CIHM 
 Microfiche 
 Series 
 (i\/lonoJ3raphs) 
 
 . - 1' 
 
 "^ 
 
 ICMH 
 Collection do 
 
 (monographles) 
 
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 Canadian Inatitut* for Historical MIcroraproductions / lifstitut Canadian da microraproductions historlquaa 
 
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TMl«n««4|l and B<blio«raphw NoMt / NoM« tachni^uM at lMblM}«fafihM)uM 
 
 TM Intlitut* tiM atlvmfiMd to obtam iM htt (Hi«in«i 
 copy •vatlatoi* for filmmf . F««lurM of ihit copy whtcb 
 m«v IM b4blto«raplitcallv uAtqtM. MrhMi m«v dlfr afiy 
 of Mm MnafM tn ttM r«p«oductlo«i. or whtcfi m«v 
 il^ificjntty chan«> ih« u«u«l m«lt«od of lilmmf. ar* 
 chackad b«t««» 
 
 L'lntti^l a microfilmA la maillauf •■ampUira quM 
 lui • At* pottibU <ta M procurar Lai dAlaili da cat 
 •HMHplair* ^1 lont p««it 4tr« ufMqum du pp«nt dt tiM 
 bthliofrapbiqwa. qut pauvani mod«()a« una imafa 
 raptoduita. o«j qui pawwnt aiiifar una modification 
 tfMN la method* norni«l« <tt filmii* lont tndlquAi 
 •I iiwout. 
 
 
 
 Colourtd eoMrt/ 
 Couvtrtlirc da eoulaur 
 
 Covari damafad/ 
 Couvartura andommaiM 
 
 □ Colourad pafat/ 
 f afat tla coulaur 
 
 Q 
 
 Pa«a« da«na«ad/ 
 Pa^H aftdofnifia^aai 
 
 □ Covart ra*tOfad and/or lamtnalad/ 
 Couvartura raa tauria a.t/ou pallteulte 
 
 Du 
 
 Covar titia mhsinf/ 
 
 titra da couiwrtura maiMiua 
 
 □ Pafat raitorad and/or lamtnatad/ 
 Pafat raitaurAat at/ou pallicul4at 
 
 EI 
 
 Pafat ditcolourad. ttainad or foHad/ 
 Pafai dAcoior^at, tachat^at ou piqu^ 
 
 □ Colourad inapt/ 
 Cartas ftefraphiquai art eoulaur 
 
 □ Pafat datachad/ 
 Pafat dAtachAat 
 
 i' 
 
 D 
 D 
 
 n 
 
 Colourad ink (i.a. otiiar tlian blua or black)/ 
 Encra da eoulaur (i.a. autra qua blaua ou noira) 
 
 Colourad platat and/or illuttrationt/ 
 Planchat at/ou illuttrationt an coulaur 
 
 Bound with othar matarial/ 
 RaM avac d'autrat dbcumantt 
 
 Tifht bindirtf may eau<a thadowt or dittortion 
 alonf intarjpr margin/ * 
 
 La raliura tarr4« paut cautar da romhc^u da la * 
 dittortfon la lonf da la marfa intkiaura 
 
 □ Blank laavat addad durinf raitoration may appaar 
 witliin tha taxt. Whanavar pottiMa. thata hava 
 baan omittad from filmirtf/ 
 II ta paut qua cartaflUt pafat blanebat aioutAat 
 . . lort d'una rattAuration apparaittant dant la taxta, 
 mait, lortqua cala Atait pottiMa.^cas pafat n'ont 
 
 pat M film^. 
 
 T 
 
 HShowtbroufb/- 
 Trantparanca 
 
 
 
 Quality of print variat/ 
 Quality in4fala da I'imprattion 
 
 □ Continuoui pagination/ 
 Pafination continua 
 
 D 
 
 D 
 
 Includat indaxlati/ 
 Comprand un (dati indax 
 
 TitIa on haadar takan from:/ 
 La titra da I'an-tlta proviant; 
 
 TitIa paga of ittua/ 
 
 Pafa da titra da ll^livraiton 
 
 I I Caption of ittua/ 
 
 □ 
 
 Titra da depart da la livraiton 
 
 Matthaad/ ' 
 
 GAniriqua (piriodiquai) da la livraiton 
 
 
 
 Additional commantt:/ f Wrinkled pages may film slightly Qut^of focus, 
 
 Commantairat tupplimantairm: . 
 
 'I«,v^'*' 
 
 Thit itam it f ilmad at tiM raduction ratio chackad bafow/ 
 
 Ca documant att film* au taux da rMuction iitdiqu* ci-dattout. 
 
 10X 14X 18X 
 
 22X 
 
 26X 
 
 XX 
 
 12X 
 
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 32X 
 
 <* . »» 
 
 JU 
 
/ \ 
 
 TIm copy f llm«d h«r« ha* b««n ypKw i Mc a d th«nli» 
 to th« g«n«ro«ltv of: 
 
 Notropollton Toronto Rofortnco Kbrcry 
 Baldwin Room 
 
 Th« ImagM appaarlng hara ara tha batt quality 
 poaalbia oonaldaring tha condition and laglbillty 
 of tha original copy and \(\ kaaping with tha 
 Irilming contract •paoiflcatlont. 
 
 L'anamptalra fHfn4 f ut raproduH ^A^ A la 
 g«n4rocltA da: 
 
 Matropolltan Toronto^ R«f a ranca Library 
 Baldwin Room 
 
 Laa Imagaa •ulvantaa ont 4t4 raprodultaa avac la 
 plus grand aoin, oompta tanu da la condition at 
 da la nattat* da I'aMamplatra fllma. at an 
 conformity avac iat oondltlona du contrat da 
 fllmaga. 
 
 
 Original coplaa In printad papar oovart ara fllmad 
 baglnning with tha front covar and anding on 
 tha last paga with a printad or llluatratad Impraa- 
 alon. or tha back covar whan appropriata. All 
 othar original coplaa ara fllmad baglnning on tha 
 first paga with a printad or llluatratad Impras- 
 slon. and anding on tha last paga with a printad 
 or llluatratad Intpraaslon. 
 
