame, in that Pilaftcr which hath Beads at its 
 Angles. 
 
 To reprefent the pcrfpeSlivc Appearances cf Flutes 
 and Fillets in the Shafts of Cclumns, Fig. C, D. 
 
 By Prob. XI. of the lonick Order, defcribe 
 the Flutes and Fillets in each Semicircle a g r, 
 and c b dy from whence draw perpendicularLines, 
 which terminate with Arches, as a; «■ Af, ifc. and 
 the Whole will be compkted,. as required. 
 
 Plate LV, LVI, LVII. 
 
 Of NICHE S. 
 
 Thefe three Plates contain fix grand Defigns 
 for Niches, of the 'Tttfcan, D:rick, Liiick, Corin- 
 thian and Compojite 0'C(\crs, whofc C.w^ties, tho' 
 here reprefented femicircular, may be made femi- 
 elliptical at Pleafure ■ when required ; and as the 
 ■working of the Heads of Niches, femiuicular 
 
 19 
 
 femi-elliptical, may be performed two different 
 Ways, which are very curious, I Ihall therefore 
 now explain thofe Operations as follows : 
 
 Plate LVIII, Fig.K. 
 
 To form the Head of a femicircular and femi elliptic 
 cal Niche y by divers Tbickneffes of Plank., &c.. 
 gleza'd together. 
 
 (i.) On the Surface of a flatPannel, Cdc. large 
 enough to contain f<>mething more than the Plan, 
 of the Nich, defcribe a Semicircle, as 1 2 3, Csfr. 
 14, 5 d Fig. K, of the lame Diameter, as that 
 of the Nich. Take the Thicknefs of your Plank, 
 (jjc. in your Compaffes; and fet that Diftance on 
 the Semidiameter a a, from a to c, from c to e,. 
 &c. and through the Points cegi, &c. draw 
 Lines parallel to the Diameter i a d. Take a 
 Piece of Plank, as Fig. A, and with a Square, 
 applied to its Edge about the Middle of its 
 Length, as at a -, draw a Line, from the under 
 to the upper Surface ; tlie Extreams of which, are 
 two Centres -, on which you are to defcribe two 
 Semicircles ; the under one with the Radius a i ; 
 the upper one with the Radius c 2. With a turn- 
 ing Saw, cut obliquely through the two Semicir- 
 cles j. and then you will have done thefirftThick- 
 nefs. Take a fecond Piece of Pl.mk, as Fig. Bj, 
 draw a Line on its Edge near its Middle, fquare 
 to both Surfaces -, whofe Extreams are two Cen- 
 tres as before. On the under Centre thereof, 
 with the (laft) Radius, c 2, defcribe a Semicir- 
 cle equal to the laft (becaufe the under Surfice of 
 this fecond Piece, is to be glew'd on the upper 
 Surface of the firft) and on its upper Centre,with 
 the Radius e 3, defcribe a Semicircle on the up- 
 per Surface; then cutting through both Pieces as 
 before ; the fecond Piece is done. 
 
 (2.) Proceed in like Manner, until the Whole 
 is complete ; the Operations of which are expref- 
 fed by the feveral Semicircles 3, 3 : 4, 4 : 4, 4; 
 5, 5 i (^c. in the Figures C, D, E, F, G, I, K, 
 L, M, N, O, whicii reprefents, the feveral Pieces 
 of Plank as their refpeftive Heights above the. 
 Bafe lad; approach the Zenith of the Nich. 
 
 (3.) Glew all thefe Thicknefles, one on the 
 other ; and with a Compafs, fmoothing Plain,, 
 whofe Arch is fomething quicker, than that ot. 
 the Nich ; clear off and finilh the Infide,. 
 
 (4.). Ahi 
 
zo 
 
 0/ N I C H E 
 
 S. 
 
 (4.; An elliptical headed Nich, m:iy be form- 
 ed in rhe fame Manner, as the preceding •, if 
 Semi-Ellipfines are defcribed on the Surfaces of 
 the Thicknefles ; as the Semicircles aforefaid. 
 
 To Jifid the long Diameter of the feveral Semi-El- 
 lipjips. 
 
