Clavius, Christoph
,
Geometria practica
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189
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189
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LIBER QVARTVS.
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<
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praxim, ſiueregulam, quæ exquiſitiſsima eſt, vt dixi, ita in triangu-
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<
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lo A B C, demonſtrabimus. </
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<
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xml:space
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">Diuiſis angulis A B C, A C B, bifariam per rectas
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BD, CD, coeuntes in D, ducantur ex D, ad ſingula latera perpendiculares D E,
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DF, DG, iungatur que recta AD. </
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<
s
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xml:space
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">Quoniamigitur duo anguli E, D B E, in trian-
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gulo DEB, æquales ſunt duobus angulis G, D B G, in triangulo DGB, & </
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<
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DB; </
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<
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<
s
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xml:space
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"> erunt tam latera DE, DG, quam BE, BG, æqualia. </
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<
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xml:space
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">26. primi.</
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modo tamlatera DF, DG, æqualia eruntin triangulis DFC, DGC: </
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<
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DE, DF, (cum vtraque ipſi D G, ſit oſtenſa æqualis) inter ſe æquales erunt: </
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<
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que omnes tres perpendiculares DE, DF, DG, æquales inter ſe erunt.</
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<
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quia quadrato ex AD, æqualia ſunt tam quadrata ex A E, E
<
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">47. primi.</
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quam quadrata ex A F, F D; </
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<
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">æqualia erunt quadrata ex A E, E D, quadratis ex
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AF, FD, Ac proinde ablatis æqualibus quadratis rectarum ED, FD, æqualium,
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reliqua quadrata rectarum A E, A F, æqualia erunt: </
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<
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120
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/189-01
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ipſæ A E, A F, æquales erunt. </
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<
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">Igitur cum latera A E,
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@A D, trianguli A D E, lateribus A F, A D, trianguli
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A D F, æqualia ſint, & </
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<
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<
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">8. primi.</
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gulus D A E, angulo D A F, æqualis.</
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<
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verò A E, ipſi A F, & </
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">E B, ipſi B G, ęqua-
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lis eſt oſtenſa, erit tota A B, duabus A F, B G, ęqua-
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lis: </
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<
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xml:space
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">additiſque æqualibus C G, C F, duę A B, C G,
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duabus A C, B G, æquales erunt. </
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xml:space
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">Tam ergo duę A B,
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C G, quam duæ A C, B G, ſemiſſem trium laterum
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A B, B C, A C, conſtituent. </
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">Quocirca C G, vel C F,
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diifferentia erit inter ſemiſſem laterum, & </
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<
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">latus A B. </
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">Item B G, vel BE, differen-
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tia inter eandem ſemiſſem, & </
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<
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">Denique cum A B, C G, ſemiſſem late-
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rum efficiant, ſitque B G, ipſi B E, æqualis, vt oſtendimus, conſtituent quo que
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B C, A E, ſemiſſem eorundem laterum: </
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<
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">ideo que A E, differentia erit inter late-
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rum ſemiſſem, & </
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<
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rum conſtituunt, & </
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<
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">tres differentias inter ſemiſſem laterum, & </
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<
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guli.</
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<
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iam A B, A C, ſit B H, ipſi C G, & </
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<
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">ita vt
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tam A H, ſemiſsi laterum, rectis videlicet A B, C G, quam A I, eidem ſemiſsi late-
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rum, rectis nimirum A C, B G, ſit ęqu
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, conſtet que ex tribus differentiis an-
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te dictis. </
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<
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">Ducta quo que H K, ad A H, perpendiculari, quę cum A D, producta
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conueniat in K; </
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<
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">Et quia duo latera A H, A K,
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trianguli AHK, duobus lateribus AI, AK, trianguli AIK, ęqualia ſunt, anguloſ-
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que ad A, continent ęquales, vt ſupra oſtendimus, æquales quo que erunt &</
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<
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<
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xlink:label
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xml:space
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">4. primi.</
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baſes HK, IK, & </
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<
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">anguli H, I. </
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">Cum ergo H, per conſtructionem ſit rectus, rectus
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etiam erit I.</
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<
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pręterea BL, ipſi C G, vel B H, æqualis, vt proinde reli-
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qua C L@ reliquę B G, vel ipſi C I, æqualis ſit, iungaturq; </
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<
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">recta KL. </
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">Producta au-
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tem B H, ſumatur H M, ipſi C I, æqualis, connectatur querecta L M. </
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<
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">Et quia duo
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latera KH, HM, trianguli HMK, duobus later bus KI, IC, trianguli CIK, æqua-
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lia ſunt, angulo ſque H, I, continent ęquales, vt pote rectos: </
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<
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<
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ſes K M, K C, ęquales: </
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<
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">at que adeò cum duo latera BM, BK, trianguli BMK, duo-
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bus lateribus B C, B K, trianguli B C K, ęqualia ſint, (eſt nam que B M, ipſi B C,
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æqualis, quod partes B H, H M, partibus B L, L C, ſint æquales) ſit que </
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