 Tha laat racordad frama on aach'microfloha 
 ahall contain tha symbol <-^ (moaning "CON- 
 TINUED"), or tHa symbol V Imaaning "£ND"). 
 whiehavar appllM. 
 
 Mapa. plataa. oharta, ato., may ba' fllmad at ^ 
 diffarant raduotlon ratloa. Thoaa too larga toiia 
 antlraly Inoludad In ona axposura 9i^% fllmad 
 baglnning In tha uppar laft hand cornar. laft to 
 right and top to bottom, as many framas as 
 raqulrad. Tha following diagrams lllustrata tha 
 mathod: 
 
 Laa axamplalraa orlginauN ddnt la couvartura ws 
 paplar aat Imprlm4a sont fllm4s mrs commandant 
 paf la pramlar plat at mn tarmlnant solt par la 
 AmKkf paga qui comporta una ampralnta 
 d'Impraasion ou d'lllustration. solt par la saoond 
 plat, salon la oas. Tous las autras axamplalraa 
 orlglnaux sont fiimis an commandant par la 
 pramlAra paga qui comporta una ampralnta 
 d'Impraaalon ou d'llluatratlon at an tarmlnant par 
 la darnlAra paga qui comporta una talla 
 ampralnta. 
 
 Un daa symbolaa sulviuits apparattra sur la . 
 darnlAra Imaga da chaqua microficha. saloh la 
 oaa: la symbols -^ signlfia "A 8UIVRE". la 
 symbola Y aignljja "FIN". 
 
 Laa oartaa. planqhaa, tablaaux. ate. pauvant Btra 
 f llmAa A daa taux da rBductlon dl'ffBranta. 
 Lorsqua la dooumant aat trop^ grand pour Btrii 
 raprodult mrx un saul ollohB, II aat flln^A partir 
 da I'angla supBrlaur gaucha, da gaucha A drolta, 
 at da haut an baa, an ^ranant la nombra 
 d'Imagas nAcaaailra. Laa dlatframmaa aulvanta 
 illuatrant°la mAthoda. 
 
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MICROCOfV IISOiUTION TI$T CHAtt 
 
 (ANSI and ISO TIST CHART No 2) 
 
 1^ ^^B . ■■■I 
 
 ■ 27 
 
 
 1.8 
 
 1:25 i 1.4 
 
 1.6 
 
 ^ APPLIED IIVHGE U^ 
 
 ^p"- 165 J EosI Main StrMi ' ~~ 
 
 =%« ?Jfr?*'*''' N'* ^o^ '14609 USA 
 
 ^^ ("6) 482 - OJOO - Phon. 
 
 BOSK (7t«) 2^-S989-raK 
 
Toronto 
 
 Library. 
 
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 GEOMETRICAL PROBLEMS, 
 
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OEOMKTRICAL PROULEMrf. 
 
 9^i / 
 
 -^.._— . mmgt4 M9rt*M, aktmm. aemt», twtU, i-iwuiw 
 
 IM, ^ganmt, pmrtlt4. pniMtm, tS^ttrfm. fn^fHuUum. Ajn**- 
 
 ikmk, e^ntUMf^, d*dmawm, f»timl»l; ^-iww, o»tmt,uU, Um,HMt 
 
 if filivV* .^'Mk . 
 
 rkgkliiu^. .. 
 
 3. If iwo eircl«ti IntunKri mpIi c»lhrrhiivJin«f"nnno»r«<ti«t, 
 tint flyurfl furmul hy joinin* ihr r KirpiiiitiM of Uml r»diiui willi lli« 
 ^nUi of inUr«*«cuon, t« • rhuiuliua, ^ 
 
 4. If ihr comnHHi radnui b« produced to m««l boili'clrrl#», 
 iIm lifntm form«d'by Joi«i»m Om pointi o(' int«>rM«<tioii •ml ih« 
 «tlr«niilMfl of ih« di*m«l«r« *Q foriiMMl, mo iM|ailal«ral irMttflei. 
 
 -.^r 6. TImi o^ilaiwrol tri«iiKl« onll»« eotnravB rMiitt* b oft* Ibird 
 •Ittabtr of Um fonnor. ^ • \ 
 
 «..T»i* ftftirp for«io«l by,J/oiiiing iho ptilnut of int#r«#cUon ) 
 #ith Ilio otlr«m<li«« of •iUior ilmni«l«r it ftiuK tinif* w greot oa tli* 
 tquiUtcril trixuiglo on Uio coininon riulitis. . . 
 
 Mt«t>ftf TIm li«i joining Iho poinU of iniaratctton dWWiit ihiit 
 4inni Into parte, viiuiek or* m throo to oii*» ^ 
 
 H. 'Hn* rhomlii.'fonn««l hy ioiniti« th« point* of ml«ni#riion 
 Mitk tlM tiMUftlMijraiyqUi oKtniiuituiit of iho dMiuiotcffis ore •» oiio 
 
 ,«tfv ftJElM KtM lotnium ih* poiittt of intanwotioii cmH^Ui* cotii* 
 mon rediaii at rif nt anglvt. ;?> . « ^' %♦ ,f^4 — = 
 
 .. 'i« 4I>,, In Urawinir a rinM Um «*mn1 to n Kiv«a rif tit IJli* (Votii A 
 ||[i¥«n point, «li9W|lMi^tiif 'ob'e'" <mIiu ol «ifhtUiir0i*W|^,i^i> 
 
 ' II. TIm ftdhMof the aacond cirola, ia equal to tht.aiuN or 
 digennu of tfa* fifaa liiifi, M ^« ■ul« of thaqquiUttand trianglr. . 
 }*. ITtw* akk J af a iffMncb ba 4M|iMl,tb»opp«aiU Miglaa ara \ 
 abw aqnaf ; pMva M whhoat piroduo«ii««li»«^lMl aid««. 
 