 As they diminilh from the Bafe of the Nich 
 to its Zenith •, defcribe an EUipfis equal to the 
 Plan, or Face of the Nich ; divide its Height 
 into Thicknefles, and drawing Lines through the 
 feveral Points of Divifions, parallel to its longeft 
 Diameter, until they meet the Curve of the Front, 
 in the fame Manner, as in the preceeding Fig. K; 
 they will be the long Diameters required. 
 
 To find their refpe5live femi-Jhort Diameters. 
 
 Defcribe a Qgadrant, whofe Radius is equal to 
 the Height of the femi-elliptical Head of the 
 Nich. Divide one of its Sides, into the fame 
 Number of Parts, as the Number of ThicknefTes 
 in the Height. From thofe Parts or Divifions, 
 draw Ordinates to the Limb •, which are the fe- 
 mifhort Diameters, refpeftively proportionate to 
 the long Diameters before found. 
 
 The Heads of Niches are fometimes, formed 
 by Ribs, as Fig. IV, where A is the Plan, and 
 B, the Elevation, of the Ribs, for a femi-circu- 
 lar headed Nich. 
 
 The Mould, by which, thefe Ribs are made, 
 is the Arch of a Quadrant, as ah. Fig. Ill -, or 
 the Arch ab, the half Front of Fig. B. When 
 the Heads of Niches are thus formed, they are 
 either lath'd or plaiiler'd within Side, or lin'd 
 ■with thin Deal or Wainfcot -, which laft if per- 
 formed in a neat Manner -, has a very good Ef- 
 fect, and may be thfUs performed. 
 
 To cut out the Lining, for the Head of a fcmicircu- 
 
 lar Nich. 
 
 Fig. I. PLite LVIII. 
 
 Let the Semicircle ^48, reprefent the Plan 
 of the Head of a fcmicircular headed Nich, which 
 divide in 16 Parts, and through every other Part 
 draw the Lines A 2, B 2, C 2, i^c. making 
 their Lengths B a, isc. equal to the Length of 
 the Arch h 4.; or half the Circumference of the 
 Nich's Head. 
 
 Complete the Circle \ 6 h, 4p, and draw the 
 -juiiieter 416, at right Angles to the Diameter 
 
 hzS. Divide the Semidiameter 2 16, in eight 
 Parts, and through them draw the Lines h p, i q, 
 k r, ice. and on the Points 9, ro, 11, ^c. with 
 the Radius pp ; 10 q ; 11 r ; &c: defcribe Semi- 
 circles, as g 10 -iV ; fifzv, &c. and divide a 
 fourth Part of each, as ^ lO; /z, &c. into 4 
 equal Parts. On the Point G, with a Radius 
 equal to the Length of the Arch 0.16, or i6w, 
 defcribe the Arch a i^j b, alfo with Radius's 
 the Lengths of the Ajches 16 « ; 16 m ; 16 I, 
 16 k ; 16 i ; 16 h ; defcribe the Arches d 1% c ; 
 e ig'f; h 20g ; k iV^', &c. On the Arches 
 ab, d c, e f, 8cc. fet off one fourth Part of the 
 Arches g 10, fz, Lfc. from the Points, 17, 18, 
 19, if^c. to the Points ab ; d c ; ef; h g ; k i ; 
 &c. through which. Lines being traced, from the 
 Point G, to the Points 6 and 7 ; the Part G 6 7. 
 will be an eighth Part compleated. In the fime 
 Manner complete the other 7 Parts, ABC, fsff. 
 and when bent into their Places, they will exadl- 
 ly complete the Lining of the Head of the Nich, 
 as required. 
 
 Note, In very large Niches, the Number of 
 Parts may be encreafed from 8 to 12, 16, lo, 
 i^c. at Pleafure. 
 
 Fig. II. is the Plan of the Head of a femi-el- 
 liptical Nich, compofed of Ribs for Lath and 
 Plaiiter, whofe Bafes are reprefented by abed 
 ef. The Front of this Nich, is the very fame 
 Scmi-ElUpfis, as the Plan afg. But the feve- 
 ral Ribs, which ftand on the Plan to form the 
 Head, are different, as being all Quarter Parts of 
 Ellipfis's, whofe longeft Diameters are lefs -, ex- 
 cepting the Front Rib, that ftands over the Bafe 
 f h, which is the fourth Part of a Circle, whofe 
 Radius is f h. 
 
