Clavius, Christoph
,
Geometria practica
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LIBER SEXTVS.
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ABCD, cum diametris AC, BD, quæ ſe mutuo bifariam diuidentin E. </
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<
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xml:space
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primi.</
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ſet vnam tantum diametrum ducere, eamquein E, ſecare bifariam. </
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<
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">Protractis
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autemlateribus DA, DC, intelligatur circa punctum B, moueriregula hincinde,
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donecita ſecet D A, D C, productas in F, & </
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<
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">G, vtrectæ emiſſæ E F, E G, ęquales
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ſint. </
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<
s
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xml:space
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">Vel certè, vt vult Apollonius, ex E, plures circulideſcribantur LI, GF,
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MN, donec chorda arcus vnius pręciſè per punctum B, incedat, qualis eſt GF.
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</
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<
s
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xml:space
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">Quod ſi chorda ſupra B, tranſeat, cuiuſmodi eſt chorda LI, deſcribendus erit cir-
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culus j
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. </
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<
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<
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xml:space
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">Si verò infra punctũ B, tranſeat, qualis
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202
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297-01
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eſt chorda MN, deſcribẽdus erit circul
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.</
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<
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que hoc opus toties iterandum, donec aliqua
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chorda, qualis eſt GF, per B, incedat. </
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<
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">Erunt enim
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hacratione EF, EG, ex centro E, ad circumferen-
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tiam GF, interſe ęquales. </
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<
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xml:space
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">Quibus ita conſtructis.
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</
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">Dico A F, C G, eſſe medio loco proportionales
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inter AB, BC: </
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<
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">hoc eſt, ita eſſe AB, ad AF, vt AF,
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ad CG, & </
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Diuiſis enim AD, CD, bi-
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primi.</
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fariam in K, & </
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<
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xml:space
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">6. ſecundi.</
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gulum ſub D F, A F, vna cum quadrato ex A K,
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quadrato ex K F, ęquale eſt; </
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<
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">addito communi
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quadrato ex E K, eritrectangulum ſub D F, A F,
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vna cum quadratis ex A K, E K, hoc eſt,
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cũ quadrato ex EA, ęquale quadratis ex KF, EF, hoceſt, quadrato ex EF,
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eſt, quadrato ex EG, quę ipſi EF, eſt æqualis. </
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">Eademratione oſtendemus, re-
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ctangulum ſub DG, GC, vna cum quadrato ex CE, id eſt, ex EA, ęquale eſſe ei-
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dem quadrato ex E G. </
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<
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">Igitur rectangulum ſub D F, A F, vna cum quadrato
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ex EA, ęquale erit rectangulo ſub DG, GC, vna cum quadrato ex EA: </
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<
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que communi quadrato EA; </
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<
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lo ſub DF, AF, ęquale. </
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<
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"> Quo circa erit DG, ad DF, vt AF, ad CG: </
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"> Vt
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DG, ad DF, ita eſt AB, ad AF. </
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<
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">Ergo erit vt AB, ad AF, ita A F, ad C G: </
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<
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tres AB, AF, CG, continuè proportionales erunt. </
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<
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"> Sed rurſuseſt, vt D G,
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DF, ita CG, ad CB. </
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<
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">Igitur erit quoque CG, ad CB, vt AB, ad A F; </
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">vt AF
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ad CG. </
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<
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">Quare erunt quatuor AB, AF, CG, CB, continuè proportionales. </
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<
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erat demonſtrandum.</
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qui Philoppono quoque tribuitur.</
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rurſus in eadem figura inter rectas A B, B C, inueniendę duę medię
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proportionales. </
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<
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">Conſtituto rectangulo ABCD, vna cum diametro CA, produ-
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ctiſq; </
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<
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culus CBA, ad interuallum E C, vel EA, qui neceſſario per angulum rectum
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tertij.</
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tranſibit. </
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<
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">Deinde circa punctum B, regula hincinde moueatur, ſecans DA, DC,
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protractas in F, & </
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<
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">circumferentiamin O, donec B G, O F, ęquales ſint.
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</
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<
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">Quod fiet, ſi per B, plurimę lineę occultę ducantur. </
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ſegmentum inter rectam DG, & </
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