 . la. On 
 
 a pplied 
 
 jlaMMiMM telha IfttMMTpartoCtbf fifth propoateion 
 logt tlw alaia»»{» of Euclid t '.■■■■■: ■ 
 
■:.'-* 
 
 ) ' ' ' ' 
 
 U In tlw contmiction for Ui« •liUipropowtion of EuoUd'i 
 elcmonta, wliM obkclion to nMaMarinf off the r«|air«d portion 
 
 ^ 15. Expbin tho nktorc of OM «x Airarib or bdirtot proccwof 
 
 proof. 
 
 16. To what purpoto in th« .orenlh propowtion ^ef "«* % " 
 W!iili.Ai^ «bn»ol'Mgtortpm made n«i off ''^^^^;^^^^^ ; 
 
 J?i INftrotb««||lali»ropo«iiioowkl»P«t««»>i^ 
 
 n^;ia If Wlto««trt ami an^i^ 
 
 ^^^i obtotaloll^hkae, aiidor what einJunKttne*^ vijr |M tort** W 
 
 iiftSwfWMoir/ttpon, orabo¥6thatflrtteA»n^ ^ 
 
 19. Inconatmctingfor the biaection of a rectilineal w>glf*«tate . 
 
 the ttltahtage of the particular poaitioti of the equiUtera! tr|ai|fl«. 
 
 '\«0. Were the vertfx aimated above inatead ©^ *J#«y th« • ^ 
 bate, Ifi wb^ caae wouW that^onatructiotf be inappbOMe? ^^^^ 
 
 81. In the biaecUon of a given finite rigbt fine, woalAtUitlr^/^^^^ 
 
 lOlit ilia liMfltat tight anglea. ' ■ • ■'■^'^t-.; "^..'u.^ -'isn W ■ '»»|p:'»wn .■ . 
 ti ilfc^lme dwwB from the YertM to the ««*«• poto^^ 
 baae of an iaoaeelea triangle, biiecta the verUetf a«(M mmmf9' 
 pe^«l»r ta thelMpf.,^ , . ,^Wt;-^:v'i^,ifta{ .''?«'V^'- ■■l^'^'t^L.^ ^' 
 
 ^»S*IbI«JthriS^ u.«u^ W. • •. 
 
 r a^ H Iff. iawedea trkpglw 
 aia«»ofa^fii|m«>^bM«,A»l««Joiw»f*^^«***^ tapwl»#t 
 
 115. ili|Hnta»n poiiil vrithw a maagte •qlp^MMM mi^^<^ 
 ■ #»gl|i>i''iwhMe: .... .,,.,/...K ••.■...:;,.. -v. ■■■■"■•,,/. -. *l'' " 
 
 ^^60^ 70^76, 80, 85, degreea. »^ i.^^^Hj .<^ .^ «m 
 39. Fiove te -wua wflw of in boterfw ti^Bm^tiMMiv 
 
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 W. T* what prop««W««i iW •* ^*'*'''^**T!f !?!f.^!!i!!!S^^ 
 A4. If ally mmib»r of k^<iw ''>t" i |> ' i ' ^' J T . u t!! l*!?.i 
 
 i , »*M irt«t Minft of • fitkt llno4o«i o ghr«np«#)iM«iifcu!ftr 
 
 40. DbtuifuiA botweeft th« foaidi. fi$h*, and tw«ngr-«xth 
 
 41. ij^ a ti»«i poiiit. imw ** tlwrtert Uiie po«Wf «•# 
 / given, figbt Uno. ■ ,; . .-: : .:;v,^ ; ■ ; : , '•■■;: ^ . -^m V^^' ;r^:^ :'*'*,* 
 
 Ift. tW» Whicll«l¥ik« gwrtof anglei with the pw^wScrfr 
 
 MfepiifMiMiir Afo fliMm 
 
 t: 
 
 ■If 
 
 
IW**^ 
 
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 '^f- •^ ,^ H »rtf* 
 
 « '*«-ff' 
 
 it:-V. 
 
 "* ^'^%. fk |«toerd» i Hnk tWM Miyf ilt^wi lirMli lbe*t«^ of i^ 
 ffUiMcl« to Om btuM ; If any two of the five (bHowtHl tqiulMis Ut 
 tiiiAU4iiHi«iNMin«yMMu€«4{*T- . . if mH 
 
 3. TlM«q«att^'Of lk»aaidM uodekthalhiedri^nMi iM laM. 
 
 4. The equality of the angles under the line dnwo UtA 0M ikiea. 
 
 5. The equaKty of the aefmenti of tho base. 
 
 :i''V 
 
 M. If«i^« trkufkiabe celliitniote4on'a^«iiiitM»n baae, tfi* 
 diffarwce iMtweeo, their vertical anglea ia the ium of the anftef 
 fiontaihed byHn,<ptar<nipoua.aidf %,/|,„.;., .^^,^ ^^minnirm -vJ: ".•<!> ■» 
 
 an 
 
 ^t .61. II |a r^iured to conatruot d eiatcm on a con«Maioa line 
 wlib^h aball he equafly distant from tvvo dwelUnf boua«a in ^^ 
 cini^, sttoated on the same or opposite sidea of the lin«. ,^ n-^'fu 
 
 id. The right line which bisects the yertiMl wt«ri«r «fi|;le of 
 Isoacelea triangle, b parallel to the base, '^v '>h^m» «> . *).M! ; 
 
 ^"^f 'llSi Oi*^^ the position of a window, determine that of a mir- 
 ror on the opposite wall.whibh trtiali reflect the imaffes of cx^n^ 
 objects to the eye of a t>enon, the position Of whi<ii is abo giiratkL 
 
 ^'^' (14. The right line drawn from the vertical an|[le of an isosc«i 
 les triangle, biaecting the base, b parallel to lines joining the ex- 
 tremiti«« of thobaae and of the aidoa, produced l»>tott|)l *# t«rtc« 
 to their own length. h!!1'..!*^i> i^m^, 
 
