id sid tid token lemma pos A47183 1 1 A a DT A47183 1 2 supplement supplement NN A47183 1 3 to to IN A47183 1 4 a a DT A47183 1 5 late late JJ A47183 1 6 treatise treatise NN A47183 1 7 , , , A47183 1 8 called call VBD A47183 1 9 An an DT A47183 1 10 essay essay NN A47183 1 11 for for IN A47183 1 12 the the DT A47183 1 13 discovery discovery NN A47183 1 14 of of IN A47183 1 15 some some DT A47183 1 16 new new JJ A47183 1 17 geometrical geometrical JJ A47183 1 18 problems problem NNS A47183 1 19 concerning concern VBG A47183 1 20 angular angular JJ A47183 1 21 sections section NNS A47183 1 22 , , , A47183 1 23 resolving resolve VBG A47183 1 24 what what WP A47183 1 25 was be VBD A47183 1 26 there there RB A47183 1 27 problematically problematically RB A47183 1 28 proposed propose VBN A47183 1 29 ; ; : A47183 1 30 and and CC A47183 1 31 with with IN A47183 1 32 some some DT A47183 1 33 rectification rectification NN A47183 1 34 made make VBN A47183 1 35 in in IN A47183 1 36 the the DT A47183 1 37 former former JJ A47183 1 38 essay essay NN A47183 1 39 , , , A47183 1 40 showing show VBG A47183 1 41 an an DT A47183 1 42 easie easie NN A47183 1 43 method method NN A47183 1 44 truly truly RB A47183 1 45 geometrical geometrical JJ A47183 1 46 , , , A47183 1 47 without without IN A47183 1 48 any any DT A47183 1 49 conick conick NN A47183 1 50 section section NN A47183 1 51 , , , A47183 1 52 or or CC A47183 1 53 cubick cubick NN A47183 1 54 æquation æquation NN A47183 1 55 , , , A47183 1 56 to to TO A47183 1 57 sect sect VB A47183 1 58 any any DT A47183 1 59 angle angle NN A47183 1 60 or or CC A47183 1 61 arch arch NN A47183 1 62 of of IN A47183 1 63 a a DT A47183 1 64 circle circle NN A47183 1 65 into into IN A47183 1 66 3 3 CD A47183 1 67 . . . A47183 2 1 5 5 CD A47183 2 2 . . . A47183 3 1 7 7 LS A47183 3 2 . . . A47183 3 3 or or CC A47183 3 4 any any DT A47183 3 5 other other JJ A47183 3 6 uneven uneven JJ A47183 3 7 number number NN A47183 3 8 of of IN A47183 3 9 equal equal JJ A47183 3 10 parts part NNS A47183 3 11 . . . A47183 4 1 By by IN A47183 4 2 G. G. NNP A47183 4 3 K. K. NNP A47183 4 4 Keith Keith NNP A47183 4 5 , , , A47183 4 6 George George NNP A47183 4 7 , , , A47183 4 8 1639?-1716 1639?-1716 CD A47183 4 9 . . . A47183 5 1 1697 1697 CD A47183 5 2 Approx Approx NNP A47183 5 3 . . . A47183 6 1 13 13 CD A47183 6 2 KB kb NN A47183 6 3 of of IN A47183 6 4 XML xml NN A47183 6 5 - - HYPH A47183 6 6 encoded encode VBN A47183 6 7 text text NN A47183 6 8 transcribed transcribed NNP A47183 6 9 from from IN A47183 6 10 4 4 CD A47183 6 11 1-bit 1-bit CD A47183 6 12 group group NN A47183 6 13 - - HYPH A47183 6 14 IV IV NNP A47183 6 15 TIFF TIFF NNP A47183 6 16 page page NN A47183 6 17 images image NNS A47183 6 18 . . . A47183 7 1 Text Text NNP A47183 7 2 Creation Creation NNP A47183 7 3 Partnership Partnership NNP A47183 7 4 , , , A47183 7 5 Ann Ann NNP A47183 7 6 Arbor Arbor NNP A47183 7 7 , , , A47183 7 8 MI MI NNP A47183 7 9 ; ; : A47183 7 10 Oxford Oxford NNP A47183 7 11 ( ( -LRB- A47183 7 12 UK UK NNP A47183 7 13 ) ) -RRB- A47183 7 14 : : : A47183 7 15 2006 2006 CD A47183 7 16 - - SYM A47183 7 17 06 06 CD A47183 7 18 ( ( -LRB- A47183 7 19 EEBO eebo NN A47183 7 20 - - HYPH A47183 7 21 TCP TCP NNP A47183 7 22 Phase Phase NNP A47183 7 23 1 1 CD A47183 7 24 ) ) -RRB- A47183 7 25 . . . A47183 8 1 A47183 A47183 NNP A47183 8 2 Wing Wing NNP A47183 8 3 K216A K216A NNP A47183 8 4 ESTC ESTC NNP A47183 8 5 R216625 R216625 NNP A47183 8 6 99828350 99828350 CD A47183 8 7 99828350 99828350 CD A47183 8 8 32777 32777 CD A47183 8 9 This this DT A47183 8 10 keyboarded keyboarded JJ A47183 8 11 and and CC A47183 8 12 encoded encode VBD A47183 8 13 edition edition NN A47183 8 14 of of IN A47183 8 15 the the DT A47183 8 16 work work NN A47183 8 17 described describe VBN A47183 8 18 above above RB A47183 8 19 is be VBZ A47183 8 20 co co VBN A47183 8 21 - - VBN A47183 8 22 owned own VBN A47183 8 23 by by IN A47183 8 24 the the DT A47183 8 25 institutions institution NNS A47183 8 26 providing provide VBG A47183 8 27 financial financial JJ A47183 8 28 support support NN A47183 8 29 to to IN A47183 8 30 the the DT A47183 8 31 Early early JJ A47183 8 32 English English NNP A47183 8 33 Books Books NNPS A47183 8 34 Online Online NNP A47183 8 35 Text Text NNP A47183 8 36 Creation Creation NNP A47183 8 37 Partnership Partnership NNP A47183 8 38 . . . A47183 9 1 This this DT A47183 9 2 Phase Phase NNP A47183 9 3 I -PRON- PRP A47183 9 4 text text NN A47183 9 5 is be VBZ A47183 9 6 available available JJ A47183 9 7 for for IN A47183 9 8 reuse reuse NN A47183 9 9 , , , A47183 9 10 according accord VBG A47183 9 11 to to IN A47183 9 12 the the DT A47183 9 13 terms term NNS A47183 9 14 of of IN A47183 9 15 Creative Creative NNP A47183 9 16 Commons Commons NNPS A47183 9 17 0 0 CD A47183 9 18 1.0 1.0 CD A47183 9 19 Universal Universal NNP A47183 9 20 . . . A47183 10 1 The the DT A47183 10 2 text text NN A47183 10 3 can can MD A47183 10 4 be be VB A47183 10 5 copied copy VBN A47183 10 6 , , , A47183 10 7 modified modify VBN A47183 10 8 , , , A47183 10 9 distributed distribute VBN A47183 10 10 and and CC A47183 10 11 performed perform VBN A47183 10 12 , , , A47183 10 13 even even RB A47183 10 14 for for IN A47183 10 15 commercial commercial JJ A47183 10 16 purposes purpose NNS A47183 10 17 , , , A47183 10 18 all all DT A47183 10 19 without without IN A47183 10 20 asking ask VBG A47183 10 21 permission permission NN A47183 10 22 . . . A47183 11 1 Early early JJ A47183 11 2 English english JJ A47183 11 3 books book NNS A47183 11 4 online online RB A47183 11 5 . . . A47183 12 1 ( ( -LRB- A47183 12 2 EEBO eebo NN A47183 12 3 - - HYPH A47183 12 4 TCP TCP NNP A47183 12 5 ; ; : A47183 12 6 phase phase NN A47183 12 7 1 1 CD A47183 12 8 , , , A47183 12 9 no no UH A47183 12 10 . . . A47183 13 1 A47183 A47183 NNP A47183 13 2 ) ) -RRB- A47183 13 3 Transcribed Transcribed NNP A47183 13 4 from from IN A47183 13 5 : : : A47183 13 6 ( ( -LRB- A47183 13 7 Early early JJ A47183 13 8 English english JJ A47183 13 9 Books book NNS A47183 13 10 Online online RB A47183 13 11 ; ; , A47183 13 12 image image NN A47183 13 13 set set NN A47183 13 14 32777 32777 CD A47183 13 15 ) ) -RRB- A47183 13 16 Images image NNS A47183 13 17 scanned scan VBN A47183 13 18 from from IN A47183 13 19 microfilm microfilm NN A47183 13 20 : : : A47183 13 21 ( ( -LRB- A47183 13 22 Early early JJ A47183 13 23 English english JJ A47183 13 24 books book NNS A47183 13 25 , , , A47183 13 26 1641 1641 CD A47183 13 27 - - SYM A47183 13 28 1700 1700 CD A47183 13 29 ; ; : A47183 13 30 1951:14 1951:14 LS A47183 13 31 ) ) -RRB- A47183 13 32 A a DT A47183 13 33 supplement supplement NN A47183 13 34 to to IN A47183 13 35 a a DT A47183 13 36 late late JJ A47183 13 37 treatise treatise NN A47183 13 38 , , , A47183 13 39 called call VBD A47183 13 40 An an DT A47183 13 41 essay essay NN A47183 13 42 for for IN A47183 13 43 the the DT A47183 13 44 discovery discovery NN A47183 13 45 of of IN A47183 13 46 some some DT A47183 13 47 new new JJ A47183 13 48 geometrical geometrical JJ A47183 13 49 problems problem NNS A47183 13 50 concerning concern VBG A47183 13 51 angular angular JJ A47183 13 52 sections section NNS A47183 13 53 , , , A47183 13 54 resolving resolve VBG A47183 13 55 what what WP A47183 13 56 was be VBD A47183 13 57 there there RB A47183 13 58 problematically problematically RB A47183 13 59 proposed propose VBN A47183 13 60 ; ; : A47183 13 61 and and CC A47183 13 62 with with IN A47183 13 63 some some DT A47183 13 64 rectification rectification NN A47183 13 65 made make VBN A47183 13 66 in in IN A47183 13 67 the the DT A47183 13 68 former former JJ A47183 13 69 essay essay NN A47183 13 70 , , , A47183 13 71 showing show VBG A47183 13 72 an an DT A47183 13 73 easie easie NN A47183 13 74 method method NN A47183 13 75 truly truly RB A47183 13 76 geometrical geometrical JJ A47183 13 77 , , , A47183 13 78 without without IN A47183 13 79 any any DT A47183 13 80 conick conick NN A47183 13 81 section section NN A47183 13 82 , , , A47183 13 83 or or CC A47183 13 84 cubick cubick NN A47183 13 85 æquation æquation NN A47183 13 86 , , , A47183 13 87 to to TO A47183 13 88 sect sect VB A47183 13 89 any any DT A47183 13 90 angle angle NN A47183 13 91 or or CC A47183 13 92 arch arch NN A47183 13 93 of of IN A47183 13 94 a a DT A47183 13 95 circle circle NN A47183 13 96 into into IN A47183 13 97 3 3 CD A47183 13 98 . . . A47183 14 1 5 5 CD A47183 14 2 . . . A47183 15 1 7 7 LS A47183 15 2 . . . A47183 15 3 or or CC A47183 15 4 any any DT A47183 15 5 other other JJ A47183 15 6 uneven uneven JJ A47183 15 7 number number NN A47183 15 8 of of IN A47183 15 9 equal equal JJ A47183 15 10 parts part NNS A47183 15 11 . . . A47183 16 1 By by IN A47183 16 2 G. G. NNP A47183 16 3 K. K. NNP A47183 16 4 Keith Keith NNP A47183 16 5 , , , A47183 16 6 George George NNP A47183 16 7 , , , A47183 16 8 1639?-1716 1639?-1716 CD A47183 16 9 . . . A47183 17 1 7 7 LS A47183 17 2 , , , A47183 17 3 [ [ -LRB- A47183 17 4 1 1 CD A47183 17 5 ] ] -RRB- A47183 17 6 p. p. NN A47183 17 7 printed print VBN A47183 17 8 for for IN A47183 17 9 the the DT A47183 17 10 author author NN A47183 17 11 , , , A47183 17 12 and and CC A47183 17 13 are be VBP A47183 17 14 to to TO A47183 17 15 be be VB A47183 17 16 had have VBN A47183 17 17 at at IN A47183 17 18 the the DT A47183 17 19 Three Three NNP A47183 17 20 Pigeons Pigeons NNPS A47183 17 21 over over RB A47183 17 22 against against IN A47183 17 23 the the DT A47183 17 24 Exchange Exchange NNP A47183 17 25 , , , A47183 17 26 and and CC A47183 17 27 at at IN A47183 17 28 his -PRON- PRP$ A47183 17 29 House House NNP A47183 17 30 in in IN A47183 17 31 Pudding Pudding NNP A47183 17 32 - - HYPH A47183 17 33 lane lane NNP A47183 17 34 , , , A47183 17 35 at at IN A47183 17 36 the the DT A47183 17 37 sign sign NN A47183 17 38 of of IN A47183 17 39 the the DT A47183 17 40 Golden Golden NNP A47183 17 41 Ball Ball NNP A47183 17 42 , , , A47183 17 43 where where WRB A47183 17 44 he -PRON- PRP A47183 17 45 teacheth teacheth VBZ A47183 17 46 the the DT A47183 17 47 mathematical mathematical JJ A47183 17 48 arts art NNS A47183 17 49 , , , A47183 17 50 [ [ -LRB- A47183 17 51 London London NNP A47183 17 52 : : : A47183 17 53 [ [ -LRB- A47183 17 54 1697 1697 CD A47183 17 55 ? ? . A47183 17 56 ] ] -RRB- A47183 17 57 ] ] -RRB- A47183 18 1 G.K. G.K. NNP A47183 18 2 = = SYM A47183 18 3 George George NNP A47183 18 4 Keith Keith NNP A47183 18 5 . . . A47183 19 1 Caption caption NN A47183 19 2 title title NN A47183 19 3 . . . A47183 20 1 Imprint imprint VB A47183 20 2 from from IN A47183 20 3 colophon colophon NN A47183 20 4 ; ; : A47183 20 5 publication publication NN A47183 20 6 date date NN A47183 20 7 conjectured conjecture VBN A47183 20 8 by by IN A47183 20 9 Wing wing NN A47183 20 10 . . . A47183 21 1 Reproduction reproduction NN A47183 21 2 of of IN A47183 21 3 the the DT A47183 21 4 original original NN A47183 21 5 in in IN A47183 21 6 the the DT A47183 21 7 British British NNP A47183 21 8 Library Library NNP A47183 21 9 . . . A47183 22 1 Created create VBN A47183 22 2 by by IN A47183 22 3 converting convert VBG A47183 22 4 TCP TCP NNP A47183 22 5 files file NNS A47183 22 6 to to IN A47183 22 7 TEI TEI NNP A47183 22 8 P5 P5 NNP A47183 22 9 using use VBG A47183 22 10 tcp2tei.xsl tcp2tei.xsl NN A47183 22 11 , , , A47183 22 12 TEI TEI NNP A47183 22 13 @ @ CC A47183 22 14 Oxford Oxford NNP A47183 22 15 . . . A47183 23 1 Re Re NNS A47183 23 2 - - VBN A47183 23 3 processed process VBN A47183 23 4 by by IN A47183 23 5 University University NNP A47183 23 6 of of IN A47183 23 7 Nebraska Nebraska NNP A47183 23 8 - - HYPH A47183 23 9 Lincoln Lincoln NNP A47183 23 10 and and CC A47183 23 11 Northwestern Northwestern NNP A47183 23 12 , , , A47183 23 13 with with IN A47183 23 14 changes change NNS A47183 23 15 