 To form the Curves of the Ribs, to ftand on 
 the Parts b c d e, confidcr their Bafes b h, c h,dh, 
 and eh, as half the long Diameters of fo many 
 Ovals and/jf» is half the fliort Di.;meter to eve- 
 ry of them in general. Then by the Rule gi- 
 ven in Plate LIV, to defcribe an ovallar Win- 
 dow of any Breadth R.nd Height ; defcribe the 
 Curves for the feveral Ribs required •, which are 
 no more than the Quarter Parts of fo many com- 
 plete Ovals. 
 
 Plate LIX, LX, 
 
 Eight Defigns for Marble Cifterns, for Buffets, 
 Side Board Tables, fcff. 
 
 Plate 
 
Of Chimney Pieces, Pavements, Altar Pieces, Pulpits, Tombs, &c. 
 
 Plate LXI,LXII, LXIII, LXIV, LXV, LXVI, 
 LXVII,LXVIII,LXIX,L*XX, LXXI,LXXir, 
 LXXIII, LXXIV, LXXV, LXXVI, LXVII, 
 
 Lxxvm, Lxxix, r -xxx,lxxxi, lxxxii, 
 
 LXXXIII, LXXXIV, LXXXV, LXXXVI, 
 LXXXVir, LXXXVIII, LXXXIX, XC, XCI, 
 XCII, XCIII. 
 
 Of Chimney Pieces, and their Enrichments. 
 In thefe thirty-three Plates, there are fixty-three of 
 the beft Defigns for Chimney Pieces, and their Orna- 
 ments (containing great Variety of Tabernacle Frames, 
 Shields, Feftoons, i^c) that have been yet publifhed 
 by any one Matter in Europe, if not in the whole 
 World. 
 
 Plate XCIV, XCV, XCVI, XCVII, XCVIII, 
 
 xcix, c, CI, cii, cm, CIV, cv. 
 
 Of Pavements, Frets, and Gulochi's. 
 Twenty-feven Defigns of Marble Pavements, for 
 Halls, Baths, ^c. the laft nine of which, are environ'd 
 with thirty-fix Varieties of Frets, Gulochi's and Bor 
 
 21 
 
 Plate CXXXVII. Of Tombs. 
 
 Here, for Variety fake, I have given a Plan, and 
 two Elevations, by which 'tis evident, that thefe 
 Kinds of Tombs are nothing more than regular Pe- 
 dettals, crowned with large Tables for Infcriptions, 
 
 To make thefe Tombs truly grand, they (hould 
 be afcended by three Steps, giving to the upper Step 
 a Breadth at leaft double that of the others. 
 
 In Plate CXXXII is fliewn, how much an ObjeA 
 appears lefs, as 'tis elevated above the Eye. Suppofe 
 the Objed D, whofe lower Part is level with the Eye 
 k, be raifed from a to c ; then its real Height c d, will 
 appear to the Eye at k, to be no higher than/^-, be- 
 caufe kg mdka are equal ; and fg is feen under the 
 fame Angle as dc. 
 
 To make a Monument, ^c. placed on the Point r, 
 appear of equal Height, with a Monument view'd 
 level with the Eye as D •, draw the Lines lo /^ ; 
 5 k ; and c k. On the Point k with any Radius, de- 
 fcribe an Arch as ^cxzz at Pleafure. Make the Arch 
 X z, equal to the Arch z z, and from k through the 
 draw the Line ^ ;t y?; f 
 
 Architraves, or other Ornamental Parts of Archi- 
 tefture, wherein they are commonly introduced, and 
 more particularly fuch that may be view'd^ from a 
 Gallery. 
 
 ders, which in general may be as well applied for "PP^/' ^'V^ l^^ ^u^^-'l '^'" fhe Height, r. 
 Borders to Pavements, as to enrich the Planceers of Tf '^ ^'ght Feet is the Height required, at fifteen 
 
 - -reet above the Lye ; that ihall appear equal to five 
 
 Feet, view'd level with the Eye. For as the Angle 
 ^ ^ f, is equal to the Angle 10^5; and as , c is per- 
 pendicular over a b, therefore the Height e c, though 
 three Feet more than a b^ will appear to the Eye at k 
 to be but of the fame Height of a h, viz. five Feet. 
 
 As very often it is required to eredt Monuments in 
 Churches, at fome confiderable Heights above the 
 Eye ; I therefore, for the fake of Mafons, thought it 
 neceflary to demonftrate the preceding, that they 
 might avoid Errors in proportioning fuch Works for 
 the future. 
 