 • '' *' 6&. It is required to divide a quadrangular field int<> three por* 
 iona, by lines drawn (Vom the exirennties of one to adme pohkt fil ,. 
 the dppoait^ side, ao that the length qf fence may he ^ abort a|i 
 posaible. ...'... ■■'.'- ' 'm'-' 
 
 Angle ^tralfel to the base, bbecy lb© verucal ekierio|^a9^1e^ . ;^ 
 
 vtl8»if'A*Knearawn.ftom the reMical «wfe .irf* • ||^«flf » 
 pa^Del to the baae, bbi^ti.tb« yerOtMtft^riwr n^, lh#papil« 
 
 68. If two right lines which interaeet eaeh olli«r'li«* paraiM 
 mf(f^^¥iP''P o^effc theanglea inqhided by tb^at ppra of 
 Uyavnll^e' equal reapertlreiyn^ , t yQi^jj:j^^^i^:'m ^i^f : *^*'#^.'^,: 
 
 IlidkMilM to pne q< tirQpMilft^wa, U 
 
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 horn wo other given potuti uity h«y«^«j|jvi|» lauji. ^ , r , 
 «^^«3. T«ui«*!t«Hfhtmn|W?. .- *« 
 
 $3. To tritAct a given fimte right line. 
 
 
 I-.*.. » 
 
 '1 .rll 
 
 ^. To dividt* given right line into onjr number of enunl 
 
 «. A fcUnk book of gWon i»ii«nUude ie t« be mW<» that 
 each opening riieU contain thirteen lineer ^»^M<»» &•« -•«*» 
 
 tSiiieli^^^ 
 and cohmz Agtirea. 
 
 67. All the exterio^ anglei of any rectilineal fignre eqnal f«mr 
 €ighta^leajlofSief with the exceiie of every reentrant angl« 
 
 aibove two right an^e^^j^;,^7j|,. ^.., J. j^n^ :;■!»'%■■• -^^'^^ ' '■• 
 
 * 0A. A triaacle cannot have A reentrwit angk, « qnadrilaternl 
 mayXve oneT ^nd a figure of n lidei mutt We at least thre* 
 onUnary anglet. 
 
 60. The tnm of the anglet of ovtiy i^tctilineal figuif it,«q«al 
 tpjmevenimn4|«rpffig*«w»l(*«*- ^ . 
 
 7a If one aii^ of a triangle contain* 90° it it equal to the 
 •umoftheotliiertwOraiid iric«tw»t. ;^^^^^^^^ . :.n *. 
 
 ^rKiMM a^lo of a triiBf ie be greater than tfie mm of the 
 other iwiik iagveftter than a ngbt angle, and tit^ tierm. 
 
 1 78. If one angle of a triangle be leia than a right "ungie, it ia 
 Jm f ^ff jp t^ min of the other two angles. 
 
 f 71. IB Ml lio«5ilet Iriaogle the ttrtkJil «xi«riof mW m^r 
 4««li>lo of oUbar of the aiigiieeal the bawi. t^v* ff ' *^ 'ttr. ' 
 
 74, In an equilateral triiingto m^ etlerior angle i« double 
 
 ■ af^«th«r0f the interior,'^' •'»'^,<i^^:>^;J^2^^^^^ -J., ,_;,,,, 
 
 ,76. Determine the «»«iitijd« of the angleof a regiil^ peniar^ 
 
 gon,ite«tioiir««»«o»»«>^ i,;:.:\wt./^t{i \*..^u 
 
 V 7«. llrtat oondittona tr» neeeaniy, that nny pw^eukr, rtgu^ 
 Ur Umm nmj oonaiititte the elements of a pavement? . . ^ , 
 
 vilM^i 
 
 
 T^T^B^ '^I 
 
 ^^^•j^ 
 
 ' iSUAow^lMitbe t«rtmrif»|le 
 
 1 - ■ w ■j-.-x 
 
1-"^ 
 
 'f.i; 
 
 ■*wr«"- • 
 
 it si. I 
 
 ^1 
 
 
 
 
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 ■0 fiflMy' SMMC^ OK^MMMMf 
 
 '^ 80. Ob ^ AIni ii n>» Aii; ' tiM lUMetor of ^ ^ & 
 «qiMl to, crmtor or Im« tkniMlf Ikt |kiiif,l««oriltmM#M vfrtical 
 
 - -^ 81. Efott « perpondkalar to ili«'«trtihhf of 1' tiio ilihout 
 
 . ».iii'' f ♦ 
 
 83. Hio tfiafomfi «ra pwdMognm UMct toch othtl;; '^ 
 
 
 i 83. iriM«>|OMli«r *^iMUttcralfl| 
 
 U. If the oppoaite m<Im (iC€(|i»«lrilAtor»I fifon Mf •%«» <v 
 •Kh oUmt, Ubi lipiro ii* p«riW0iniafc*^ttvv. .. fuft^^l ^» ; : 
 
 " 86. I)r tho dia|onala of a qnadrflatcriJ biMCt itio icnrii; It ll» h 
 
 ^^86^ If th« opposite ingtei of « qtoiiiftiiifjto fptito^'l^^ ^^iii 
 to each other, the figure ia « pandlelognitn. 
 
 '8i. I^a righ^ attiKM parill«l6grAin, thiB 
 
 i... 4 
 
 'si! if the diagonal* of a parallelogram are equal to pna^.mr 
 {MTf it is a rectangle. 
 