to to TO A47183 23 16 facilitate facilitate VB A47183 23 17 morpho morpho NN A47183 23 18 - - HYPH A47183 23 19 syntactic syntactic JJ A47183 23 20 tagging tagging NN A47183 23 21 . . . A47183 24 1 Gap Gap NNP A47183 24 2 elements element NNS A47183 24 3 of of IN A47183 24 4 known know VBN A47183 24 5 extent extent NN A47183 24 6 have have VBP A47183 24 7 been be VBN A47183 24 8 transformed transform VBN A47183 24 9 into into IN A47183 24 10 placeholder placeholder NN A47183 24 11 characters character NNS A47183 24 12 or or CC A47183 24 13 elements element NNS A47183 24 14 to to TO A47183 24 15 simplify simplify VB A47183 24 16 the the DT A47183 24 17 filling filling NN A47183 24 18 in in RP A47183 24 19 of of IN A47183 24 20 gaps gap NNS A47183 24 21 by by IN A47183 24 22 user user NN A47183 24 23 contributors contributor NNS A47183 24 24 . . . A47183 25 1 EEBO EEBO NNP A47183 25 2 - - HYPH A47183 25 3 TCP TCP NNP A47183 25 4 is be VBZ A47183 25 5 a a DT A47183 25 6 partnership partnership NN A47183 25 7 between between IN A47183 25 8 the the DT A47183 25 9 Universities Universities NNPS A47183 25 10 of of IN A47183 25 11 Michigan Michigan NNP A47183 25 12 and and CC A47183 25 13 Oxford Oxford NNP A47183 25 14 and and CC A47183 25 15 the the DT A47183 25 16 publisher publisher NN A47183 25 17 ProQuest ProQuest NNP A47183 25 18 to to TO A47183 25 19 create create VB A47183 25 20 accurately accurately RB A47183 25 21 transcribed transcribe VBN A47183 25 22 and and CC A47183 25 23 encoded encode VBN A47183 25 24 texts text NNS A47183 25 25 based base VBN A47183 25 26 on on IN A47183 25 27 the the DT A47183 25 28 image image NN A47183 25 29 sets set NNS A47183 25 30 published publish VBN A47183 25 31 by by IN A47183 25 32 ProQuest ProQuest NNP A47183 25 33 via via IN A47183 25 34 their -PRON- PRP$ A47183 25 35 Early early JJ A47183 25 36 English english JJ A47183 25 37 Books book NNS A47183 25 38 Online Online NNP A47183 25 39 ( ( -LRB- A47183 25 40 EEBO EEBO NNP A47183 25 41 ) ) -RRB- A47183 25 42 database database NN A47183 25 43 ( ( -LRB- A47183 25 44 http://eebo.chadwyck.com http://eebo.chadwyck.com ADD A47183 25 45 ) ) -RRB- A47183 25 46 . . . A47183 26 1 The the DT A47183 26 2 general general JJ A47183 26 3 aim aim NN A47183 26 4 of of IN A47183 26 5 EEBO eebo NN A47183 26 6 - - HYPH A47183 26 7 TCP TCP NNP A47183 26 8 is be VBZ A47183 26 9 to to TO A47183 26 10 encode encode VB A47183 26 11 one one CD A47183 26 12 copy copy NN A47183 26 13 ( ( -LRB- A47183 26 14 usually usually RB A47183 26 15 the the DT A47183 26 16 first first JJ A47183 26 17 edition edition NN A47183 26 18 ) ) -RRB- A47183 26 19 of of IN A47183 26 20 every every DT A47183 26 21 monographic monographic JJ A47183 26 22 English English NNP A47183 26 23 - - HYPH A47183 26 24 language language NN A47183 26 25 title title NN A47183 26 26 published publish VBN A47183 26 27 between between IN A47183 26 28 1473 1473 CD A47183 26 29 and and CC A47183 26 30 1700 1700 CD A47183 26 31 available available JJ A47183 26 32 in in IN A47183 26 33 EEBO EEBO NNP A47183 26 34 . . . A47183 27 1 EEBO EEBO NNP A47183 27 2 - - HYPH A47183 27 3 TCP TCP NNP A47183 27 4 aimed aim VBN A47183 27 5 to to TO A47183 27 6 produce produce VB A47183 27 7 large large JJ A47183 27 8 quantities quantity NNS A47183 27 9 of of IN A47183 27 10 textual textual JJ A47183 27 11 data datum NNS A47183 27 12 within within IN A47183 27 13 the the DT A47183 27 14 usual usual JJ A47183 27 15 project project NN A47183 27 16 restraints restraint NNS A47183 27 17 of of IN A47183 27 18 time time NN A47183 27 19 and and CC A47183 27 20 funding funding NN A47183 27 21 , , , A47183 27 22 and and CC A47183 27 23 therefore therefore RB A47183 27 24 chose choose VBD A47183 27 25 to to TO A47183 27 26 create create VB A47183 27 27 diplomatic diplomatic JJ A47183 27 28 transcriptions transcription NNS A47183 27 29 ( ( -LRB- A47183 27 30 as as IN A47183 27 31 opposed oppose VBN A47183 27 32 to to IN A47183 27 33 critical critical JJ A47183 27 34 editions edition NNS A47183 27 35 ) ) -RRB- A47183 27 36 with with IN A47183 27 37 light light JJ A47183 27 38 - - HYPH A47183 27 39 touch touch NN A47183 27 40 , , , A47183 27 41 mainly mainly RB A47183 27 42 structural structural JJ A47183 27 43 encoding encoding NN A47183 27 44 based base VBN A47183 27 45 on on IN A47183 27 46 the the DT A47183 27 47 Text Text NNP A47183 27 48 Encoding Encoding NNP A47183 27 49 Initiative Initiative NNP A47183 27 50 ( ( -LRB- A47183 27 51 http://www.tei-c.org http://www.tei-c.org NFP A47183 27 52 ) ) -RRB- A47183 27 53 . . . A47183 28 1 The the DT A47183 28 2 EEBO EEBO NNP A47183 28 3 - - HYPH A47183 28 4 TCP TCP NNP A47183 28 5 project project NN A47183 28 6 was be VBD A47183 28 7 divided divide VBN A47183 28 8 into into IN A47183 28 9 two two CD A47183 28 10 phases phase NNS A47183 28 11 . . . A47183 29 1 The the DT A47183 29 2 25,363 25,363 CD A47183 29 3 texts text NNS A47183 29 4 created create VBN A47183 29 5 during during IN A47183 29 6 Phase Phase NNP A47183 29 7 1 1 CD A47183 29 8 of of IN A47183 29 9 the the DT A47183 29 10 project project NN A47183 29 11 have have VBP A47183 29 12 been be VBN A47183 29 13 released release VBN A47183 29 14 into into IN A47183 29 15 the the DT A47183 29 16 public public JJ A47183 29 17 domain domain NN A47183 29 18 as as IN A47183 29 19 of of IN A47183 29 20 1 1 CD A47183 29 21 January January NNP A47183 29 22 2015 2015 CD A47183 29 23 . . . A47183 30 1 Anyone anyone NN A47183 30 2 can can MD A47183 30 3 now now RB A47183 30 4 take take VB A47183 30 5 and and CC A47183 30 6 use use VB A47183 30 7 these these DT A47183 30 8 texts text NNS A47183 30 9 for for IN A47183 30 10 their -PRON- PRP$ A47183 30 11 own own JJ A47183 30 12 purposes purpose NNS A47183 30 13 , , , A47183 30 14 but but CC A47183 30 15 we -PRON- PRP A47183 30 16 respectfully respectfully RB A47183 30 17 request request VBP A47183 30 18 that that DT A47183 30 19 due due JJ A47183 30 20 credit credit NN A47183 30 21 and and CC A47183 30 22 attribution attribution NN A47183 30 23 is be VBZ A47183 30 24 given give VBN A47183 30 25 to to IN A47183 30 26 their -PRON- PRP$ A47183 30 27 original original JJ A47183 30 28 source source NN A47183 30 29 . . . A47183 31 1 Users user NNS A47183 31 2 should should MD A47183 31 3 be be VB A47183 31 4 aware aware JJ A47183 31 5 of of IN A47183 31 6 the the DT A47183 31 7 process process NN A47183 31 8 of of IN A47183 31 9 creating create VBG A47183 31 10 the the DT A47183 31 11 TCP TCP NNP A47183 31 12 texts text NNS A47183 31 13 , , , A47183 31 14 and and CC A47183 31 15 therefore therefore RB A47183 31 16 of of IN A47183 31 17 any any DT A47183 31 18 assumptions assumption NNS A47183 31 19 that that WDT A47183 31 20 can can MD A47183 31 21 be be VB A47183 31 22 made make VBN A47183 31 23 about about IN A47183 31 24 the the DT A47183 31 25 data datum NNS A47183 31 26 . . . A47183 32 1 Text text NN A47183 32 2 selection selection NN A47183 32 3 was be VBD A47183 32 4 based base VBN A47183 32 5 on on IN A47183 32 6 the the DT A47183 32 7 New New NNP A47183 32 8 Cambridge Cambridge NNP A47183 32 9 Bibliography Bibliography NNP A47183 32 10 of of IN A47183 32 11 English English NNP A47183 32 12 Literature Literature NNP A47183 32 13 ( ( -LRB- A47183 32 14 NCBEL NCBEL NNP A47183 32 15 ) ) -RRB- A47183 32 16 . . . A47183 33 1 If if IN A47183 33 2 an an DT A47183 33 3 author author NN A47183 33 4 ( ( -LRB- A47183 33 5 or or CC A47183 33 6 for for IN A47183 33 7 an an DT A47183 33 8 anonymous anonymous JJ A47183 33 9 work work NN A47183 33 10 , , , A47183 33 11 the the DT A47183 33 12 title title NN A47183 33 13 ) ) -RRB- A47183 33 14 appears appear VBZ A47183 33 15 in in IN A47183 33 16 NCBEL NCBEL NNP A47183 33 17 , , , A47183 33 18 then then RB A47183 33 19 their -PRON- PRP$ A47183 33 20 works work NNS A47183 33 21 are be VBP A47183 33 22 eligible eligible JJ A47183 33 23 for for IN A47183 33 24 inclusion inclusion NN A47183 33 25 . . . A47183 34 1 Selection selection NN A47183 34 2 was be VBD A47183 34 3 intended intend VBN A47183 34 4 to to TO A47183 34 5 range range VB A47183 34 6 over over RP A47183 34 7 a a DT A47183 34 8 wide wide JJ A47183 34 9 variety variety NN A47183 34 10 of of IN A47183 34 11 subject subject JJ A47183 34 12 areas area NNS A47183 34 13 , , , A47183 34 14 to to TO A47183 34 15 reflect reflect VB A47183 34 16 the the DT A47183 34 17 true true JJ A47183 34 18 nature nature NN A47183 34 19 of of IN A47183 34 20 the the DT A47183 34 21 print print NN A47183 34 22 record record NN A47183 34 23 of of IN A47183 34 24 the the DT A47183 34 25 period period NN A47183 34 26 . . . A47183 35 1 In in IN A47183 35 2 general general JJ A47183 35 3 , , , A47183 35 4 first first JJ A47183 35 5 editions edition NNS A47183 35 6 of of IN A47183 35 7 a a DT A47183 35 8 works work NNS A47183 35 9 in in IN A47183 35 10 English English NNP A47183 35 11 were be VBD A47183 35 12 prioritized prioritize VBN A47183 35 13 , , , A47183 35 14 although although IN A47183 35 15 there there EX A47183 35 16 are be VBP A47183 35 17 a a DT A47183 35 18 number number NN A47183 35 19 of of IN A47183 35 20 works work NNS A47183 35 21 in in IN A47183 35 22 other other JJ A47183 35 23 languages language NNS A47183 35 24 , , , A47183 35 25 notably notably RB A47183 35 26 Latin Latin NNP A47183 35 27 and and CC A47183 35 28 Welsh Welsh NNP A47183 35 29 , , , A47183 35 30 included include VBD A47183 35 31 and and CC A47183 35 32 sometimes sometimes RB A47183 35 33 a a DT A47183 35 34 second second JJ A47183 35 35 or or CC A47183 35 36 later later JJ A47183 35 37 edition edition NN A47183 35 38 of of IN A47183 35 39 a a DT A47183 35 40 work work NN A47183 35 41 was be VBD A47183 35 42 chosen choose VBN A47183 35 43 if if IN A47183 35 44 there there EX A47183 35 45 was be VBD A47183 35 46 a a DT A47183 35 47 compelling compelling JJ A47183 35 48 reason reason NN A47183 35 49 to to TO A47183 35 50 do do VB A47183 35 51 so so RB A47183 35 52 . . . A47183 36 1 Image image NN A47183 36 2 sets set NNS A47183 36 3 were be VBD A47183 36 4 sent send VBN A47183 36 5 to to IN A47183 36 6 external external JJ A47183 36 7 keying keying NN A47183 36 8 companies company NNS A47183 36 9 for for IN A47183 36 10 transcription transcription NN A47183 36 11 and and CC A47183 36 12 basic basic JJ A47183 36 13 encoding encoding NN A47183 36 14 . . . A47183 37 1 Quality quality JJ A47183 37 2 assurance assurance NN A47183 37 3 was be VBD A47183 37 4 then then RB A47183 37 5 carried carry VBN A47183 37 6 out out RP A47183 37 7 by by IN A47183 37 8 editorial editorial JJ A47183 37 9 teams team NNS A47183 37 10 in in IN A47183 37 11 Oxford Oxford NNP A47183 37 12 and and CC A47183 37 13 Michigan Michigan NNP A47183 37 14 . . . A47183 38 1 5 5 CD A47183 38 2 % % NN A47183 38 3 ( ( -LRB- A47183 38 4 or or CC A47183 38 5 5 5 CD A47183 38 6 pages page NNS A47183 38 7 , , , A47183 38 8 whichever whichever WDT A47183 38 9 is be VBZ A47183 38 10 the the DT A47183 38 11 greater great JJR A47183 38 12 ) ) -RRB- A47183 38 13 of of IN A47183 38 14 each each DT A47183 38 15 text text NN A47183 38 16 was be VBD A47183 38 17 proofread proofread NN A47183 38 18 for for IN A47183 38 19 accuracy accuracy NN A47183 38 20 and and CC A47183 38 21 those those DT A47183 38 22 which which WDT A47183 38 23 did do VBD A47183 38 24 not not RB A47183 38 25 meet meet VB A47183 38 26 QA qa NN A47183 38 27 standards standard NNS A47183 38 28 were be VBD A47183 38 29 returned return VBN A47183 38 30 to to IN A47183 38 31 the the DT A47183 38 32 keyers keyer NNS A47183 38 33 to to TO A47183 38 34 be be VB A47183 38 35 redone redone NN A47183 38 36 . . . A47183 39 1 After after IN A47183 39 2 proofreading proofreading NN A47183 39 3 , , , A47183 39 4 the the DT A47183 39 5 encoding encoding NN A47183 39 6 was be VBD A47183 39 