 Plate CVI, CVII, CVIII, CIX, CX, CXI. 
 
 Of Altar Pieces. 
 Six Altar Pieces, of which the firft two are for 
 Chapels, and the others for Churches. 
 
 Plate CXII, CXIII,CXIV,CXV,CXVI, CXVII. 
 Of Pulpits. 
 
 Six Defigns for Pulpits, which in general have their 
 Plans, Types and Members reprefented at large ; 
 which the ingenious Workman may perform with 
 Pleafure. 
 
 Plate CXVIII, CXIX, CXX, CXXI, CXXII. 
 
 Tables for Monumental Infcriptions. 
 Twenty-two Defigns for Tables of Renown, for 
 perpetuating to Pofterity, the Memoirs of worthy 
 Perfons deceafed. 
 
 Plate CXXIII, CXXIV, CXXV, CXXVI, 
 CXXVII, CXXVIII, CXX IX, CXXX, CXXXI, 
 CXXXII, CXXXIII, CXXXIV, CXXXV, 
 CXXX VI. 
 
 Of Monuments. 
 Twenty-one Dtfigns for Monuments, enriched 
 with Vales, Bafs-Rclicvo's, Bufto's, ^c. from which 
 the ingenious Workman may receive fuch Hints, as 
 to invent others innumerable. 
 
 Plate CXXXVIII. O/" Obellfques. 
 Here I have given four Varieties of Obelifques, 
 fiz. Fig. A whofe Bafe is a geometrical Square ; 
 Fig. B an equilateral Triangle i Fig. C an Odtagon ; 
 and Fig. D a Circle. 
 
 Plate CXXXIX, CXL. 0/ Time Pieces. 
 Two Time Pieces for the Infide of Churches ; as 
 againft a Gallery, i^c. 
 
 Pl A t E CXLI, CXLII, CXLIII, CXLIV, CXLY, 
 CXLVI, CXLVII. 
 
 Frames for Marble Tables in Rooms of State, &c. 
 Ten Defigns for the Feet and Frames of Marble 
 Tables, after the French Manner. 
 
 Plate CXLVIII, CXLIX. 
 
 0/ Marble and Stone Tables //rGrotto'j and Arbors 
 in Gardens. 
 
 Here are four Varieties of Tables, and as many of 
 H their 
 
Of Ohcrtfqnes, Time Pieces, Fonts, Ciellngs, kc 
 
 22 
 
 their Pedeftals, whofe Plans explain their Figures to 
 be circular, oftangular, hexangular and fquare. 
 
 Plate CL. 
 0/Chriftening Fonts/or Churcber, and their Pedeftals, 
 
 Four Fonts forthcBaptifm of Children in Churches, 
 which to be grand, fhould be ere<5ted on a fpacious 
 Afccnt of three Sreps, that thereby, during the Per- 
 formance of Baptifm, the Prieft may be elevated a- 
 bove the Congregation. 
 
 Plate CLI, CLII. 
 Pedeftals /w- Sun-Diais, flwiBufto's. 
 
 The firft fix Pedeftals are defigned for Horizontal 
 Sun-Dials, which, when erefted, ftiould be elevated a- 
 bout three Steps from the Ground-, whereby they will 
 be lefs liable to be difplaccd by Accident, and there- 
 by rendered ufelefs. The laft four Pedeftals are de- 
 figijed for Bufto's, placed in Buildings or Gardens. 
 
 Plate CLIII, CUV, CLV, CLVI. 
 A Cheft of Draws, i Medal Cafe, a Cabinet of 
 Draws, and a Drefting Table enriched after the 
 French Manner. 
 
 Plate CLVII, CLVlIf, CLIX, CLX, CLXI, 
 CLXII, CLXIII, CLXIV. 
 
 Eight Defigns for Book Cafes. 
 
 Plate CLXV, CLXVI, CLXVIT, CLXVIII, 
 
 3> 4 ■» 5> 6 ; ^c. and make the Ordinates i, 2 ; 3, 
 4 ; 5,6; &c. on a b the Bafe of the Angle Bracket, 
 equal to the Ordinates 1,2-, 3, 4 ; 5, 6 % &c. on 
 a c, the Bafe of the front Bracket. Then fixing Nails 
 in the Points g 7 46, ^c. to a j bend a thin Lath 
 of equal thicknefs to them, and trace the Curve ^ 2 
 4 6, (jjc. a, which is the Curve of the Angle Brack- 
 et, for the Cove as required. 
 