 ' '' iltt: til geiiiirti, Ifin a qua4»4|fleiul ftWe, ^iWIpwiPSf 
 pertiea be catablbhed, the others may be dedoeetf, . ^ ^_^, ^ 
 
 •»^' ^li* Cthepwalleliaraof «iiWlM»T^< ' 
 
 1» 4. The equality of either pair of ojfpwatmndw.^ 
 
 Wl!* 
 
 ,H'J- f^f 
 
 Tho «amdi^ V iitlbr pair of OTi»«iita ati^ 
 
 - ^ », K>- ,3n»e hiawtipi^ of tNi aren by ^it^r di»gpffl;|^ ^ ^r 
 7 9o! These fen data co«Miiad in ^ iitJ>ttfpr.«tiB«flbra«lt 
 
 eomliii.ptiwaa.1 lo m!i!iii^.^^ ^fn ^^. Agyj^rf 
 propertiea, *ere wiU ariaa i*w» fc a<i i || i. ( i l l< lia» |iw'W i «<) U*" 
 tiMisres|pei>ting.w^,<jna^n^t<^ . L:-,o:fv-p. n-" .''./t^? 
 . 91.' The ri^ht line drawn ftom the vailM •! alliaBgIa Jliate- 
 
 ^ ting the ,bas<shisecjs the ara^.^^^-^_ ^^^^^^ 
 
 - 98. Wlil data are neceasary to «<|abUsh the eqnahty J" t»f » 
 
 • ;«'• 
 
 .-(-». 
 
 .iJ» 
 
 "'T 
 
 C/ ^ 
 
 equal; slMwrthattlM 
 
 ..'-. 
 
■p' r'i^^wvw"* 
 
 i. 
 
 i 
 
 • JV^ • 
 
 Nipni^Sm^ 
 
 *i 4iw«riNrifiMi|l« hit* ■• mmiKf 
 
 il 
 
 . . M. 11m Hot jotniUfr iIm poiati of biMction «r iMt pHM ofs 
 
 Vn<)ll^ A nvi^M t*tteiMM«rairiMtkaHroiiihiM t»ftll^iof 
 
 ^ "M. tilt tine lauiiiif Ui« poitita^f biMetibit oIt l^dlJEM of^« 
 trfiittSHi mt» ontiWtLiagU which MonefoorUiorUM fiv«iitriMi|ii. 
 
 ' m. Th« line* which iom the m^H polnft of lh« «hr«« lU^ 
 i# • irluflft <l^vi(l« the UTMOfle into foai^|Kiai4 p«rtf. 
 
 .Kll* 
 
 tidMr M c(|IIb| to hw the tbiid iide. 
 
 ibn bf tuli'ipiiif.iff 
 
 >*|dl. Tho aroa of a triuigle U eqnM U» «|W WCr^ 1*Hi *»•*« 
 )Mf t||o DorpeiKlioalar altitude. , , . v i • ; 'uk 
 
 1(J0. If Ibe four aides of a qaadrilateral figure be biiected, and 
 the fiddle poinU of each poir of conlerniibuouf eidee joiiied, the 
 joiniHc ^Ij^ ^ffl fonu a puroUelogram, wUoie ana ia equ«| to half 
 IJ^I ^ le pal^loiram. 
 
 *<^ )i^. The area' o? a irapi^t^^^W Wo^' W^ -^«| . 
 tfnal to half the bate into we laui of those paiayvl sides. 
 
 nkd pr twice the altittide. li -r'?''- 
 
 465. If a parallelogram and a triangle haveyAJnal altitudes, and 
 Um Vk^ ^ tb^^atiglb be double dkat of the ^araUelogram, tiiey 
 WilllMTcr'^iialKrew. ;■■ , .. ; . Mhcmm 
 
 r 109. Describe a square which d^ill have the same are* as • 
 giir«ii«<l^tM^l^aitd equiAtoguUr o^tagort. 
 
 107. Dotannino the aide of a sqiinre, which shall be ennal to 
 die sum of two others, whose sides are given. '^ 
 
 ^ iOB. iFaiklaiiclttliiie Mfho^Miaanlia tq^ ^ th^ difiP|K^co 
 of tj|V#9«iinii, whoee aidea ase giveK^> tuiD^^r^- -t^ti^i^i*^ i^ntn", 
 
 
 '■^. 
 
 
 ,f All 
 
 
 H^ >4«L>(llii Mi^Muwoi'ilie baao or>a>tri«nff|e m lept t)iaii» «)q<>M 
 iKliknliil tllfaiAo avni pf the iaqiMfOs of the akttfy aeoofduw 
 aa tbe vettieia angle is |ep than, eqnol to, or grentef thpn a ngUt 
 
 
 _ -V- 
 
 

 10 
 
 «f III* 
 
 >-^:. :■ 
 
 /^ 
 
 lMillMi,«^t#,9rff«iitttlMitttb»,fMB«f lit 
 
 : lill» DatenniM » •qaara w^th «luiJI b* •qual l» tiM MUn of 
 ftnx numlMir of aqtuurMrwIiOM sidct mt* fivts. ."^tiii "^t -Mtimn. 
 
 y* I13. Hm rootattcto «iiil«r ainr two li»M, ui|' <i fc twteg tte ree- 
 tMifl* ttMd«r «itiMr Mlli«ni, «ttd mlf th* «th«r, 1<» tfir«« tim^ th« 
 r«H3t«ugt« ttitdM «ither of tl^rin and a third of the other, to « limei 
 tbt fe«ltm»* irtldw;^!^ Of ?^«l*» •»«> •« •«* I*'^*^ -^ ^^• 
 
 11 
 
 umglo 
 
 14. Th« «|ii»re of tk* mmi of any twf ^aof fftqll 
 I rtttdor th4l tkn ubd •ithor of them. :^ / 
 
 under 
 differeueo. 
 