7 enhanced enhance VBN A47183 39 8 and/or and/or CC A47183 39 9 corrected correct VBD A47183 39 10 and and CC A47183 39 11 characters character NNS A47183 39 12 marked mark VBN A47183 39 13 as as IN A47183 39 14 illegible illegible JJ A47183 39 15 were be VBD A47183 39 16 corrected correct VBN A47183 39 17 where where WRB A47183 39 18 possible possible JJ A47183 39 19 up up IN A47183 39 20 to to IN A47183 39 21 a a DT A47183 39 22 limit limit NN A47183 39 23 of of IN A47183 39 24 100 100 CD A47183 39 25 instances instance NNS A47183 39 26 per per IN A47183 39 27 text text NN A47183 39 28 . . . A47183 40 1 Any any DT A47183 40 2 remaining remain VBG A47183 40 3 illegibles illegible NNS A47183 40 4 were be VBD A47183 40 5 encoded encode VBN A47183 40 6 as as IN A47183 40 7 < < XX A47183 40 8 gap gap NN A47183 40 9 > > XX A47183 40 10 s s XX A47183 40 11 . . . A47183 41 1 Understanding understand VBG A47183 41 2 these these DT A47183 41 3 processes process NNS A47183 41 4 should should MD A47183 41 5 make make VB A47183 41 6 clear clear JJ A47183 41 7 that that IN A47183 41 8 , , , A47183 41 9 while while IN A47183 41 10 the the DT A47183 41 11 overall overall JJ A47183 41 12 quality quality NN A47183 41 13 of of IN A47183 41 14 TCP TCP NNP A47183 41 15 data datum NNS A47183 41 16 is be VBZ A47183 41 17 very very RB A47183 41 18 good good JJ A47183 41 19 , , , A47183 41 20 some some DT A47183 41 21 errors error NNS A47183 41 22 will will MD A47183 41 23 remain remain VB A47183 41 24 and and CC A47183 41 25 some some DT A47183 41 26 readable readable JJ A47183 41 27 characters character NNS A47183 41 28 will will MD A47183 41 29 be be VB A47183 41 30 marked mark VBN A47183 41 31 as as IN A47183 41 32 illegible illegible JJ A47183 41 33 . . . A47183 42 1 Users user NNS A47183 42 2 should should MD A47183 42 3 bear bear VB A47183 42 4 in in IN A47183 42 5 mind mind NN A47183 42 6 that that IN A47183 42 7 in in IN A47183 42 8 all all DT A47183 42 9 likelihood likelihood NN A47183 42 10 such such JJ A47183 42 11 instances instance NNS A47183 42 12 will will MD A47183 42 13 never never RB A47183 42 14 have have VB A47183 42 15 been be VBN A47183 42 16 looked look VBN A47183 42 17 at at IN A47183 42 18 by by IN A47183 42 19 a a DT A47183 42 20 TCP TCP NNP A47183 42 21 editor editor NN A47183 42 22 . . . A47183 43 1 The the DT A47183 43 2 texts text NNS A47183 43 3 were be VBD A47183 43 4 encoded encode VBN A47183 43 5 and and CC A47183 43 6 linked link VBN A47183 43 7 to to IN A47183 43 8 page page NN A47183 43 9 images image NNS A47183 43 10 in in IN A47183 43 11 accordance accordance NN A47183 43 12 with with IN A47183 43 13 level level NN A47183 43 14 4 4 CD A47183 43 15 of of IN A47183 43 16 the the DT A47183 43 17 TEI TEI NNP A47183 43 18 in in IN A47183 43 19 Libraries Libraries NNP A47183 43 20 guidelines guideline NNS A47183 43 21 . . . A47183 44 1 Copies copy NNS A47183 44 2 of of IN A47183 44 3 the the DT A47183 44 4 texts text NNS A47183 44 5 have have VBP A47183 44 6 been be VBN A47183 44 7 issued issue VBN A47183 44 8 variously variously RB A47183 44 9 as as IN A47183 44 10 SGML SGML NNP A47183 44 11 ( ( -LRB- A47183 44 12 TCP TCP NNP A47183 44 13 schema schema NN A47183 44 14 ; ; : A47183 44 15 ASCII ASCII NNP A47183 44 16 text text NN A47183 44 17 with with IN A47183 44 18 mnemonic mnemonic NNP A47183 44 19 sdata sdata NNP A47183 44 20 character character NNP A47183 44 21 entities entity NNS A47183 44 22 ) ) -RRB- A47183 44 23 ; ; : A47183 44 24 displayable displayable JJ A47183 44 25 XML xml NN A47183 44 26 ( ( -LRB- A47183 44 27 TCP TCP NNP A47183 44 28 schema schema NN A47183 44 29 ; ; : A47183 44 30 characters character NNS A47183 44 31 represented represent VBD A47183 44 32 either either CC A47183 44 33 as as IN A47183 44 34 UTF-8 UTF-8 NNP A47183 44 35 Unicode Unicode NNP A47183 44 36 or or CC A47183 44 37 text text NN A47183 44 38 strings string NNS A47183 44 39 within within IN A47183 44 40 braces brace NNS A47183 44 41 ) ) -RRB- A47183 44 42 ; ; : A47183 44 43 or or CC A47183 44 44 lossless lossless JJ A47183 44 45 XML xml NN A47183 44 46 ( ( -LRB- A47183 44 47 TEI TEI NNP A47183 44 48 P5 P5 NNP A47183 44 49 , , , A47183 44 50 characters character NNS A47183 44 51 represented represent VBD A47183 44 52 either either CC A47183 44 53 as as IN A47183 44 54 UTF-8 UTF-8 NNP A47183 44 55 Unicode Unicode NNP A47183 44 56 or or CC A47183 44 57 TEI TEI NNP A47183 44 58 g g NN A47183 44 59 elements element NNS A47183 44 60 ) ) -RRB- A47183 44 61 . . . A47183 45 1 Keying keying NN A47183 45 2 and and CC A47183 45 3 markup markup NN A47183 45 4 guidelines guideline NNS A47183 45 5 are be VBP A47183 45 6 available available JJ A47183 45 7 at at IN A47183 45 8 the the DT A47183 45 9 Text Text NNP A47183 45 10 Creation Creation NNP A47183 45 11 Partnership Partnership NNP A47183 45 12 web web NN A47183 45 13 site site NN A47183 45 14 . . . A47183 46 1 eng eng NNP A47183 46 2 Geometry Geometry NNP A47183 46 3 -- -- : A47183 46 4 Early early RB A47183 46 5 works work NNS A47183 46 6 to to IN A47183 46 7 1800 1800 CD A47183 46 8 . . . A47183 47 1 2005 2005 CD A47183 47 2 - - SYM A47183 47 3 05 05 CD A47183 47 4 TCP TCP NNP A47183 47 5 Assigned assign VBN A47183 47 6 for for IN A47183 47 7 keying keying NN A47183 47 8 and and CC A47183 47 9 markup markup NNP A47183 47 10 2005 2005 CD A47183 47 11 - - SYM A47183 47 12 08 08 CD A47183 47 13 SPi SPi NNS A47183 47 14 Global Global NNP A47183 47 15 Keyed Keyed NNP A47183 47 16 and and CC A47183 47 17 coded code VBN A47183 47 18 from from IN A47183 47 19 ProQuest ProQuest NNP A47183 47 20 page page NN A47183 47 21 images image NNS A47183 47 22 2006 2006 CD A47183 47 23 - - SYM A47183 47 24 01 01 CD A47183 47 25 Judith Judith NNP A47183 47 26 Siefring Siefring NNP A47183 47 27 Sampled Sampled NNP A47183 47 28 and and CC A47183 47 29 proofread proofread JJ A47183 47 30 2006 2006 CD A47183 47 31 - - SYM A47183 47 32 01 01 CD A47183 47 33 Judith Judith NNP A47183 47 34 Siefring Siefring NNP A47183 47 35 Text Text NNP A47183 47 36 and and CC A47183 47 37 markup markup NN A47183 47 38 reviewed review VBD A47183 47 39 and and CC A47183 47 40 edited edit VBD A47183 47 41 2006 2006 CD A47183 47 42 - - SYM A47183 47 43 04 04 CD A47183 47 44 pfs pfs NN A47183 47 45 Batch Batch NNP A47183 47 46 review review NN A47183 47 47 ( ( -LRB- A47183 47 48 QC QC NNP A47183 47 49 ) ) -RRB- A47183 47 50 and and CC A47183 47 51 XML xml NN A47183 47 52 conversion conversion NN A47183 47 53 A a DT A47183 47 54 SUPPLEMENT SUPPLEMENT NNP A47183 47 55 TO to IN A47183 47 56 A a DT A47183 47 57 Late late JJ A47183 47 58 TREATISE TREATISE NNP A47183 47 59 , , , A47183 47 60 CALLED call VBN A47183 47 61 An an DT A47183 47 62 Essay Essay NNP A47183 47 63 for for IN A47183 47 64 the the DT A47183 47 65 Discovery Discovery NNP A47183 47 66 of of IN A47183 47 67 some some DT A47183 47 68 New New NNP A47183 47 69 Geometrical Geometrical NNP A47183 47 70 Problems Problems NNPS A47183 47 71 , , , A47183 47 72 Concerning concern VBG A47183 47 73 Angular Angular NNP A47183 47 74 Sections Sections NNPS A47183 47 75 , , , A47183 47 76 resolving resolve VBG A47183 47 77 what what WP A47183 47 78 was be VBD A47183 47 79 there there RB A47183 47 80 Problematically problematically RB A47183 47 81 proposed propose VBN A47183 47 82 ; ; : A47183 47 83 and and CC A47183 47 84 with with IN A47183 47 85 some some DT A47183 47 86 Rectification rectification NN A47183 47 87 made make VBN A47183 47 88 in in IN A47183 47 89 the the DT A47183 47 90 former former JJ A47183 47 91 Essay Essay NNP A47183 47 92 , , , A47183 47 93 showing show VBG A47183 47 94 an an DT A47183 47 95 easie easie NN A47183 47 96 method method NN A47183 47 97 truly truly RB A47183 47 98 Geometrical geometrical JJ A47183 47 99 , , , A47183 47 100 without without IN A47183 47 101 any any DT A47183 47 102 Conick Conick NNP A47183 47 103 Section Section NNP A47183 47 104 , , , A47183 47 105 or or CC A47183 47 106 Cubick Cubick NNP A47183 47 107 Aequation Aequation NNP A47183 47 108 , , , A47183 47 109 to to TO A47183 47 110 sect sect VB A47183 47 111 any any DT A47183 47 112 Angle Angle NNP A47183 47 113 or or CC A47183 47 114 Arch Arch NNP A47183 47 115 of of IN A47183 47 116 a a DT A47183 47 117 Circle Circle NNP A47183 47 118 into into IN A47183 47 119 3.5.7 3.5.7 NNP A47183 47 120 . . . A47183 48 1 or or CC A47183 48 2 any any DT A47183 48 3 other other JJ A47183 48 4 Uneven Uneven NNP A47183 48 5 Number number NN A47183 48 6 of of IN A47183 48 7 equal equal JJ A47183 48 8 parts part NNS A47183 48 9 . . . A47183 49 1 By by IN A47183 49 2 G.K. G.K. NNP A47183 50 1 WHereas whereas IN A47183 50 2 it -PRON- PRP A47183 50 3 was be VBD A47183 50 4 supposed suppose VBN A47183 50 5 in in IN A47183 50 6 the the DT A47183 50 7 former former JJ A47183 50 8 Proposal proposal NN A47183 50 9 , , , A47183 50 10 that that IN A47183 50 11 a a DT A47183 50 12 straight straight JJ A47183 50 13 Line line NN A47183 50 14 could could MD A47183 50 15 be be VB A47183 50 16 drawn draw VBN A47183 50 17 through through IN A47183 50 18 the the DT A47183 50 19 extream extream JJ A47183 50 20 Points point NNS A47183 50 21 of of IN A47183 50 22 three three CD A47183 50 23 or or CC A47183 50 24 more more JJR A47183 50 25 Concentrick Concentrick NNP A47183 50 26 Arches Arches NNPS A47183 50 27 at at IN A47183 50 28 both both DT A47183 50 29 ends end NNS A47183 50 30 ( ( -LRB- A47183 50 31 the the DT A47183 50 32 Arches Arches NNP A47183 50 33 beginning begin VBG A47183 50 34 or or CC A47183 50 35 ending end VBG A47183 50 36 upon upon IN A47183 50 37 a a DT A47183 50 38 straight straight JJ A47183 50 39 Line Line NNP A47183 50 40 ● ● CD A47183 50 41 oming oming NN A47183 50 42 from from IN A47183 50 43 the the DT A47183 50 44 Center Center NNP A47183 50 45 of of IN A47183 50 46 those those DT A47183 50 47 Concentrick Concentrick NNP A47183 50 48 Arches Arches NNPS A47183 50 49 ) ) -RRB- A47183 50 50 having have VBG A47183 50 51 equal equal JJ A47183 50 52 Cords cord NNS A47183 50 53 , , , A47183 50 54 though though IN A47183 50 55 not not RB A47183 50 56 equal equal JJ A47183 50 57 Arches arch NNS A47183 50 58 . . . A47183 51 1 Upon upon IN A47183 51 2 further further JJ A47183 51 3 consideration consideration NN A47183 51 4 , , , A47183 51 5 it -PRON- PRP A47183 51 6 is be VBZ A47183 51 7 found find VBN A47183 51 8 , , , A47183 51 9 that that IN A47183 51 10 however however RB A47183 51 11 seemingly seemingly RB A47183 51 12 such such PDT A47183 51 13 a a DT A47183 51 14 Line Line NNP A47183 51 15 may may MD A47183 51 16 appear appear VB A47183 51 17 to to TO A47183 51 18 be be VB A47183 51 19 straight straight JJ A47183 51 20 in in IN A47183 51 21 many many JJ A47183 51 22 cases case NNS A47183 51 23 , , , A47183 51 24 as as IN A47183 51 25 when when WRB A47183 51 26 the the DT A47183 51 27 Radius Radius NNP A47183 51 28 is be VBZ A47183 51 29 short short JJ A47183 51 30 , , , A47183 51 31 or or CC A47183 51 32 the the DT A47183 51 33 Angle Angle NNP A47183 51 34 very very RB A47183 51 35 acute acute JJ A47183 51 36 , , , A47183 51 37 yet yet RB A47183 51 38 in in IN A47183 51 39 no no DT A47183 51 40 case case NN A47183 51 41 is be VBZ A47183 51 42 such such PDT A47183 51 43 a a DT A47183 51 44 Line line NN A47183 51 45 mathematically mathematically RB A47183 51 46 straight straight RB A47183 51 47 , , , A47183 51 48 but but CC A47183 51 49 is be VBZ A47183 51 50 a a DT A47183 51 51 regular regular JJ A47183 51 52 Curve curve NN A47183 51 53 , , , A47183 51 54 and and CC A47183 51 55 can can MD A47183 51 56 be be VB A47183 51 57 as as RB A47183 51 58 regularly regularly RB A47183 51 59 drawn draw VBN A47183 51 60 , , , A47183 51 61 and and CC A47183 51 62 by by IN A47183 51 63 as as RB A47183 51 64 true true JJ A47183 51 65 Geometrical Geometrical