 II. To form an Angle Bracket for a Plaifler Cornice. 
 Fig. A. Plate CLXVIII. 
 
 Let hfh c, be a front Bracket, d a its Height ; d b 
 its Proje6i:ion, and the Line e a its Bafe, when erecfl- 
 ed in i»s Place, at the Angle a. Draw n a, the Bafe 
 of the Angle Bracket, and raife the Perpendiculars <7, 
 s ', and «, r •, each equal to d a the Height of the 
 front Bracket. From the Points /and hy draw down 
 the Lines f i, h k^ and continue them to ml. Draw 
 m q, and lo, parallel to n r. Make / 0, equal to k h\ 
 and mq^ equal to //. Then drawing the Lines a o^ 
 of, p q, and q r, the Angle Bracket will be finiflied, 
 as required. 
 
 Note, That a Bracket for an external Angle has 
 no Difference from a Bracket for an internal Angle, 
 the Backifig ou]y excepted ; the Back of the former 
 having its Angle convex ; and the latter (if ftridtly 
 performed, which is feldom done) concave to its 
 central Line. And what is here faid for finding the 
 Curve or Form of a Bracket at a right Angle ; is 
 to be alfo obforved and pradtifed for finding the 
 Curve or Form of a Bracket at any acute or obtufe 
 
 CLXIX,CLXX,CLXXI,CLXX1I,CLXXIII, Angle whatfoever, after having found the Bafe Lines 
 CLXXIV, CLXXV, CLXXVI, CLXXVH, of the Front and Angle, over which the two Brack- 
 CLXXVIII. ets are to ftand, when in their Places, as ea, and « a, 
 
 in the laft Example. 
 
 Plate CLXXIX, CLXXX, CLXXXF, CLXXXII, 
 CLXXXIII, CLXXXIV, CLXXXV, CLXXXVI. 
 
 Twenty-two Defigns for Iron Works of the moft 
 exquifite Tafte, from which many curious Enrich- 
 ments may be compofed, for the Embelliftiments of 
 Cabinet Works, Ceilings, [3'c. 
 
 In Plate CLXXIX, Fig. A contains four Varie- 
 'Let B be a front Bracket, ftanding at the Angle ^?, ties of Pannelling for Balconies ; and Figures B and 
 
 Fourteen Defigns for Cielings, with great Variety 
 of Enrichments ; wherein is contained, for the Ufe 
 of Carpenters, the Manner of forming Angle Brack- 
 ets, for a Plaifter Cove of a Cornice, as follows : 
 
 I. To form the Curve of the J>j^!e Bracket A, for a 
 Plaijier Cove, Plate CLXV. 
 
 TN'hofe Projection is equal to a c ; and when up in its 
 Place will ftand over the Line a c ; for which Reafon 
 I call it, the Bafe of that Bracket, Draw « />, the 
 Bafe of the Angle Bracket, and divide a c and a h, 
 the two Bafes, each in the fame Number of equal 
 Parts, fuppofe, 6, 8, \o,i3c. as at the Points i, 3, 
 ^,i3c. From the Points I, 3, 5, ^r. draw Ordi- 
 nates, perpendicular to the two Bafcs, as c/; i, 2 ; 
 
 C are two Varieties for fquare Pannels to Gates, i^c. 
 In Plate CLXXX is four Varieties of Raking Pan- 
 nels for Stair Cafes-, and in Plate CLXXXII is three 
 other Varieties for the fame Ufe. 
 
 Plate CLXXXI contains fiveVarieties of pannelling 
 for Iron Gates; and Plates CLXXX 1 1 1,CLXXXIV, 
 CLXXXV, CLXXX VI, four grand Defigns for 
 Iron Piers, with their Gates and Ornaments. 
 
 ADDENDA, of Fourteen Plates of R O O F S, ^c. 
 
 F 
 
 I 
 
 N 
 
 S. 
 
ZJ^e/u7V lAc younf J'fzi</^/Ur can pix^cf<-d eo z/teAxt of lllakiji^" Deligns cf t/ie CrruirnefUa/ ^J^arH' of QiuMtntj/j , 
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