 115. Thoiqiim of the greeter of two line* eoadathe reotanglo 
 n ihoM Unee, together with the rectpigte lUMfer the greater aiid 
 
 ^'^'^ 116. The rectangle under the lutn of two lloea/ and ohe of 
 them eonab the iquare of that one, together with the rectangle 
 
 ' 117. Th«i%diif^Hiite^ 
 Iffi, together with the rectangle under the leM and diflWreii^t^^;/ 
 
 118. Tbe diflerence of the Mjuaree of two luwa ^^^ ^ 
 rectaiigle noder their aatn and diflercnco.% ■' ^l"?- j,^^/ , l-':%isr ' 
 
 119. The diflference between the rectangle under twoiinea, 
 and' the square of one of thom i« the rectangle under thatoae and 
 their difference. n 
 
 ISO. The difference of the pquarea of two Unflf,. ccKOMda the 
 ilqflare df their difference by twice the recUngto imflfjy.ghj m^md 
 diffeienee. » '^ 
 
 1S3. Half the aquare of « Une is 4enblo limi$liu0itl00 
 
 n- 
 
 . Ir" 
 
 
 iv^ .■' 
 
 ■V 
 
 m''i 
 
 ifQ 
 
 'H. 
 
 A 
 
 19X Tboaqiianofl^niiBofanyMro •qvalathesua 
 
 oftbeir aquarea, together with twice the rectangle under them. > 
 
 194. The aqnar* of aUnooqnali IhtMintof theaqliaMaof all 
 tM v«rts» Wgnlbor with twie^ the rectaii|lo nudor ortty itoHUMl ^ 
 
 .Ittk The arithmetio mean between anr two linea, ia hap* Hm 
 ferento of Ibo oxtrenrat. . . 
 
 ••S*-! .► 
 
 I < ' . «' 
 
 K'^'.ro 'j.fjly 'f\t .^i%- -"U .fe^'yiwKii •-• 
 
 iirii'rniiii1iiir^-'-"'T'^-^^-^ 
 
 h -A-iU I »i 
 
 "jStM&aLjbl. 
 
 
 Ji^ . ki • f^MiitfitJii^i 
 
-^STW 
 
 
 i''r»,-f'" 
 
 -™<f. 
 
 n-, 
 
 under ilit 
 
 u 
 
 \ 
 
 '••■.«■ 
 
 '\ 
 
 
 '.»V 
 
 
 •quart of hdlf llieir di<r«r«Rce, equaU Um M|aar« M lairlMif M|M|. 
 
 u MB. TiM -laM* of lb« ium .f two limm •^<mW^ r«etwnt« 
 nnder Uitin, tog«th«r with tba pquare of half lh«ir 4a mt ^ m »* 
 
 .'k M. Tke r«oUngl« •n4er tJwi muu jiikI difl«r«k«« »f IWf lln#«, > 
 
 — m%e wctonfl* nndm the parte of • litte » ^ i»»*U<t 
 wh«n ^e parts are equal. 
 
 ^^ i«. The ^Sdt the aqnaree of the part* into which a line ie 
 divi<fed i« a minimum, wheu th« line ia hiaected and equal- the 
 
 «uartofh«iftfH»iin«;:::-'' .-, ''/,. r „,., ,A ;.;.^., 
 
 {tl •#*«•) <^ 
 
 ■V 
 
 
 138. Of all roctanflea having tlie tame perimeter, the Miouri 
 contain* the groateat area. 
 
 »■• 
 
 i; 
 
 '' ''.'^' 
 
 ■ - '*'i»,- 
 
 ■~M^- 
 
 i 
 
 183. Of all reetanglec equal in aroi; the aqiioht la eotitilltfi 
 hy tho least perimeter^ • 
 
 134. If a perpendicukr h» drawn from th* rerlox of a vwniw 
 t© 1h* haae, the reotfen^ under the anni and difference of the «idea 
 i^tiaJa the rectangle nnder the sura and dilferenoe of the segments. 
 
 'ids. The difference between the squares of the sides of 4 
 triangle eqnals twice the reetangle nnder ihebaaa and the dManoe 
 of the perpendicular from the middle point, i ", ' ,,' 
 
 '■%- 136 If a line be drawn IVom^e vertex oraiii l*Mi««ba W- 
 
 \ ilAloto the base or its production, the diflTerenee between *« 
 
 nqoarea of this line and the side of the tritngle is the rectaQglo 
 
 under'tbesegraenta of tlie baae*;4fe;v ^:j..^'^ . \^. ■ ^H-^U:.'^ - ,, 
 
 137, The square of the aura of two lines, the siim of thtll 
 sonarea and the square of their difference are lu arithmetic pro- 
 
 S aaioii, the common HiffsiMoa ^og twiofl Oie if^^iiflt ¥»4«r 
 
 V & 138. The square of the sum of two Hnee eonak iMr m«l 
 :--'-.m* r»otan|de under therit, together with the 
 
 .,'J;>' 
 
 :m.;Hi 
 
 , 136. iSie iam of the aquirea of anir two A 
 
 
 reaoranyr 
 itwie<the 
 
 ^of liaf'tfwr I M P , ind twie< the n|nare <^i 
 
 iheir 
 
 tbt nuaitttilM themMlKr ta. 
 
 / 
 
 4. 
 
 .''# 
 

 j^rS ^ •y * ^y yyw-ff ■■■ * 
 
 ^',t'"- 
 
 t* 
 
 Wft 
 
 «♦• 
 
 !■< ■! i|i,Hiiifaiton)iigiin" i~ 
 
 1^ Tk«MIIB9f <lMiUM. 
 
 4 TM ■•& ^ *'** a^njir** of tk« ■m« 
 
 iP^^ftr' 
 
 ' .^•*<« lit.' IT « IM Ini tfOt Itt ««tfiwi« Mi#nM«ii ratio,** 
 
 i^ 1^ On lh« Mina Mppotition. V li F«#f IMfflli*rr 
 l«t*»y tfi« #▼«!< Ujkjj Oi* gwattr Mid Utmt pwt, ** T f£l ^ 
 
 144. To divkl. a tivan rif ht Iim Into two mi^ ^•M^. W «w 
 rttenfle contatnad by the whole line and one of th#|MiU iMIl IM 
 
 MiMtSHM....!! tioMa Um aqutif of *a otliar part. V> i^( 
 
 146. If a I'ma ba drawn f^voi the anjnilar point of a trwof U 
 ••ilK polntorMMCtion of tliaopp<»aite*la.tha««o#tli;agafeji 
 
 of the other aidea equals twice ihe aum of tha aqnarea. of Ife^ |^ 
 
 - - - #...,. .♦•■* ' 
 