NNP A47183 51 66 Art Art NNP A47183 51 67 , , , A47183 51 68 as as IN A47183 51 69 any any DT A47183 51 70 Parabola Parabola NNP A47183 51 71 , , , A47183 51 72 or or CC A47183 51 73 other other JJ A47183 51 74 Conick Conick NNP A47183 51 75 Section Section NNP A47183 51 76 can can MD A47183 51 77 , , , A47183 51 78 and and CC A47183 51 79 with with IN A47183 51 80 greater great JJR A47183 51 81 facility facility NN A47183 51 82 and and CC A47183 51 83 readiness readiness NN A47183 51 84 , , , A47183 51 85 and and CC A47183 51 86 which which WDT A47183 51 87 any any DT A47183 51 88 Tiro Tiro NNP A47183 51 89 who who WP A47183 51 90 understands understand VBZ A47183 51 91 nothing nothing NN A47183 51 92 of of IN A47183 51 93 Conick Conick NNP A47183 51 94 Sections Sections NNPS A47183 51 95 , , , A47183 51 96 and and CC A47183 51 97 Cubick Cubick NNP A47183 51 98 Equations Equations NNPS A47183 51 99 may may MD A47183 51 100 do do VB A47183 51 101 . . . A47183 52 1 The the DT A47183 52 2 way way NN A47183 52 3 of of IN A47183 52 4 drawing draw VBG A47183 52 5 the the DT A47183 52 6 said say VBN A47183 52 7 Curve curve NN A47183 52 8 is be VBZ A47183 52 9 this this DT A47183 52 10 : : : A47183 52 11 Let let VB A47183 52 12 a a DT A47183 52 13 short short JJ A47183 52 14 cross cross NN A47183 52 15 - - NNS A47183 52 16 Rule rule NN A47183 52 17 be be VB A47183 52 18 set set VBN A47183 52 19 at at IN A47183 52 20 right right JJ A47183 52 21 Angles angle NNS A47183 52 22 with with IN A47183 52 23 another another DT A47183 52 24 longer long JJR A47183 52 25 Rule rule NN A47183 52 26 , , , A47183 52 27 and and CC A47183 52 28 let let VB A47183 52 29 the the DT A47183 52 30 length length NN A47183 52 31 of of IN A47183 52 32 the the DT A47183 52 33 cross cross NN A47183 52 34 Rule rule NN A47183 52 35 be be VB A47183 52 36 at at IN A47183 52 37 pleasure pleasure NN A47183 52 38 2 2 CD A47183 52 39 or or CC A47183 52 40 3 3 CD A47183 52 41 Inches inch NNS A47183 52 42 , , , A47183 52 43 or or CC A47183 52 44 more more RBR A47183 52 45 , , , A47183 52 46 as as IN A47183 52 47 6 6 CD A47183 52 48 or or CC A47183 52 49 7 7 CD A47183 52 50 , , , A47183 52 51 as as IN A47183 52 52 ye ye NNP A47183 52 53 have have VBP A47183 52 54 a a DT A47183 52 55 mind mind NN A47183 52 56 to to TO A47183 52 57 make make VB A47183 52 58 the the DT A47183 52 59 length length NN A47183 52 60 of of IN A47183 52 61 the the DT A47183 52 62 Cord Cord NNP A47183 52 63 of of IN A47183 52 64 each each DT A47183 52 65 part part NN A47183 52 66 of of IN A47183 52 67 the the DT A47183 52 68 Section Section NNP A47183 52 69 of of IN A47183 52 70 your -PRON- PRP$ A47183 52 71 Angle angle NN A47183 52 72 , , , A47183 52 73 which which WDT A47183 52 74 as as IN A47183 52 75 in in IN A47183 52 76 the the DT A47183 52 77 following follow VBG A47183 52 78 Figure figure NN A47183 52 79 let let VBD A47183 52 80 be be VB A47183 52 81 3 3 CD A47183 52 82 Inches inch NNS A47183 52 83 , , , A47183 52 84 and and CC A47183 52 85 let let VB A47183 52 86 the the DT A47183 52 87 just just RB A47183 52 88 half half NN A47183 52 89 of of IN A47183 52 90 the the DT A47183 52 91 cross cross NN A47183 52 92 - - NN A47183 52 93 Rule rule NN A47183 52 94 be be VB A47183 52 95 on on IN A47183 52 96 the the DT A47183 52 97 left left JJ A47183 52 98 side side NN A47183 52 99 of of IN A47183 52 100 the the DT A47183 52 101 long long JJ A47183 52 102 Rule Rule NNP A47183 52 103 , , , A47183 52 104 and and CC A47183 52 105 let let VB A47183 52 106 a a DT A47183 52 107 small small JJ A47183 52 108 Brass Brass NNP A47183 52 109 or or CC A47183 52 110 Steel Steel NNP A47183 52 111 - - , A47183 52 112 Pin Pin NNP A47183 52 113 be be VB A47183 52 114 fixed fix VBN A47183 52 115 on on IN A47183 52 116 the the DT A47183 52 117 right right JJ A47183 52 118 end end NN A47183 52 119 of of IN A47183 52 120 the the DT A47183 52 121 said say VBN A47183 52 122 cross cross NN A47183 52 123 Rule Rule NNP A47183 52 124 , , , A47183 52 125 that that IN A47183 52 126 as as IN A47183 52 127 the the DT A47183 52 128 Rule Rule NNP A47183 52 129 is be VBZ A47183 52 130 moved move VBN A47183 52 131 , , , A47183 52 132 may may MD A47183 52 133 make make VB A47183 52 134 an an DT A47183 52 135 Impression Impression NNP A47183 52 136 on on IN A47183 52 137 the the DT A47183 52 138 Paper Paper NNP A47183 52 139 , , , A47183 52 140 as as IN A47183 52 141 the the DT A47183 52 142 point point NN A47183 52 143 of of IN A47183 52 144 the the DT A47183 52 145 Compass Compass NNP A47183 52 146 doth doth NN A47183 52 147 in in IN A47183 52 148 drawing draw VBG A47183 52 149 a a DT A47183 52 150 Circle Circle NNP A47183 52 151 . . . A47183 53 1 The the DT A47183 53 2 length length NN A47183 53 3 of of IN A47183 53 4 the the DT A47183 53 5 longer long JJR A47183 53 6 Rule Rule NNP A47183 53 7 is be VBZ A47183 53 8 to to TO A47183 53 9 be be VB A47183 53 10 as as IN A47183 53 11 occasion occasion NN A47183 53 12 requireth requireth NN A47183 53 13 , , , A47183 53 14 as as IN A47183 53 15 double double JJ A47183 53 16 or or CC A47183 53 17 triple triple JJ A47183 53 18 the the DT A47183 53 19 length length NN A47183 53 20 of of IN A47183 53 21 the the DT A47183 53 22 other other JJ A47183 53 23 . . . A47183 54 1 Having have VBG A47183 54 2 thus thus RB A47183 54 3 prepared prepare VBN A47183 54 4 your -PRON- PRP$ A47183 54 5 two two CD A47183 54 6 Rules Rules NNPS A47183 54 7 , , , A47183 54 8 the the DT A47183 54 9 one one NN A47183 54 10 cutting cut VBG A47183 54 11 the the DT A47183 54 12 other other JJ A47183 54 13 at at IN A47183 54 14 right right JJ A47183 54 15 Angles Angles NNP A47183 54 16 , , , A47183 54 17 and and CC A47183 54 18 the the DT A47183 54 19 cross cross NN A47183 54 20 - - : A47183 54 21 Rule rule NN A47183 54 22 fixed fix VBN A47183 54 23 to to IN A47183 54 24 it -PRON- PRP A47183 54 25 , , , A47183 54 26 ( ( -LRB- A47183 54 27 though though IN A47183 54 28 it -PRON- PRP A47183 54 29 may may MD A47183 54 30 be be VB A47183 54 31 made make VBN A47183 54 32 also also RB A47183 54 33 moveable moveable JJ A47183 54 34 on on IN A47183 54 35 it -PRON- PRP A47183 54 36 ) ) -RRB- A47183 54 37 suppose suppose VB A47183 54 38 the the DT A47183 54 39 Angle Angle NNP A47183 54 40 given give VBN A47183 54 41 to to TO A47183 54 42 be be VB A47183 54 43 trisected trisect VBN A47183 54 44 is be VBZ A47183 54 45 BAC BAC NNP A47183 54 46 , , , A47183 54 47 measured measure VBN A47183 54 48 by by IN A47183 54 49 the the DT A47183 54 50 arch arch JJ A47183 54 51 BMC bmc NN A47183 54 52 . . . A47183 55 1 in in IN A47183 55 2 order order NN A47183 55 3 to to TO A47183 55 4 draw draw VB A47183 55 5 the the DT A47183 55 6 curve curve NN A47183 55 7 Line line NN A47183 55 8 with with IN A47183 55 9 one one CD A47183 55 10 draught draught NN A47183 55 11 of of IN A47183 55 12 the the DT A47183 55 13 Hand Hand NNP A47183 55 14 , , , A47183 55 15 set set VBD A47183 55 16 the the DT A47183 55 17 left left JJ A47183 55 18 end end NN A47183 55 19 of of IN A47183 55 20 the the DT A47183 55 21 cross cross NN A47183 55 22 - - NN A47183 55 23 Rule rule NN A47183 55 24 , , , A47183 55 25 on on IN A47183 55 26 the the DT A47183 55 27 point point NN A47183 55 28 B b NN A47183 55 29 , , , A47183 55 30 and and CC A47183 55 31 from from IN A47183 55 32 B B NNP A47183 55 33 let let VB A47183 55 34 it -PRON- PRP A47183 55 35 run run VB A47183 55 36 or or CC A47183 55 37 slide slide VB A47183 55 38 along along IN A47183 55 39 the the DT A47183 55 40 line line NN A47183 55 41 BA BA NNP A47183 55 42 , , , A47183 55 43 and and CC A47183 55 44 as as IN A47183 55 45 it -PRON- PRP A47183 55 46 runs run VBZ A47183 55 47 along along IN A47183 55 48 the the DT A47183 55 49 said say VBN A47183 55 50 Line Line NNP A47183 55 51 , , , A47183 55 52 let let VB A47183 55 53 the the DT A47183 55 54 left left JJ A47183 55 55 side side NN A47183 55 56 of of IN A47183 55 57 the the DT A47183 55 58 long long JJ A47183 55 59 Rule Rule NNP A47183 55 60 still still RB A47183 55 61 run run VB A47183 55 62 through through IN A47183 55 63 the the DT A47183 55 64 Center Center NNP A47183 55 65 , , , A47183 55 66 or or CC A47183 55 67 vertical vertical JJ A47183 55 68 point point NN A47183 55 69 A A NNP A47183 55 70 , , , A47183 55 71 which which WDT A47183 55 72 is be VBZ A47183 55 73 most most RBS A47183 55 74 easily easily RB A47183 55 75 done do VBN A47183 55 76 ; ; : A47183 55 77 and and CC A47183 55 78 let let VB A47183 55 79 it -PRON- PRP A47183 55 80 run run VB A47183 55 81 or or CC A47183 55 82 slide slide VB A47183 55 83 along along IN A47183 55 84 from from IN A47183 55 85 B b NN A47183 55 86 towards towards IN A47183 55 87 A a DT A47183 55 88 , , , A47183 55 89 until until IN A47183 55 90 the the DT A47183 55 91 other other JJ A47183 55 92 end end NN A47183 55 93 of of IN A47183 55 94 the the DT A47183 55 95 cross cross NN A47183 55 96 - - JJ A47183 55 97 Rule rule NN A47183 55 98 reach reach NN A47183 55 99 at at IN A47183 55 100 least least JJS A47183 55 101 to to IN A47183 55 102 the the DT A47183 55 103 line line NN A47183 55 104 AC AC NNP A47183 55 105 , , , A47183 55 106 or or CC A47183 55 107 further further RB A47183 55 108 as as IN A47183 55 109 one one CD A47183 55 110 pleaseth pleaseth NN A47183 55 111 , , , A47183 55 112 and and CC A47183 55 113 the the DT A47183 55 114 Brass Brass NNP A47183 55 115 Pin Pin NNP A47183 55 116 on on IN A47183 55 117 the the DT A47183 55 118 other other JJ A47183 55 119 end end NN A47183 55 120 of of IN A47183 55 121 the the DT A47183 55 122 cross cross NN A47183 55 123 Rule rule NN A47183 55 124 shall shall MD A47183 55 125 describe describe VB A47183 55 126 the the DT A47183 55 127 regular regular JJ A47183 55 128 curve curve NN A47183 55 129 FIG FIG NNP A47183 55 130 Having have VBG A47183 55 131 thus thus RB A47183 55 132 drawn draw VBN A47183 55 133 the the DT A47183 55 134 curve curve NN A47183 55 135 Line line NN A47183 55 136 , , , A47183 55 137 at at IN A47183 55 138 the the DT A47183 55 139 distance distance NN A47183 55 140 of of IN A47183 55 141 one one CD A47183 55 142 half half NN A47183 55 143 of of IN A47183 55 144 the the DT A47183 55 145 cross cross NN A47183 55 146 Rule rule NN A47183 55 147 draw draw VB A47183 55 148 the the DT A47183 55 149 straight straight JJ A47183 55 150 Line Line NNP A47183 55 151 DE DE NNP A47183 55 152 paralel paralel NN A47183 55 153 to to IN A47183 55 154 AC AC NNP A47183 55 155 . . . A47183 56 1 and and CC A47183 56 2 where where WRB A47183 56 3 the the DT A47183 56 4 Curve Curve NNP A47183 56 5 Line Line NNP A47183 56 6 cuts cut VBZ A47183 56 7 the the DT A47183 56 8 straight straight JJ A47183 56 9 line line NN A47183 56 10 DE de NN A47183 56 11 as as IN A47183 56 12 at at IN A47183 56 13 I -PRON- PRP A47183 56 14 , , , A47183 56 15 a a DT A47183 56 16 Line Line NNP A47183 56 17 drawn draw VBN A47183 56 18 from from IN A47183 56 19 the the DT A47183 56 20 center center NN A47183 56 21 A a NN A47183 56 22 to to IN A47183 56 23 I -PRON- PRP A47183 56 24 , , , A47183 56 25 shall shall MD A47183 56 26 by by IN A47183 56 27 true true JJ A47183 56 28 Geometry Geometry NNP A47183 56 29 , , , A47183 56 30 trisect trisect VB A47183 56 31 the the DT A47183 56 32 given give VBN A47183 56 33 angle angle NN A47183 56 34 BAC BAC NNP A47183 56 35 . . . A47183 57 1 The the DT A47183 57 2 Demonstration Demonstration NNP A47183 57 3 . . . A47183 58 1 Seeing see VBG A47183 58 2 it -PRON- PRP A47183 58 3 is be VBZ A47183 58 4 the the DT A47183 58 5 property property NN A47183 58 6 of of IN A47183 58 7 these these DT A47183 58 8 two two CD A47183 58 9 Rules rule NNS A47183 58 10 crossing cross VBG A47183 58 11 each each DT A47183 58 12 other other JJ A47183 58 13 at at IN A47183 58 14 right right JJ A47183 58 15 Angles Angles NNP A47183 58 16 , , , A47183 