Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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<
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ergo poterit quælibet figura rectilinea in quotuis partes æquales
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">Quo pacto fi-
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gura data ſe-
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c{et}ur per li-
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ne{as} parallel{as}
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in quotuis par
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t{es} æqual{es}.</
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per lineas, quæ datæ cuiuis rectæ lineæ æquidiſtent. </
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<
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gura ſecanda ſit in 8. </
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<
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">partes æquales per lineas datæ rectæ parallelas, diuidemus
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eam primum in duas partes inter ſe proportionem habentes 1. </
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prior pars erit {1/8}. </
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<
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<
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xml:space
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">Deinde poſteriorem partem ſecabimus in pro-
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portionem 1. </
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<
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<
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">ita vt prior pars huius diuiſionis ſit {1/7}. </
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<
s
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">illius partis diuiſæ, hoc
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eſt, {1/7}. </
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<
s
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">totius figuræ, cum pars illa diuiſa complectatur {7/8}. </
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partem poſt eriorem proximæ diuiſionis partiemur in proportionem 1. </
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poſteriorem huius diuiſionis partem in proportionem 1. </
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<
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ceps, minuendo ſemper, don@c ad partem deueniamus, quæ ſecanda ſit in pro-
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portionem 1. </
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<
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">hoc eſt, in partes æquales.</
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idem effici poterit ea ratione, quam ad finem ſcholij propoſ. </
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ſuimus: </
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">ſi videlicetlatus quadrati H I, quod rectilineo dato conſtructum eſt
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æquale, in tot æquales partes ſecetur, in quot partes datum rectilineum diuiden-
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dum eſt, & </
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">primo rectilineum diuidatur in proportionem primæ partis ad reli-
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quas: </
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">Deinde poſterior pars rectilinei in proportionem ſecundæ partis lateris
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H I, ad reliquas: </
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hic finem habet noſtra Geodæſia complectens diuiſionem omnium
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figurarum rectilinearum: </
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">ſequuntur iam particulares nonnullæ diuiſiones qua-
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rundam figurarum, quæ tum, quia ſubtiles acutaſque demonſtrationes conti-
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nent, tum quia pleraſque earum eruditi quo que Geometræ, vt Leonardus Pi-
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ſanus, Frater Lucas Pacciolus, & </
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">Nicolaus Tartalea tradiderunt, omittendæ
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nullo modo viſæ ſunt: </
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ſunt Theoremata nonnulla, quorum primum ſit hoc.</
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partes vergant: </
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communi bifariam ſecatur.</
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<
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æqualia duo triangula A B C, A B D, habentia latus A B, commune, & </
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diuerſas partes vergentia. </
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ſecari in E, bifariam à latere com̃uni A B. </
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<
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">1. ſexti.</
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triangulum A C E, ad triangulum A D E, quàm triangulum B C E,
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ad triangulum B D E, vt C E, ad E D; </
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<
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triangulum A D E, vt triangulum B C E, ad triangulum B D E.
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Igitur erunt quo que duo triangula ſimul A C E, B C E, hoc eſt, totum triangulum A B C, ad duo triangula ſimul A D E, B D E, id
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eſt, ad totum triangulum A B D, vt A C E, ad A D E, hoc eſt, vt
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C E, ad E D. </
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<
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<
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que rectæ C E, E D, æquales, ac proinde C D, in E, ſecta eſt bifariam. </
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<
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oſtendendum.</
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