 •I' 14l.^Tk»'iiiii«f tha aqnaraaof thaaMaaofi liimllii™ 
 
 aactof.and half tb« 
 
 eou 
 
 iiii i f»jt 
 
 il|l«it 
 
 nda ami fi«»r 
 
 r'tfuatir Ik arnn of th« a^naraa of the djB|onMa mmI 
 ^ ai}i|(ire of die line joininf their pointa of bueetio9« 
 
 m-ffhrn nmi of the aivavaaAf the aidea oC,iif<lf«Ua|afr«a 
 equaia that of the diag0iMlt.<$!t)iif m, '*"tT itnwr vu»tr.')4tM< A| ' : ''^• 
 
 , Ji«. U t|»a aum of Ao •quarea of the ridea of »»;*iJ2«;J ' 
 «giil9 o4m¥ M i^w of *• aqnaiea of tha ^i^|^J|^l^^;^f«i(f^ 
 
 ' 149. If from the three anglca of 4 tfiangla llii«aho'*iWt» t« 
 
 IMK Ojl«to 11^^ *• aiUB of flio ■ilJii^J'W ii» 
 
 pM«»> aqoala three timea the aam of the aquarea of the mmmm 
 
 ^.f».k«« ih^lNfiiM iiMdIo poiM of aioiift liiibt Ihi^Jii OM«i» 
 
 of the diatooMA of 
 tbon|htfiAO> » ft 
 
 " *•, 
 
 
 V 
 
 -•^ 
 
 
 
 Mil 
 
^T 
 
 ,j$Z^'^ 
 
 
 
 V • 
 
 
 1 .« 
 
 . . 1 
 
 
 Im 
 
 
 ir 
 
 r 
 
 
 » if,'. 
 
 ^^♦.• 
 
 • .-. ^ !*• 
 
 »» 
 
 
 
 > ■ #■',■ 
 
 1 
 
 ■< , * 
 
 tw 
 
 . ■:, 
 
 r«4 
 
 
 . ,' ■ . if 
 
 tw«33w. wbkk aw not pa^UI, •ii4{t#ta«'<WH«M«||i *«•*•« 
 * Itt. Of ill •iwilht Hnw which c«n h« attwii iV«» wr» ,■»'•• 
 
 . SZpf%?Jiwd will b* the i,Mi whwi «Hw,-n^ ^.'^'^ 
 
 ^1^ Ui* uuif cut •* Ihe pmat oi concoartt. ^t^...^ y^...-^' ^^^^ ^u '-^1;^' > 
 
 .a.-- 
 
 r-t- 
 
 4 r 
 
 •t*-, 
 
 '^•<; • 
 
 iBfl. If • cif«l« ba dmribfd on Uw rad»u. of •««*•» £f|i» 
 wiy unifht lint drawn from Ui« point wh«r« tbcy w«« to u^^fg 
 tor droomAiropOP. ;» bi««cU»a by Uio intanor oiio. 
 
 187. If two circlw out aiich othor and ftrom aithur point of 
 intemietloa. dbmotaia b« drawn ; tha cxtreontma of rt»*««^«V;- 
 So^tS oXrpolnIi of intamctinn .hail bo in tha tamo atraifht 
 
 r^f 166. I)rawaatraIfhtlHi€ii«ilAtl*flti»Atwi»fb««#ll«Mi 
 *»^ IM. If from a point in tho cirennifarance of a ci*c*a any 
 ibiinb«f of ehof^M4»M»%l*-»<»«^»f *•« 9^mfMo( UtmMm 
 wtil b« a ciida. ^ ';,,|^-' ■'' .''*' •' ^'^'-^ •••■^ ^:«''i»tii*'^ .;*•.//: -»«.^' 
 1^ leO. Pmfina fc^thmaik,. faomatfic, and harmohic 
 
 *. m. If from an? two pointa in tha ilrenmfaran** bttiilmi, 
 . dMfn^4»WBtwo'atraiflit lino., to a pokjl in • •^••^••Jj;; 
 
 ofeovteet • ■ ■'* ■'n^^*''^^;:-' ■■;■'■:, ^.it^';''»2 " *''-^ , ' 
 
 it) Itt. if ft'nw any point witkin an •qnitM^fnl triangle pnrpan- 
 
 akmhui b« dmwn to tha .daa. Aay ar. \««;£;«' •J-^L^ * '•'^ 
 
 p«M^«l«r dtawB from any of tha an^lea to the oppoaite Ma. 
 
 .JM 
 
 
 ** 
 
 beioiaiti; H^e wn^ ^ formed wiU be one fourth of the |pven 
 
 , ■ 164. Of an toriwnl^,lipo| the ^^i^ZJZJt^^ 
 ttke peMbli, the ieoileelea tiluigle haa iM fciirf pertaieief . 
 
 uMniikf 
 
 «^U.".V4S|- •-i-U. 
 
 J li-,'(i » 
 
 eqildpttli. 
 
 ^^^mflg^-^^p" ^^^^^ 
 
 lip. To trieeet • trit|#i IfOfB •!«!•• P<*«* '»**«■ ^ 
 

 MO. T« Mmm ■ MffdfolAgffMi If tlfet 
 
 ^^tif'.*S »-'^ 
 
 ikiM of •» Mmilauinil Ml l^ti(*Mf«l«r |M*(iI9n 
 
 170. IfllM 
 Iw pro<lucii4l to mrmi 
 
 171. If tb« lidM of an •q«tfat«r«I'atidl «4^kiicul«r li«iifii 
 
 178 Ganfrall/. if atery pair oT alMriiata liiii V if^imfM 
 Of lira b« pnMlacwl to m««t tlia aiim of tiia ansfaa m nmnaa, w 
 }iit— « Hf ht anf laa. « bailif <ha ntHnbar of tba aidat. 
 