58 17 where where WRB A47183 58 18 ever ever RB A47183 58 19 the the DT A47183 58 20 two two CD A47183 58 21 ends end NNS A47183 58 22 of of IN A47183 58 23 the the DT A47183 58 24 cross cross NN A47183 58 25 Rule rule NN A47183 58 26 terminates terminate NNS A47183 58 27 , , , A47183 58 28 to to TO A47183 58 29 make make VB A47183 58 30 an an DT A47183 58 31 Isosceles Isosceles NNP A47183 58 32 triangle triangle NN A47183 58 33 , , , A47183 58 34 making make VBG A47183 58 35 always always RB A47183 58 36 two two CD A47183 58 37 right right JJ A47183 58 38 angle angle NN A47183 58 39 triangles triangle NNS A47183 58 40 , , , A47183 58 41 whose whose WP$ A47183 58 42 Bases basis NNS A47183 58 43 are be VBP A47183 58 44 equal equal JJ A47183 58 45 , , , A47183 58 46 and and CC A47183 58 47 the the DT A47183 58 48 Perpendicular Perpendicular NNP A47183 58 49 common common JJ A47183 58 50 to to IN A47183 58 51 both both DT A47183 58 52 , , , A47183 58 53 therefore therefore RB A47183 58 54 by by IN A47183 58 55 the the DT A47183 58 56 4 4 CD A47183 58 57 . . . A47183 59 1 1 1 LS A47183 59 2 . . . A47183 59 3 el el NNP A47183 59 4 . . . A47183 60 1 Eucl eucl VB A47183 60 2 . . . A47183 61 1 the the DT A47183 61 2 Hypotenusals Hypotenusals NNPS A47183 61 3 are be VBP A47183 61 4 equal equal JJ A47183 61 5 . . . A47183 62 1 Therefore therefore RB A47183 62 2 with with IN A47183 62 3 Radius Radius NNP A47183 62 4 AI AI NNP A47183 62 5 describing describe VBG A47183 62 6 the the DT A47183 62 7 arch arch JJ A47183 62 8 HLIS HLIS NNP A47183 62 9 , , , A47183 62 10 draw draw VB A47183 62 11 the the DT A47183 62 12 Cord Cord NNP A47183 62 13 HI HI NNP A47183 62 14 . . . A47183 63 1 and and CC A47183 63 2 from from IN A47183 63 3 I -PRON- PRP A47183 63 4 let let VBD A47183 63 5 fall fall VB A47183 63 6 a a DT A47183 63 7 perpendicular perpendicular NN A47183 63 8 on on IN A47183 63 9 the the DT A47183 63 10 line line NN A47183 63 11 AC AC NNP A47183 63 12 . . . A47183 64 1 as as IN A47183 64 2 IK IK NNP A47183 64 3 , , , A47183 64 4 making make VBG A47183 64 5 HI HI NNP A47183 64 6 = = SYM A47183 64 7 LI LI NNP A47183 64 8 = = SYM A47183 64 9 IK IK NNP A47183 64 10 , , , A47183 64 11 therefore therefore RB A47183 64 12 the the DT A47183 64 13 arches arch NNS A47183 64 14 of of IN A47183 64 15 those those DT A47183 64 16 equal equal JJ A47183 64 17 Sines sine NNS A47183 64 18 are be VBP A47183 64 19 equal equal JJ A47183 64 20 , , , A47183 64 21 as as IN A47183 64 22 HL HL NNP A47183 64 23 = = SYM A47183 64 24 LI LI NNP A47183 64 25 = = SYM A47183 64 26 IS be VBZ A47183 64 27 . . . A47183 65 1 q.e.d q.e.d NNP A47183 65 2 . . . A47183 66 1 The the DT A47183 66 2 same same JJ A47183 66 3 or or CC A47183 66 4 any any DT A47183 66 5 other other JJ A47183 66 6 Angle Angle NNP A47183 66 7 obtruse obtruse NN A47183 66 8 or or CC A47183 66 9 acute acute NN A47183 66 10 may may MD A47183 66 11 be be VB A47183 66 12 trisected trisect VBN A47183 66 13 into into IN A47183 66 14 3 3 CD A47183 66 15 equal equal JJ A47183 66 16 parts part NNS A47183 66 17 , , , A47183 66 18 without without IN A47183 66 19 the the DT A47183 66 20 curve curve NN A47183 66 21 Line line NN A47183 66 22 , , , A47183 66 23 or or CC A47183 66 24 any any DT A47183 66 25 part part NN A47183 66 26 of of IN A47183 66 27 it -PRON- PRP A47183 66 28 , , , A47183 66 29 by by IN A47183 66 30 finding find VBG A47183 66 31 the the DT A47183 66 32 point point NN A47183 66 33 I -PRON- PRP A47183 66 34 , , , A47183 66 35 which which WDT A47183 66 36 can can MD A47183 66 37 be be VB A47183 66 38 found find VBN A47183 66 39 without without IN A47183 66 40 the the DT A47183 66 41 curve curve NN A47183 66 42 line line NN A47183 66 43 by by IN A47183 66 44 letting let VBG A47183 66 45 the the DT A47183 66 46 cross cross NN A47183 66 47 Rule rule NN A47183 66 48 slide slide NN A47183 66 49 or or CC A47183 66 50 run run VB A47183 66 51 along along IN A47183 66 52 the the DT A47183 66 53 line line NN A47183 66 54 AB AB NNP A47183 66 55 , , , A47183 66 56 ( ( -LRB- A47183 66 57 while while IN A47183 66 58 the the DT A47183 66 59 left left JJ A47183 66 60 side side NN A47183 66 61 of of IN A47183 66 62 the the DT A47183 66 63 long long JJ A47183 66 64 Rule Rule NNP A47183 66 65 still still RB A47183 66 66 runneth runneth VB A47183 66 67 through through IN A47183 66 68 the the DT A47183 66 69 center center NN A47183 66 70 A a NN A47183 66 71 ) ) -RRB- A47183 66 72 either either CC A47183 66 73 upwards upward NNS A47183 66 74 or or CC A47183 66 75 downwards downwards RB A47183 66 76 , , , A47183 66 77 until until IN A47183 66 78 the the DT A47183 66 79 right right JJ A47183 66 80 side side NN A47183 66 81 of of IN A47183 66 82 the the DT A47183 66 83 cross cross NN A47183 66 84 Rule Rule NNP A47183 66 85 touch touch VB A47183 66 86 the the DT A47183 66 87 straight straight JJ A47183 66 88 line line NN A47183 66 89 DE de NN A47183 66 90 which which WDT A47183 66 91 shall shall MD A47183 66 92 be be VB A47183 66 93 at at IN A47183 66 94 I. i. NN A47183 67 1 And and CC A47183 67 2 thus thus RB A47183 67 3 without without IN A47183 67 4 any any DT A47183 67 5 need need NN A47183 67 6 of of IN A47183 67 7 noticing notice VBG A47183 67 8 or or CC A47183 67 9 regarding regard VBG A47183 67 10 the the DT A47183 67 11 Curve Curve NNP A47183 67 12 Line Line NNP A47183 67 13 , , , A47183 67 14 the the DT A47183 67 15 Point Point NNP A47183 67 16 1 1 CD A47183 67 17 is be VBZ A47183 67 18 found find VBN A47183 67 19 , , , A47183 67 20 where where WRB A47183 67 21 the the DT A47183 67 22 two two CD A47183 67 23 straight straight JJ A47183 67 24 lines line NNS A47183 67 25 HI HI NNP A47183 67 26 and and CC A47183 67 27 DE DE NNP A47183 67 28 meet meet VB A47183 67 29 together together RB A47183 67 30 : : : A47183 67 31 And and CC A47183 67 32 as as IN A47183 67 33 thus thus RB A47183 67 34 any any DT A47183 67 35 Angle Angle NNP A47183 67 36 may may MD A47183 67 37 be be VB A47183 67 38 trisected trisect VBN A47183 67 39 without without IN A47183 67 40 drawing draw VBG A47183 67 41 any any DT A47183 67 42 Curve Curve NNP A47183 67 43 Line line NN A47183 67 44 , , , A47183 67 45 so so IN A47183 67 46 it -PRON- PRP A47183 67 47 may may MD A47183 67 48 easily easily RB A47183 67 49 and and CC A47183 67 50 truly truly RB A47183 67 51 be be VB A47183 67 52 done do VBN A47183 67 53 without without IN A47183 67 54 either either DT A47183 67 55 Scale Scale NNP A47183 67 56 or or CC A47183 67 57 Compass Compass NNP A47183 67 58 , , , A47183 67 59 other other JJ A47183 67 60 than than IN A47183 67 61 what what WP A47183 67 62 the the DT A47183 67 63 two two CD A47183 67 64 cross cross NN A47183 67 65 Rules rule NNS A47183 67 66 are be VBP A47183 67 67 , , , A47183 67 68 as as IN A47183 67 69 any any DT A47183 67 70 Artist Artist NNP A47183 67 71 may may MD A47183 67 72 easily easily RB A47183 67 73 perceive perceive VB A47183 67 74 . . . A47183 68 1 If if IN A47183 68 2 any any DT A47183 68 3 object object NN A47183 68 4 against against IN A47183 68 5 this this DT A47183 68 6 Method Method NNP A47183 68 7 , , , A47183 68 8 as as IN A47183 68 9 Mechanical Mechanical NNP A47183 68 10 , , , A47183 68 11 and and CC A47183 68 12 not not RB A47183 68 13 Mathematical mathematical JJ A47183 68 14 and and CC A47183 68 15 truly truly RB A47183 68 16 Geometrical geometrical JJ A47183 68 17 , , , A47183 68 18 because because IN A47183 68 19 performed perform VBN A47183 68 20 by by IN A47183 68 21 an an DT A47183 68 22 Instrument Instrument NNP A47183 68 23 , , , A47183 68 24 I -PRON- PRP A47183 68 25 shall shall MD A47183 68 26 refer refer VB A47183 68 27 them -PRON- PRP A47183 68 28 to to IN A47183 68 29 two two CD A47183 68 30 great great JJ A47183 68 31 Geometricians Geometricians NNPS A47183 68 32 for for IN A47183 68 33 its -PRON- PRP$ A47183 68 34 Vindication vindication NN A47183 68 35 , , , A47183 68 36 to to IN A47183 68 37 wit wit NN A47183 68 38 , , , A47183 68 39 Des Des NNP A47183 68 40 Cartes Cartes NNP A47183 68 41 in in IN A47183 68 42 his -PRON- PRP$ A47183 68 43 second second JJ A47183 68 44 Book Book NNP A47183 68 45 of of IN A47183 68 46 Geometry Geometry NNP A47183 68 47 , , , A47183 68 48 and and CC A47183 68 49 Franciscus Franciscus NNP A47183 68 50 a a DT A47183 68 51 Schoten Schoten NNP A47183 68 52 in in IN A47183 68 53 his -PRON- PRP$ A47183 68 54 Commentary Commentary NNP A47183 68 55 on on IN A47183 68 56 him -PRON- PRP A47183 68 57 , , , A47183 68 58 argum argum NNP A47183 68 59 . . . A47183 69 1 lib lib NNP A47183 69 2 . . . A47183 70 1 2 2 LS A47183 70 2 . . . A47183 70 3 both both DT A47183 70 4 which which WDT A47183 70 5 do do VBP A47183 70 6 prove prove VB A47183 70 7 that that IN A47183 70 8 what what WP A47183 70 9 is be VBZ A47183 70 10 performed perform VBN A47183 70 11 by by IN A47183 70 12 Instruments Instruments NNPS A47183 70 13 Geometrically Geometrically NNP A47183 70 14 made make VBN A47183 70 15 , , , A47183 70 16 is be VBZ A47183 70 17 Geometrical geometrical JJ A47183 70 18 , , , A47183 70 19 otherwise otherwise RB A47183 70 20 the the DT A47183 70 21 plainest plain JJS A47183 70 22 Geometry Geometry NNP A47183 70 23 must must MD A47183 70 24 be be VB A47183 70 25 rejected reject VBN A47183 70 26 , , , A47183 70 27 because because IN A47183 70 28 its -PRON- PRP$ A47183 70 29 Figures figure NNS A47183 70 30 are be VBP A47183 70 31 drawn draw VBN A47183 70 32 by by IN A47183 70 33 Rule Rule NNP A47183 70 34 and and CC A47183 70 35 Compass Compass NNP A47183 70 36 , , , A47183 70 37 both both DT A47183 70 38 which which WDT A47183 70 39 are be VBP A47183 70 40 Instruments Instruments NNPS A47183 70 41 , , , A47183 70 42 and and CC A47183 70 43 not not RB A47183 70 44 only only RB A47183 70 45 Parabolas parabola NNS A47183 70 46 , , , A47183 70 47 and and CC A47183 70 48 other other JJ A47183 70 49 Conick Conick NNP A47183 70 50 Sections Sections NNPS A47183 70 51 which which WDT A47183 70 52 are be VBP A47183 70 53 Curves curve NNS A47183 70 54 , , , A47183 70 55 but but CC A47183 70 56 divers diver VBZ A47183 70 57 other other JJ A47183 70 58 Curves Curves NNPS A47183 70 59 , , , A47183 70 60 yea yea NNP A47183 70 61 , , , A47183 70 62 all all DT A47183 70 63 such such JJ A47183 70 64 that that WDT A47183 70 65 can can MD A47183 70 66 be be VB A47183 70 67 drawn draw VBN A47183 70 68 by by IN A47183 70 69 Art art NN A47183 70 70 , , , A47183 70 71 with with IN A47183 70 72 the the DT A47183 70 73 help help NN A47183 70 74 of of IN A47183 70 75 Instruments Instruments NNPS A47183 70 76 , , , A47183 70 77 such such JJ A47183 70 78 as as IN A47183 70 79 they -PRON- PRP A47183 70 80 have have VBP A47183 70 81 devised devise VBN A47183 70 82 , , , A47183 70 83 they -PRON- PRP A47183 70 84 contend contend VBP A47183 70 85 to to TO A47183 70 86 be be VB A47183 70 87 truly truly RB A47183 70 88 Geometrical geometrical JJ A47183 70 89 ; ; : A47183 70 90 and and CC A47183 70 91 both both DT A47183 70 92 of of IN A47183 70 93 them -PRON- PRP A47183 70 94 in in IN A47183 70 95 their -PRON- PRP$ A47183 70 96 Geometrical Geometrical NNP A47183 70 97 Treatises Treatises NNPS A47183 70 98 , , , A47183 70 99 use use VB A47183 70 100 divers diver NNS A47183 70 101 Instruments instrument NNS A47183 70 102 for for IN A47183 70 103 describing describe VBG A47183 70 104 Curves Curves NNP A47183 70 105 Geometrically geometrically RB A47183 70 106 much much RB A47183 70 107 more more RBR A47183 70 108 difficult difficult JJ A47183 70 109 to to TO A47183 70 110 be be VB A47183 70 111 made make VBN A47183 70 112 , , , A47183 70 113 and and CC A47183 70 114 with with IN A47183 70 115 more more JJR A47183 70 116 difficulty difficulty NN A47183 70 117 to to TO A47183 70 118 be be VB A47183 70 119 used use VBN A47183 70 120 , , , A47183 70 121 than than IN A47183 