 175. *Tiia arwi of ai^ two paraOatofriBM di 
 two iwiaa of a triaof la, ia aqiial to tliii of a partllalognm on th«i 
 biaa wbow aiaa ia aqnal and par^H^T lo tha 1in«i driwn (Wnn l^o 
 vartex of tha triaofla to the intaraMtion of tlia two iidaa of 1||| 
 iNlBor paraHologviaM prodaead to naat, 
 
 ^« : 74. Tha parinatar of oaiM»oa«loa triaiula ia ffiwaiar tbtntho 
 fwriniatar of m rattuifvlar pnraOalocraw, whkb la of tba aoMt aj- 
 titttdo with, and cqaalto, Iha given triangle. y^^ f >'|i;<«/, 
 
 170. Doitrmina a point In a ttao tiran in M ^^^H <» ^W** 
 Unas drawn from two given poilMa, dUiy>luiv«i4lM^pP0MNiPP^ 
 enCf poaMble. .,^.a,j.uA:rAu wnw; ' ^'^i '■.»>- 
 
 ' ttOw T» 4kM§ mgmm ifcH Mil lu l ■4Wo audi pmla* teib4 
 tiywto of tba otJiliairbo oqnal i&^ihn lao t ai ^ i OrfM^H hf ^ 
 other and a givoa line. ^ , ■ . j ' ' > 
 
 177. lr« Oo«;ribo Mil l i i i itf' i i iii it e npmtik #«i*Mlt 
 
 178. To i^ijka^m^y^^ •v^A pS^ 
 
 9lilM#iaii|l0t 'I' -itl^t#-'a^>'t '<v '!i H^rl '\' 
 
 '^'^ 11^. Hiving given th« aur*r«ne« boWetn tba dUuiilif|r.^ 
 aide of a aqui^re. to doaertbe the aqnare. r . . 
 
 1^ T» diridi • ckA ln^» w M«»l^^ 
 
 ' ttil; Itl My <|Mdi<lMeral figare I«i4'i0.6^ i 4fiM|^« th^ 
 »pp1iio Mm ■>» fnl 10 half ftp petknior. ' 
 
 ^ "f|fli:fil'^! llNJiiilf l-OffaajN b»;i«wHbodii» ^di>oli« tho. 
 iiMi£o^ibMiMr«Ei^« IkiM^li- OfWl- t» ili iliiiilOiiiil>0. 
 a^Mie dMTibod npoA'Ao Mdiiif. ^iL^^-k^ ^V^^i.j-^^I^^V - 
 
 • ';»- 
 
 
 
 •Jf 
 
 V«^'-' 
 

 •' » » f 
 
 ■^^^i^Si^- 
 
 *#' 
 
 •f t eIrtU. 
 
 •i*' 
 
 11 
 
 comb. 
 jiiWa, Or«tt tvfanglc* OB tiM wm^lMM lad lMlw0«n tli« mom 
 
 191 If •« •quiUlurtl triancl« *»« inacribcd in « elwfe, WW 
 ihroDfli'riM miuoLr poinu. •iiuih«r b#«k ffittm i nn i wd , to ilftoraiuM 
 IJht mitt wliidi tlMjr Mar U> •■ck <MlM»iffi 
 
 -*«»»Mf ,'(. , til 
 
 ** IM lA^ns tfUofl*. tf n«fp«iidicul*fi b«dfiwii from lh« 
 
 •iiflOT, to Um oppoMia •idt* ; Uwy will aU matt hi ft point. ^ , 
 
 ]g$i GiTtn 004 infto* • tid* ftdiftOlili to it and th« dif^iwmct 
 
 il*D|^ two iklfMo CQdttnict Oio tfllHlo- ip« .>*n^ ^..4.^ 
 
 . IM. Oivw ono anf l«. a uda oppoaita to it and tha dMip^ 
 
 •ith$ oCliar two aidaa, to conauuct tha ti^aitgla. 
 
 tiWk OWoii om angle ft aido opp«iiC» lo< UfMd l|»*«i|| ^ 
 tbodbiitwo iMoa, to contract tha iffioHt*' ^" nMn/i hh^^-' 
 
 M. Gi^an tha Tartical angla tl^o tino iiiafctinc th« biM a^^ 
 Iba anglo wkich iko blaooting lino inakaa with tha baae, to coMtfucI 
 
 1*1 Sam. ^^ E miifiii^y^^i^hmi'^fM 
 
 118 Qireatiio ▼•rikol aiifla, tba diffarancaof tho.two iidoo^ 
 contfthihu U and tlM difkrenco of th« poimanta of tha baao mado 
 hf ft porpMidiooUur from tko vaitax, to eonatnict tha triftiiila. 
 
 lie. Ghran tho ▼oftiridftnila and tha radU oT tho * 
 and ciftwawcrilbiag ciwlaa, to coafttract the tmntlo. 
 
 •Mm 
 
 MO. What 
 twolnftB|)aaf 
 
 dote an ncooaaary to- aatahUah tho aiailitiido of 
 
 
 101. Ininjr 
 a«m oC tbt^f^Mroi 
 
 IftMWiul, if mo opppaitt aidaabo hia o ct a d , tto 
 ^MTSdbTM^ hiJt£raid«t, togctlMr with So^ 
 
»P%1 
 
 » 'J 
 
 
 
 
 
 
 ' 
 
 >v MS. T^ MM mi 1km JisMaafa of « t>»pMiui«^|| ImkiImA 
 
 '■>■ 
 ■%'« 
 
 ■♦ •(» 
 
 wpevw Of UM mm of a trep«dium atul m r»(k>, to |M ,inift 
 
 •IttM. 
 
 wiM«tt(o6ro^ 
 
 «io^Miw ocnte MiiiM o 
 
 ^ fW . If •quaroi Im) 
 
 ^ 
 
 •»^,>M 
 
 
 from thoMUiM 
 
 •I 
 
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 '^"il-f»?^^^^^^^v '^^mrm^'-' 
 
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