70 122 what what WP A47183 70 123 is be VBZ A47183 70 124 here here RB A47183 70 125 proposed propose VBN A47183 70 126 of of IN A47183 70 127 two two CD A47183 70 128 simple simple JJ A47183 70 129 Rules rule NNS A47183 70 130 , , , A47183 70 131 cutting cut VBG A47183 70 132 one one CD A47183 70 133 another another DT A47183 70 134 at at IN A47183 70 135 right right JJ A47183 70 136 Angles Angles NNP A47183 70 137 . . . A47183 71 1 And and CC A47183 71 2 seeing see VBG A47183 71 3 it -PRON- PRP A47183 71 4 hath hath NN A47183 71 5 no no DT A47183 71 6 dependance dependance NN A47183 71 7 on on IN A47183 71 8 Solids solid NNS A47183 71 9 , , , A47183 71 10 or or CC A47183 71 11 Algebra Algebra NNP A47183 71 12 Equations Equations NNPS A47183 71 13 , , , A47183 71 14 and and CC A47183 71 15 may may MD A47183 71 16 be be VB A47183 71 17 done do VBN A47183 71 18 without without IN A47183 71 19 any any DT A47183 71 20 Curve Curve NNP A47183 71 21 Line Line NNP A47183 71 22 , , , A47183 71 23 as as IN A47183 71 24 is be VBZ A47183 71 25 above above RB A47183 71 26 showed show VBN A47183 71 27 , , , A47183 71 28 and and CC A47183 71 29 whose whose WP$ A47183 71 30 demonstration demonstration NN A47183 71 31 wholly wholly RB A47183 71 32 depends depend VBZ A47183 71 33 on on IN A47183 71 34 a a DT A47183 71 35 few few JJ A47183 71 36 easie easie JJ A47183 71 37 Propositions proposition NNS A47183 71 38 of of IN A47183 71 39 the the DT A47183 71 40 first first JJ A47183 71 41 Book Book NNP A47183 71 42 of of IN A47183 71 43 Euclid Euclid NNP A47183 71 44 , , , A47183 71 45 I -PRON- PRP A47183 71 46 see see VBP A47183 71 47 not not RB A47183 71 48 why why WRB A47183 71 49 it -PRON- PRP A47183 71 50 may may MD A47183 71 51 not not RB A47183 71 52 be be VB A47183 71 53 called call VBN A47183 71 54 Plain Plain NNP A47183 71 55 Geometry Geometry NNP A47183 71 56 : : : A47183 71 57 And and CC A47183 71 58 as as IN A47183 71 59 the the DT A47183 71 60 word word NN A47183 71 61 Mechanical Mechanical NNP A47183 71 62 is be VBZ A47183 71 63 used use VBN A47183 71 64 to to TO A47183 71 65 signifie signifie VB A47183 71 66 a a DT A47183 71 67 thing thing NN A47183 71 68 not not RB A47183 71 69 Mathematically mathematically RB A47183 71 70 exact exact JJ A47183 71 71 , , , A47183 71 72 but but CC A47183 71 73 coming come VBG A47183 71 74 near near RB A47183 71 75 to to IN A47183 71 76 it -PRON- PRP A47183 71 77 by by IN A47183 71 78 Approximation approximation NN A47183 71 79 , , , A47183 71 80 in in IN A47183 71 81 this this DT A47183 71 82 sense sense NN A47183 71 83 it -PRON- PRP A47183 71 84 is be VBZ A47183 71 85 not not RB A47183 71 86 Mechanical mechanical JJ A47183 71 87 , , , A47183 71 88 but but CC A47183 71 89 Mathematical Mathematical NNP A47183 71 90 , , , A47183 71 91 and and CC A47183 71 92 purely purely RB A47183 71 93 Geometrical Geometrical NNP A47183 71 94 , , , A47183 71 95 being be VBG A47183 71 96 grounded ground VBN A47183 71 97 on on IN A47183 71 98 as as RB A47183 71 99 good good JJ A47183 71 100 demonstration demonstration NN A47183 71 101 , , , A47183 71 102 as as IN A47183 71 103 any any DT A47183 71 104 Propositions Propositions NNPS A47183 71 105 in in IN A47183 71 106 Euclid Euclid NNP A47183 71 107 , , , A47183 71 108 and and CC A47183 71 109 being being NN A47183 71 110 but but CC A47183 71 111 a a DT A47183 71 112 Corrolary Corrolary NNP A47183 71 113 from from IN A47183 71 114 some some DT A47183 71 115 of of IN A47183 71 116 them -PRON- PRP A47183 71 117 . . . A47183 72 1 The the DT A47183 72 2 next next JJ A47183 72 3 thing thing NN A47183 72 4 to to TO A47183 72 5 be be VB A47183 72 6 shown show VBN A47183 72 7 is be VBZ A47183 72 8 the the DT A47183 72 9 Quinquisection Quinquisection NNP A47183 72 10 , , , A47183 72 11 where where WRB A47183 72 12 to to TO A47183 72 13 make make VB A47183 72 14 one one CD A47183 72 15 Figure figure NN A47183 72 16 serve serve VB A47183 72 17 to to IN A47183 72 18 both both DT A47183 72 19 , , , A47183 72 20 I -PRON- PRP A47183 72 21 make make VBP A47183 72 22 the the DT A47183 72 23 Cross Cross NNP A47183 72 24 Rule Rule NNP A47183 72 25 only only RB A47183 72 26 one one CD A47183 72 27 Inch Inch NNP A47183 72 28 and and CC A47183 72 29 one one CD A47183 72 30 4th 4th JJ A47183 72 31 part part NN A47183 72 32 from from IN A47183 72 33 the the DT A47183 72 34 middle middle JJ A47183 72 35 line line NN A47183 72 36 AM AM NNP A47183 72 37 , , , A47183 72 38 setting set VBG A47183 72 39 off off RP A47183 72 40 on on IN A47183 72 41 both both DT A47183 72 42 sides side NNS A47183 72 43 one one CD A47183 72 44 half half NN A47183 72 45 of of IN A47183 72 46 the the DT A47183 72 47 length length NN A47183 72 48 of of IN A47183 72 49 the the DT A47183 72 50 cross cross NN A47183 72 51 Rule rule NN A47183 72 52 , , , A47183 72 53 draw draw VB A47183 72 54 the the DT A47183 72 55 paralel paralel NNS A47183 72 56 Lines line NNS A47183 72 57 ad ad NN A47183 72 58 and and CC A47183 72 59 be be VB A47183 72 60 , , , A47183 72 61 then then RB A47183 72 62 let let VB A47183 72 63 the the DT A47183 72 64 cross cross NN A47183 72 65 Rule rule NN A47183 72 66 side side NN A47183 72 67 along along IN A47183 72 68 the the DT A47183 72 69 line line NN A47183 72 70 AB AB NNP A47183 72 71 , , , A47183 72 72 as as IN A47183 72 73 in in IN A47183 72 74 the the DT A47183 72 75 Trisection Trisection NNP A47183 72 76 , , , A47183 72 77 while while IN A47183 72 78 the the DT A47183 72 79 left left JJ A47183 72 80 side side NN A47183 72 81 of of IN A47183 72 82 the the DT A47183 72 83 long long JJ A47183 72 84 Rule rule NN A47183 72 85 slides slide VBZ A47183 72 86 through through IN A47183 72 87 the the DT A47183 72 88 center center NN A47183 72 89 A a NN A47183 72 90 , , , A47183 72 91 the the DT A47183 72 92 other other JJ A47183 72 93 end end NN A47183 72 94 of of IN A47183 72 95 the the DT A47183 72 96 cross cross NN A47183 72 97 Rule rule NN A47183 72 98 shall shall MD A47183 72 99 describe describe VB A47183 72 100 a a DT A47183 72 101 Curve curve NN A47183 72 102 , , , A47183 72 103 a a DT A47183 72 104 part part NN A47183 72 105 of of IN A47183 72 106 which which WDT A47183 72 107 shall shall MD A47183 72 108 be be VB A47183 72 109 g g NN A47183 72 110 h h NN A47183 72 111 , , , A47183 72 112 that that WDT A47183 72 113 may may MD A47183 72 114 be be VB A47183 72 115 continued continue VBN A47183 72 116 at at IN A47183 72 117 pleasure pleasure NN A47183 72 118 . . . A47183 73 1 Again again RB A47183 73 2 , , , A47183 73 3 setting set VBG A47183 73 4 the the DT A47183 73 5 right right JJ A47183 73 6 end end NN A47183 73 7 of of IN A47183 73 8 the the DT A47183 73 9 cross cross NN A47183 73 10 Rule rule NN A47183 73 11 one one CD A47183 73 12 the the DT A47183 73 13 Point Point NNP A47183 73 14 d d XX A47183 73 15 , , , A47183 73 16 let let VB A47183 73 17 it -PRON- PRP A47183 73 18 slide slide VB A47183 73 19 or or CC A47183 73 20 move move VB A47183 73 21 along along IN A47183 73 22 the the DT A47183 73 23 Line Line NNP A47183 73 24 da da NNP A47183 73 25 , , , A47183 73 26 ( ( -LRB- A47183 73 27 while while IN A47183 73 28 the the DT A47183 73 29 left left JJ A47183 73 30 side side NN A47183 73 31 of of IN A47183 73 32 the the DT A47183 73 33 long long JJ A47183 73 34 Rule Rule NNP A47183 73 35 runneth runneth NN A47183 73 36 through through IN A47183 73 37 the the DT A47183 73 38 center center NN A47183 73 39 A a NN A47183 73 40 , , , A47183 73 41 ) ) -RRB- A47183 73 42 the the DT A47183 73 43 left left JJ A47183 73 44 end end NN A47183 73 45 of of IN A47183 73 46 the the DT A47183 73 47 cross cross NN A47183 73 48 Rule rule NN A47183 73 49 shall shall MD A47183 73 50 describe describe VB A47183 73 51 a a DT A47183 73 52 part part NN A47183 73 53 of of IN A47183 73 54 another another DT A47183 73 55 Curve Curve NNP A47183 73 56 , , , A47183 73 57 meeting meet VBG A47183 73 58 at at IN A47183 73 59 h h NN A47183 73 60 the the DT A47183 73 61 other other JJ A47183 73 62 Curve curve NN A47183 73 63 . . . A47183 74 1 And and CC A47183 74 2 having have VBG A47183 74 3 found find VBN A47183 74 4 the the DT A47183 74 5 point point NN A47183 74 6 h h NN A47183 74 7 with with IN A47183 74 8 radius radius NN A47183 74 9 A a NN A47183 74 10 h h NN A47183 74 11 describe describe VB A47183 74 12 the the DT A47183 74 13 Arch Arch NNP A47183 74 14 v v NN A47183 74 15 h h NN A47183 74 16 z z NN A47183 74 17 x x SYM A47183 74 18 y y NN A47183 74 19 N n NN A47183 74 20 which which WDT A47183 74 21 shall shall MD A47183 74 22 give give VB A47183 74 23 v v NN A47183 74 24 h h NN A47183 74 25 = = SYM A47183 74 26 one one CD A47183 74 27 fifth fifth NN A47183 74 28 of of IN A47183 74 29 the the DT A47183 74 30 whole whole JJ A47183 74 31 Arch Arch NNP A47183 74 32 , , , A47183 74 33 as as IN A47183 74 34 is be VBZ A47183 74 35 evident evident JJ A47183 74 36 from from IN A47183 74 37 the the DT A47183 74 38 foregoing foregoing NN A47183 74 39 demonstration demonstration NN A47183 74 40 . . . A47183 75 1 The the DT A47183 75 2 Quinquisection Quinquisection NNP A47183 75 3 also also RB A47183 75 4 may may MD A47183 75 5 be be VB A47183 75 6 made make VBN A47183 75 7 without without IN A47183 75 8 any any DT A47183 75 9 Curve curve NN A47183 75 10 , , , A47183 75 11 if if IN A47183 75 12 two two CD A47183 75 13 long long JJ A47183 75 14 Rules rule NNS A47183 75 15 be be VB A47183 75 16 jointed joint VBN A47183 75 17 together together RB A47183 75 18 like like IN A47183 75 19 a a DT A47183 75 20 Sector sector NN A47183 75 21 , , , A47183 75 22 and and CC A47183 75 23 each each DT A47183 75 24 have have VBP A47183 75 25 a a DT A47183 75 26 moveable moveable JJ A47183 75 27 cross cross NN A47183 75 28 Rule rule NN A47183 75 29 to to TO A47183 75 30 move move VB A47183 75 31 on on IN A47183 75 32 them -PRON- PRP A47183 75 33 at at IN A47183 75 34 right right JJ A47183 75 35 Angles Angles NNPS A47183 75 36 , , , A47183 75 37 with with IN A47183 75 38 the the DT A47183 75 39 long long JJ A47183 75 40 Rules rule NNS A47183 75 41 . . . A47183 76 1 For for IN A47183 76 2 let let VBN A47183 76 3 the the DT A47183 76 4 center center NN A47183 76 5 of of IN A47183 76 6 the the DT A47183 76 7 two two CD A47183 76 8 long long JJ A47183 76 9 Rules rule NNS A47183 76 10 be be VB A47183 76 11 fixed fix VBN A47183 76 12 on on IN A47183 76 13 the the DT A47183 76 14 center center NN A47183 76 15 A a NN A47183 76 16 , , , A47183 76 17 and and CC A47183 76 18 let let VB A47183 76 19 the the DT A47183 76 20 2 2 CD A47183 76 21 cross cross NN A47183 76 22 Rules rule NNS A47183 76 23 be be VB A47183 76 24 moved move VBN A47183 76 25 together together RB A47183 76 26 from from IN A47183 76 27 B b NN A47183 76 28 and and CC A47183 76 29 d d XX A47183 76 30 , , , A47183 76 31 until until IN A47183 76 32 ( ( -LRB- A47183 76 33 the the DT A47183 76 34 left left JJ A47183 76 35 end end NN A47183 76 36 of of IN A47183 76 37 the the DT A47183 76 38 one one NN A47183 76 39 still still RB A47183 76 40 touching touch VBG A47183 76 41 the the DT A47183 76 42 right right JJ A47183 76 43 end end NN A47183 76 44 of of IN A47183 76 45 the the DT A47183 76 46 other other JJ A47183 76 47 ) ) -RRB- A47183 76 48 the the DT A47183 76 49 right right JJ A47183 76 50 end end NN A47183 76 51 of of IN A47183 76 52 the the DT A47183 76 53 Cross Cross NNP A47183 76 54 nearest nearest RB A47183 76 55 to to IN A47183 76 56 the the DT A47183 76 57 Line Line NNP A47183 76 58 a a DT A47183 76 59 d d NN A47183 76 60 touch touch NN A47183 76 61 upon upon IN A47183 76 62 some some DT A47183 76 63 Point point NN A47183 76 64 of of IN A47183 76 65 it -PRON- PRP A47183 76 66 as as IN A47183 76 67 at at IN A47183 76 68 W w NN A47183 76 69 , , , A47183 76 70 the the DT A47183 76 71 Point Point NNP A47183 76 72 at at IN A47183 76 73 W w NN A47183 76 74 shall shall MD A47183 76 75 give give VB A47183 76 76 the the DT A47183 76 77 Quinquisection Quinquisection NNP A47183 76 78 as as IN A47183 76 79 above above RB A47183 76 80 . . . A47183 77 1 And and CC A47183 77 2 thus thus RB A47183 77 3 a a DT A47183 77 4 true true JJ A47183 77 5 Geometrical Geometrical NNP A47183 77 6 Line Line NNP A47183 77 7 of of IN A47183 77 8 Cords Cords NNPS A47183 77 9 may may MD A47183 77 10 be be VB A47183 77 11 made make VBN A47183 77 12 by by IN A47183 77 13 any any DT A47183 77 14 Tiro Tiro NNP A47183 77 15 , , , A47183 77 16 without without IN A47183 77 17 any any DT A47183 77 18 Conick Conick NNP A47183 77 19 Section Section NNP A47183 77 20 , , , A47183 77 21 or or CC A47183 77 22 Algebra Algebra NNP A47183 77 23 Equation Equation NNP A47183 77 24 , , , A47183 77 25 and and CC A47183 77 26 without without IN A47183 77 27 any any DT A47183 77 28 Table table NN A47183 77 29 of of IN A47183 77 30 Natural Natural NNP A47183 77 31 Sines Sines NNPS A47183 77 32 or or CC A47183 77 33 Arithmetical Arithmetical NNP A47183 77 34 Operation Operation NNP A47183 77 35 ; ; : A47183 77 36 for for IN A47183 77 37 whereas whereas IN A47183 77 38 Euclid Euclid NNP A47183 77 39 ( ( -LRB- A47183 77 40 11.4 11.4 CD A47183 77 41 . . . A47183 77 42 ) ) -RRB- A47183 78 1 hath hath NNP A47183 78 2 taught teach VBD A47183 78 3 how how WRB A47183 78 4 to to TO A47183 78 5 find find VB A47183 78 6 the the DT A47183 78 7 Cord Cord NNP A47183 78 8 of of IN A47183 78 9 36 36 CD A47183 78 10 degr degr NN A47183 78 11 . . . A47183 79 1 and and CC A47183 79 2 also also RB A47183 79 3 it -PRON- PRP A47183 79 4 is be VBZ A47183 79 5 found find VBN A47183 79 6 by by IN A47183 79 7 Quinquisecting quinquisecte VBG A47183 79 8 the the DT A47183 79 9 half half NN A47183 79 10 Circle Circle NNP A47183 79 11 , , , A47183 79 12 as as IN A47183 79 13 is be VBZ A47183 79 14 above above RB A47183 79 15 shewed shew VBN A47183 79 16 , , , A47183 79 17 it -PRON- PRP A47183 79 18 remains remain VBZ A47183 79 19 only only RB A47183 79 20 to to TO A47183 79 21 trisect trisect VB A47183 79 22 the the DT A47183 79 23 Arch Arch NNP A47183 79 24 of of IN A47183 79 25 120 120 CD A47183 79 26 degr degr NN A47183 79 27 . . . A47183 80 1 which which WDT A47183 80 2 giveth giveth VBZ A47183 80 3 the the DT A47183 80 4 Cord Cord NNP A47183 80 5 of of IN A47183 80 6 40 40 CD A47183 80 7 , , , A47183 80 8 and and CC A47183 80 9 36 36 CD A47183 80 10 taken take VBN A47183 80 11 from from IN A47183 80 12 40 40 CD A47183 80 13 , , , A47183 80 14 leaveth leaveth NNP A47183 80 15 4 4 CD A47183 80 16 degr degr NN A47183 80 17 . . . A47183 81 1 which which WDT A47183 81 2 bisected bisect VBD A47183 81 3 gives give VBZ A47183 81 4 2 2 CD A47183 81 5 , , , A47183 81 6 and and CC A47183 81 7 that that DT A47183 81 8 bisected bisect VBD A47183 81 9 giveth giveth NNP A47183 81 10 1 1 CD A47183 81 11 , , , A47183 81 12 which which WDT A47183 81 13 is be VBZ A47183 81 14 the the DT A47183 81 15 one one CD A47183 81 16 360th 360th JJ A47183 81 17 part part NN A47183 81 18 of of IN A47183 81 19 the the DT A47183 81 20 Circle Circle NNP A47183 81 21 , , , A47183 81 22 and and CC A47183 81 23 one one CD A47183 81 24 90th 90th NN A47183 81 25 of of IN A47183 81 26 the the DT A47183 81 27 Quadrant Quadrant NNP A47183 81 28 ; ; : A47183 81 29 and and CC A47183 81 30 this this DT A47183 81 31 is be VBZ A47183 81 32 more more RBR A47183 81 33 methodical methodical JJ A47183 81 34 than than IN A47183 81 35 to to TO A47183 81 36 teach teach VB A47183 81 37 a a DT A47183 81 38 beginner beginner NN A47183 81 39 to to TO A47183 81 40 make make VB A47183 81 41 his -PRON- PRP$ A47183 81 42 Line Line NNP A47183 81 43 of of IN A47183 81 44 Cords Cords NNPS A47183 81 45 , , , A47183 81 46 for for IN A47183 81 47 projecting projecting NN A47183 81 48 of of IN A47183 81 49 Angles angle NNS A47183 81 50 , , , A47183 81 51 by by IN A47183 81 52 sending send VBG A47183 81 53 him -PRON- PRP A47183 81 54 to to IN A47183 81 55 Conick Conick NNP A47183 81 56 Sections Sections NNPS A47183 81 57 , , , A47183 81 58 and and CC A47183 81 59 Algebra Algebra NNP A47183 81 60 Equations Equations NNPS A47183 81 61 or or CC A47183 81 62 the the DT A47183 81 63 Table table NN A47183 81 64 of of IN A47183 81 65 Natural Natural NNP A47183 81 66 Sines Sines NNPS A47183 81 67 , , , A47183 81 68 which which WDT A47183 81 69 he -PRON- PRP A47183 81 70 is be VBZ A47183 81 71 not not RB A47183 81 72 capable capable JJ A47183 81 73 at at IN A47183 81 74 his -PRON- PRP$ A47183 81 75 entry entry NN A47183 81 76 , , , A47183 81 77 nor nor CC A47183 81 78 after after IN A47183 81 79 he -PRON- PRP A47183 81 80 has have VBZ A47183 81 81 made make VBN A47183 81 82 some some DT A47183 81 83 good good JJ A47183 81 84 progress progress NN A47183 81 85 to to TO A47183 81 86 understand understand VB A47183 81 87 ( ( -LRB- A47183 81 88 it -PRON- PRP A47183 81 89 being be VBG A47183 81 90 to to TO A47183 81 91 teach teach VB A47183 81 92 ignotum ignotum NN A47183 81 93 per per IN A47183 81 94 ignotius ignotius NN A47183 81 95 an an DT A47183 81 96 unknown unknown JJ A47183 81 97 thing thing NN A47183 81 98 by by IN A47183 81 99 a a DT A47183 81 100 more more RBR A47183 81 101 unknown unknown JJ A47183 81 102 ) ) -RRB- A47183 81 103 quite quite RB A47183 81 104 contrary contrary JJ A47183 81 105 to to IN A47183 81 106 all all DT A47183 81 107 good good JJ A47183 81 108 method method NN A47183 81 109 of of IN A47183 81 110 true true JJ A47183 81 111 Science Science NNP A47183 81 112 , , , A47183 81 113 such such JJ A47183 81 114 as as IN A47183 81 115 Geometry Geometry NNP A47183 81 116 is be VBZ A47183 81 117 . . . A47183 82 1 The the DT A47183 82 2 method method NN A47183 82 3 of of IN A47183 82 4 the the DT A47183 82 5 Quinquisection Quinquisection NNP A47183 82 6 here here RB A47183 82 7 delivered deliver VBD A47183 82 8 , , , A47183 82 9 sufficiently sufficiently RB A47183 82 10 showeth showeth VBZ A47183 82 11 without without IN A47183 82 12 example example NN A47183 82 13 , , , A47183 82 14 any any DT A47183 82 15 other other JJ A47183 82 16 Section Section NNP A47183 82 17 desired desire VBN A47183 82 18 . . . A47183 83 1 The the DT A47183 83 2 Corrolaries Corrolaries NNPS A47183 83 3 mentioned mention VBD A47183 83 4 in in IN A47183 83 5 the the DT A47183 83 6 former former JJ A47183 83 7 Treatise Treatise NNP A47183 83 8 , , , A47183 83 9 with with IN A47183 83 10 the the DT A47183 83 11 Rectification Rectification NNP A47183 83 12 here here RB A47183 83 13 made make VBN A47183 83 14 , , , A47183 83 15 are be VBP A47183 83 16 all all DT A47183 83 17 valid valid JJ A47183 83 18 , , , A47183 83 19 some some DT A47183 83 20 of of IN A47183 83 21 the the DT A47183 83 22 chief chief NN A47183 83 23 of of IN A47183 83 24 them -PRON- PRP A47183 83 25 I -PRON- PRP A47183 83 26 shall shall MD A47183 83 27 here here RB A47183 83 28 mention mention VB A47183 83 29 . . . A47183 84 1 1 1 LS A47183 84 2 . . . A47183 85 1 One one CD A47183 85 2 great great JJ A47183 85 3 Use Use NNP A47183 85 4 is be VBZ A47183 85 5 to to TO A47183 85 6 teach teach VB A47183 85 7 a a DT A47183 85 8 beginner beginner NN A47183 85 9 how how WRB A47183 85 10 to to TO A47183 85 11 make make VB A47183 85 12 a a DT A47183 85 13 true true JJ A47183 85 14 Line Line NNP A47183 85 15 of of IN A47183 85 16 Cords Cords NNPS A47183 85 17 , , , A47183 85 18 as as IN A47183 85 19 is be VBZ A47183 85 20 above above RB A47183 85 21 showed show VBN A47183 85 22 , , , A47183 85 23 and and CC A47183 85 24 how how WRB A47183 85 25 to to TO A47183 85 26 divide divide VB A47183 85 27 a a DT A47183 85 28 Circle Circle NNP A47183 85 29 into into IN A47183 85 30 any any DT A47183 85 31 parts part NNS A47183 85 32 required require VBN A47183 85 33 . . . A47183 86 1 2 2 LS A47183 86 2 . . . A47183 87 1 Another another DT A47183 87 2 great great JJ A47183 87 3 use use NN A47183 87 4 Descartes Descartes NNPS A47183 87 5 showeth showeth VBZ A47183 87 6 in in IN A47183 87 7 his -PRON- PRP$ A47183 87 8 third third JJ A47183 87 9 Book Book NNP A47183 87 10 of of IN A47183 87 11 Geometry Geometry NNP A47183 87 12 , , , A47183 87 13 for for IN A47183 87 14 the the DT A47183 87 15 resolving resolve VBG A47183 87 16 any any DT A47183 87 17 such such JJ A47183 87 18 Equation Equation NNP A47183 87 19 in in IN A47183 87 20 Algebra Algebra NNP A47183 87 21 as as IN A47183 87 22 z z NN A47183 87 23 3 3 CD A47183 87 24 = = SYM A47183 87 25 + + CC A47183 87 26 p p NN A47183 87 27 zq zq NN A47183 87 28 , , , A47183 87 29 where where WRB A47183 87 30 the the DT A47183 87 31 Root Root NNP A47183 87 32 z z NNP A47183 87 33 is be VBZ A47183 87 34 an an DT A47183 87 35 unknown unknown JJ A47183 87 36 quantity quantity NN A47183 87 37 , , , A47183 87 38 and and CC A47183 87 39 can can MD A47183 87 40 be be VB A47183 87 41 found find VBN A47183 87 42 by by IN A47183 87 43 the the DT A47183 87 44 Trisection Trisection NNP A47183 87 45 of of IN A47183 87 46 an an DT A47183 87 47 Angle angle NN A47183 87 48 . . . A47183 88 1 3 3 LS A47183 88 2 . . . A47183 89 1 A a DT A47183 89 2 third third JJ A47183 89 3 great great JJ A47183 89 4 use use NN A47183 89 5 is be VBZ A47183 89 6 to to TO A47183 89 7 give give VB A47183 89 8 some some DT A47183 89 9 New New NNP A47183 89 10 Promblems Promblems NNPS A47183 89 11 in in IN A47183 89 12 Practical Practical NNP A47183 89 13 Geometry Geometry NNP A47183 89 14 , , , A47183 89 15 one one CD A47183 89 16 whereof whereof IN A47183 89 17 I -PRON- PRP A47183 89 18 shall shall MD A47183 89 19 here here RB A47183 89 20 show show VB A47183 89 21 . . . A47183 90 1 Let let VB A47183 90 2 a a DT A47183 90 3 straight straight JJ A47183 90 4 Line line NN A47183 90 5 A A NNP A47183 90 6 F f NN A47183 90 7 be be VB A47183 90 8 given give VBN A47183 90 9 , , , A47183 90 10 ( ( -LRB- A47183 90 11 see see VB A47183 90 12 the the DT A47183 90 13 second second JJ A47183 90 14 Figure figure NN A47183 90 15 ) ) -RRB- A47183 90 16 and and CC A47183 90 17 it -PRON- PRP A47183 90 18 is be VBZ A47183 90 19 required require VBN A47183 90 20 on on IN A47183 90 21 the the DT A47183 90 22 point point NN A47183 90 23 A a NN A47183 90 24 to to TO A47183 90 25 erect erect VB A47183 90 26 an an DT A47183 90 27 Isosceles Isosceles NNP A47183 90 28 ABC ABC NNP A47183 90 29 , , , A47183 90 30 whose whose WP$ A47183 90 31 side side NN A47183 90 32 BC BC NNP A47183 90 33 produced produce VBD A47183 90 34 , , , A47183 90 35 shall shall MD A47183 90 36 terminate terminate VB A47183 90 37 on on IN A47183 90 38 a a DT A47183 90 39 limited limited JJ A47183 90 40 point point NN A47183 90 41 D d NN A47183 90 42 , , , A47183 90 43 under under IN A47183 90 44 the the DT A47183 90 45 given give VBN A47183 90 46 straight straight JJ A47183 90 47 line line NN A47183 90 48 AF AF NNP A47183 90 49 . . . A47183 91 1 The the DT A47183 91 2 construction construction NN A47183 91 3 is be VBZ A47183 91 4 thus thus RB A47183 91 5 , , , A47183 91 6 draw draw VB A47183 91 7 a a DT A47183 91 8 straight straight JJ A47183 91 9 Line line NN A47183 91 10 from from IN A47183 91 11 D d NN A47183 91 12 to to IN A47183 91 13 A a NN A47183 91 14 , , , A47183 91 15 as as IN A47183 91 16 D D NNP A47183 91 17 A A NNP A47183 91 18 , , , A47183 91 19 next next JJ A47183 91 20 make make VB A47183 91 21 the the DT A47183 91 22 right right JJ A47183 91 23 Angle Angle NNP A47183 91 24 FAE FAE NNP A47183 91 25 . . . A47183 92 1 Divide divide VB A47183 92 2 the the DT A47183 92 3 angle angle NN A47183 92 4 EAD ead NN A47183 92 5 into into IN A47183 92 6 three three CD A47183 92 7 equal equal JJ A47183 92 8 parts part NNS A47183 92 9 , , , A47183 92 10 and and CC A47183 92 11 with with IN A47183 92 12 radius radius NN A47183 92 13 AD ad NN A47183 92 14 describe describe VBP A47183 92 15 the the DT A47183 92 16 Semicircle Semicircle NNP A47183 92 17 GFE GFE NNP A47183 92 18 . . . A47183 93 1 From from IN A47183 93 2 C C NNP A47183 93 3 to to IN A47183 93 4 B b NN A47183 93 5 set set VBD A47183 93 6 off off RP A47183 93 7 GB GB NNP A47183 93 8 = = SYM A47183 93 9 ED ED NNP A47183 93 10 . . . A47183 94 1 Then then RB A47183 94 2 draw draw VB A47183 94 3 the the DT A47183 94 4 line line NN A47183 94 5 AB AB NNP A47183 94 6 , , , A47183 94 7 and and CC A47183 94 8 from from IN A47183 94 9 B b NN A47183 94 10 draw draw VB A47183 94 11 the the DT A47183 94 12 line line NN A47183 94 13 BCD BCD NNP A47183 94 14 , , , A47183 94 15 which which WDT A47183 94 16 shall shall MD A47183 94 17 form form VB A47183 94 18 the the DT A47183 94 19 Isosceles Isosceles NNPS A47183 94 20 triangle triangle VBP A47183 94 21 ABC ABC NNP A47183 94 22 , , , A47183 94 23 whose whose WP$ A47183 94 24 side side NN A47183 94 25 BC BC NNP A47183 94 26 being be VBG A47183 94 27 produced produce VBN A47183 94 28 , , , A47183 94 29 shall shall MD A47183 94 30 terminate terminate VB A47183 94 31 on on IN A47183 94 32 D. D. NNP A47183 94 33 q.e.f q.e.f NNP A47183 94 34 . . . A47183 95 1 the the DT A47183 95 2 use use NN A47183 95 3 of of IN A47183 95 4 this this DT A47183 95 5 is be VBZ A47183 95 6 obvious obvious JJ A47183 95 7 in in IN A47183 95 8 Architecture Architecture NNP A47183 95 9 . . . A47183 96 1 4 4 LS A47183 96 2 . . . A47183 97 1 A a DT A47183 97 2 fourth fourth JJ A47183 97 3 great great JJ A47183 97 4 use use NN A47183 97 5 is be VBZ A47183 97 6 to to TO A47183 97 7 give give VB A47183 97 8 us -PRON- PRP A47183 97 9 some some DT A47183 97 10 New New NNP A47183 97 11 Problems Problems NNPS A47183 97 12 in in IN A47183 97 13 Geography Geography NNP A47183 97 14 and and CC A47183 97 15 Navigation Navigation NNP A47183 97 16 . . . A47183 98 1 Example example NN A47183 98 2 . . . A47183 99 1 There there EX A47183 99 2 are be VBP A47183 99 3 four four CD A47183 99 4 places place NNS A47183 99 5 A. a. NN A47183 100 1 B B NNP A47183 100 2 C. C. NNP A47183 100 3 D D NNP A47183 100 4 so so RB A47183 100 5 situated situated JJ A47183 100 6 . . . A47183 101 1 A a DT A47183 101 2 is be VBZ A47183 101 3 distant distant JJ A47183 101 4 from from IN A47183 101 5 D D NNP A47183 101 6 100 100 CD A47183 101 7 Leagues Leagues NNPS A47183 101 8 , , , A47183 101 9 and and CC A47183 101 10 beareth beareth NNP A47183 101 11 South South NNP A47183 101 12 - - : A47183 101 13 Easterly easterly RB A47183 101 14 from from IN A47183 101 15 it -PRON- PRP A47183 101 16 70 70 CD A47183 101 17 degr degr NN A47183 101 18 . . . A47183 102 1 B b NN A47183 102 2 is be VBZ A47183 102 3 distant distant JJ A47183 102 4 from from IN A47183 102 5 A A NNP A47183 102 6 100 100 CD A47183 102 7 Leagues Leagues NNPS A47183 102 8 South South NNP A47183 102 9 - - HYPH A47183 102 10 Westerly Westerly NNP A47183 102 11 . . . A47183 103 1 C C NNP A47183 103 2 is be VBZ A47183 103 3 distant distant JJ A47183 103 4 from from IN A47183 103 5 B B NNP A47183 103 6 100 100 CD A47183 103 7 Leagues Leagues NNPS A47183 103 8 North North NNP A47183 103 9 - - HYPH A47183 103 10 Westerly Westerly NNP A47183 103 11 C C NNP A47183 103 12 and and CC A47183 103 13 A a NN A47183 103 14 are be VBP A47183 103 15 in in IN A47183 103 16 the the DT A47183 103 17 same same JJ A47183 103 18 Latitude Latitude NNP A47183 103 19 and and CC A47183 103 20 so so IN A47183 103 21 that that IN A47183 103 22 these these DT A47183 103 23 three three CD A47183 103 24 places place NNS A47183 103 25 B. B. NNP A47183 103 26 C. C. NNP A47183 103 27 D D NNP A47183 103 28 lie lie NN A47183 103 29 in in IN A47183 103 30 a a DT A47183 103 31 straight straight JJ A47183 103 32 Line line NN A47183 103 33 one one NN A47183 103 34 from from IN A47183 103 35 another another DT A47183 103 36 . . . A47183 104 1 Q. Q. NNP A47183 105 1 What what WP A47183 105 2 is be VBZ A47183 105 3 the the DT A47183 105 4 distance distance NN A47183 105 5 betwixt betwixt VBP A47183 105 6 these these DT A47183 105 7 two two CD A47183 105 8 places place NNS A47183 105 9 , , , A47183 105 10 B b NN A47183 105 11 and and CC A47183 105 12 D D NNP A47183 105 13 , , , A47183 105 14 and and CC A47183 105 15 the the DT A47183 105 16 Course course NN A47183 105 17 on on IN A47183 105 18 the the DT A47183 105 19 Rhumb Rhumb NNP A47183 105 20 Line Line NNP A47183 105 21 betwixt betwixt VBP A47183 105 22 A a NN A47183 105 23 and and CC A47183 105 24 B b NN A47183 105 25 , , , A47183 105 26 and and CC A47183 105 27 the the DT A47183 105 28 distance distance NN A47183 105 29 betwixt betwixt VBP A47183 105 30 A A NNP A47183 105 31 and and CC A47183 105 32 C. C. NNP A47183 105 33 The The NNP A47183 105 34 Resolution Resolution NNP A47183 105 35 . . . A47183 106 1 Divide divide VB A47183 106 2 the the DT A47183 106 3 angle angle NN A47183 106 4 EAD ead NN A47183 106 5 into into IN A47183 106 6 three three CD A47183 106 7 equal equal JJ A47183 106 8 parts part NNS A47183 106 9 , , , A47183 106 10 and and CC A47183 106 11 make make VB A47183 106 12 CAB CAB NNP A47183 106 13 = = SYM A47183 106 14 one one CD A47183 106 15 third third JJ A47183 106 16 part part NN A47183 106 17 of of IN A47183 106 18 EAD EAD NNP A47183 106 19 , , , A47183 106 20 and and CC A47183 106 21 draw draw VB A47183 106 22 the the DT A47183 106 23 line line NN A47183 106 24 BAD bad JJ A47183 106 25 . . . A47183 107 1 Thus thus RB A47183 107 2 the the DT A47183 107 3 four four CD A47183 107 4 places place NNS A47183 107 5 A. a. NN A47183 108 1 B. B. NNP A47183 108 2 C. C. NNP A47183 108 3 D D NNP A47183 108 4 shall shall MD A47183 108 5 be be VB A47183 108 6 duly duly RB A47183 108 7 situated situate VBN A47183 108 8 , , , A47183 108 9 and and CC A47183 108 10 an an DT A47183 108 11 Isosceles Isosceles NNP A47183 108 12 Triangle Triangle NNP A47183 108 13 shall shall MD A47183 108 14 be be VB A47183 108 15 formed form VBN A47183 108 16 ABD ABD NNP A47183 108 17 , , , A47183 108 18 whose whose WP$ A47183 108 19 side side NN A47183 108 20 AB AB NNP A47183 108 21 = = SYM A47183 108 22 AD ad NN A47183 108 23 = = SYM A47183 108 24 100 100 CD A47183 108 25 Leagues league NNS A47183 108 26 , , , A47183 108 27 and and CC A47183 108 28 the the DT A47183 108 29 angle angle NN A47183 108 30 BAD BAD NNP A47183 108 31 = = SYM A47183 108 32 86 86 CD A47183 108 33 degr degr NN A47183 108 34 . . . A47183 109 1 40 40 CD A47183 109 2 . . . A47183 109 3 consequently consequently RB A47183 109 4 by by IN A47183 109 5 plain plain JJ A47183 109 6 Trigonometry Trigonometry NNP A47183 109 7 , , , A47183 109 8 the the DT A47183 109 9 angle angle NN A47183 109 10 of of IN A47183 109 11 the the DT A47183 109 12 course course NN A47183 109 13 GAB GAB NNP A47183 109 14 being be VBG A47183 109 15 found find VBN A47183 109 16 , , , A47183 109 17 which which WDT A47183 109 18 is be VBZ A47183 109 19 23 23 CD A47183 109 20 degr degr NNS A47183 109 21 . . . A47183 110 1 30 30 CD A47183 110 2 min min NN A47183 110 3 . . . A47183 111 1 the the DT A47183 111 2 angle angle NN A47183 111 3 ABD ABD NNP A47183 111 4 , , , A47183 111 5 its -PRON- PRP$ A47183 111 6 double double JJ A47183 111 7 is be VBZ A47183 111 8 46 46 CD A47183 111 9 degr degr NN A47183 111 10 . . . A47183 112 1 40 40 CD A47183 112 2 = = SYM A47183 112 3 ADB ADB NNP A47183 112 4 , , , A47183 112 5 by by IN A47183 112 6 the the DT A47183 112 7 Rule Rule NNP A47183 112 8 of of IN A47183 112 9 Opposits Opposits NNPS A47183 112 10 . . . A47183 113 1 As as IN A47183 113 2 the the DT A47183 113 3 Sine Sine NNP A47183 113 4 of of IN A47183 113 5 46 46 CD A47183 113 6 d. d. NN A47183 113 7 40 40 CD A47183 113 8 to to IN A47183 113 9 AD ad NN A47183 113 10 100 100 CD A47183 113 11 Leagues league NNS A47183 113 12 , , , A47183 113 13 so so CC A47183 113 14 the the DT A47183 113 15 Sine Sine NNP A47183 113 16 of of IN A47183 113 17 86 86 CD A47183 113 18 . . . A47183 114 1 40 40 CD A47183 114 2 Log Log NNP A47183 114 3 . . . A47183 115 1 9.861757 9.861757 CD A47183 115 2 2.000000 2.000000 CD A47183 115 3 9.999265 9.999265 CD A47183 115 4 11.999265 11.999265 CD A47183 115 5 9.861757 9.861757 CD A47183 115 6 to to IN A47183 115 7 BD BD NNP A47183 115 8 137 137 CD A47183 115 9 . . . A47183 116 1 ● ● NFP A47183 116 2 . . . A47183 117 1 fere fere RB A47183 117 2 2.137508 2.137508 CD A47183 117 3 From from IN A47183 117 4 which which WDT A47183 117 5 substracting substracte VBG A47183 117 6 BC BC NNP A47183 117 7 100 100 CD A47183 117 8 Leagues Leagues NNPS A47183 117 9 , , , A47183 117 10 there there RB A47183 117 11 remaineth remaineth NNP A47183 117 12 CD CD NNP A47183 117 13 37 37 CD A47183 117 14 . . . A47183 118 1 ● ● NFP A47183 118 2 . . . A47183 119 1 as as IN A47183 119 2 was be VBD A47183 119 3 required require VBN A47183 119 4 . . . A47183 120 1 A a DT A47183 120 2 Fifth fifth JJ A47183 120 3 great great JJ A47183 120 4 use use NN A47183 120 5 of of IN A47183 120 6 the the DT A47183 120 7 Trisection Trisection NNP A47183 120 8 , , , A47183 120 9 and and CC A47183 120 10 other other JJ A47183 120 11 Sections Sections NNPS A47183 120 12 is be VBZ A47183 120 13 , , , A47183 120 14 having have VBG A47183 120 15 the the DT A47183 120 16 Ratio Ratio NNP A47183 120 17 of of IN A47183 120 18 any any DT A47183 120 19 2 2 CD A47183 120 20 Angles angle NNS A47183 120 21 given give VBN A47183 120 22 in in IN A47183 120 23 any any DT A47183 120 24 plain plain NN A47183 120 25 . . . A47183 121 1 Triangle Triangle NNP A47183 121 2 , , , A47183 121 3 to to TO A47183 121 4 find find VB A47183 121 5 the the DT A47183 121 6 quantity quantity NN A47183 121 7 of of IN A47183 121 8 them -PRON- PRP A47183 121 9 , , , A47183 121 10 if if IN A47183 121 11 the the DT A47183 121 12 quantity quantity NN A47183 121 13 of of IN A47183 121 14 the the DT A47183 121 15 3d 3d NNP A47183 121 16 Angle Angle NNP A47183 121 17 be be VB A47183 121 18 given give VBN A47183 121 19 , , , A47183 121 20 without without IN A47183 121 21 any any DT A47183 121 22 regard regard NN A47183 121 23 to to IN A47183 121 24 their -PRON- PRP$ A47183 121 25 sides side NNS A47183 121 26 . . . A47183 122 1 What what WDT A47183 122 2 other other JJ A47183 122 3 uses use VBZ A47183 122 4 these these DT A47183 122 5 Angular Angular NNP A47183 122 6 Sections Sections NNPS A47183 122 7 may may MD A47183 122 8 have have VB A47183 122 9 , , , A47183 122 10 is be VBZ A47183 122 11 left leave VBN A47183 122 12 to to IN A47183 122 13 the the DT A47183 122 14 search search NN A47183 122 15 of of IN A47183 122 16 Industrious Industrious NNP A47183 122 17 Artists Artists NNP A47183 122 18 . . . A47183 123 1 London London NNP A47183 123 2 , , , A47183 123 3 Printed Printed NNP A47183 123 4 for for IN A47183 123 5 the the DT A47183 123 6 Author author NN A47183 123 7 , , , A47183 123 8 and and CC A47183 123 9 are be VBP A47183 123 10 to to TO A47183 123 11 be be VB A47183 123 12 had have VBN A47183 123 13 at at IN A47183 123 14 the the DT A47183 123 15 Three Three NNP A47183 123 16 Pigeons Pigeons NNPS A47183 123 17 over over RB A47183 123 18 against against IN A47183 123 19 the the DT A47183 123 20 Exchange Exchange NNP A47183 123 21 , , , A47183 123 22 and and CC A47183 123 23 at at IN A47183 123 24 his -PRON- PRP$ A47183 123 25 House House NNP A47183 123 26 in in IN A47183 123 27 Pudding Pudding NNP A47183 123 28 - - HYPH A47183 123 29 lane lane NNP A47183 123 30 , , , A47183 123 31 at at IN A47183 123 32 the the DT A47183 123 33 Sign Sign NNP A47183 123 34 of of IN A47183 123 35 the the DT A47183 123 36 Golden Golden NNP A47183 123 37 Ball Ball NNP A47183 123 38 , , , A47183 123 39 where where WRB A47183 123 40 he -PRON- PRP A47183 123 41 Teacheth Teacheth NNP A47183 123 42 the the DT A47183 123 43 Mathematical Mathematical NNP A47183 123 44 Arts Arts NNPS A47183 123 45 . . .