Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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cus LF, FC, CG, GB, bifariam, & </
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<
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">rectas,
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donec fiat exceſſus minor ex ceſſu H, per ſuperius principium Cardani. </
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<
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niam igitur arcus L B, prima quantitas ſuperat ſecundam, videlicet rectas L F,
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FC, CG, GB, ſimul exceſſu I; </
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<
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">Et tertia quantitas, nimirum ſumma rectarum AL,
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AB, ſuperat quartam, id eſt, ſummam rectarum LD, DE, EB, exceſſu H: </
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<
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exceſſus I, minor exceſſu H; </
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<
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">Et prima quantitas, hoc eſt, arcus BL, ponitur non
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minor, quam tertia ex AB, AL, conflata; </
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<
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">item tertia AB, AI, maior, quam quar-
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ta LD, DE, EB: </
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<
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<
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">Lemma, minor proportio arcus BL, primæ quantita-
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tis ad ſecundam LF, FC, CG, GB q@iam tertiæ quantitatis AL, AB, ad quartam
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L D, D E, E B; </
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<
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"> Et permutando minor erit proportio arcus L B, ad A L, A
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quinti.</
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ſimul, quam rectarum LF, FC, CG, GB, ſimul ad rectas LD, DE, EB, ſimul. </
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ergo vt compoſita ex LF, FC, CG, GB, ad compoſitam ex LD, DE, EB, ita ar-
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cus BK, ad rectas AL, AB, ſimul: </
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">Eritque propterea minor etiam proportio ar-
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cus B L, ad AL, AB, ſimul, quam arcus B L, ad arcum BK; </
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maior erit arcu BL. </
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<
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">Cum ergo eadem ſit proportio rectarum LF, FC, CG, GB,
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ſimul ad LD, DE, EB, ſimul, quæ arcus BK, ad AL, AB, ſimul: </
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ma, rectæ LF, FC, CG, GB, ſimul minores, quam LD, DE, EB, ſimul; </
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<
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que arcus B K, minor, quam AL, AB, ſimul. </
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duabus AL, AB, ſimul. </
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">Quare rectæ tangentes AL, AB, ſimul maiores ſunt ar-
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cu BL, quod erat oſtendendum.</
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autem hæc demonſtratio Cardani admirabilis, & </
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Eucl, in propoſ. </
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tione affirmatiua ex eius oppoſito, vt patet.</
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hanc demonſtrationem Cardani, non quòd verè Geometrica ſit,
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niſi principium illud ſuum admittatur, ſed quod ingenioſa ſit & </
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men hac demonſtratione concedendum erit, ambitum figuræ circumſcriptæ eſ-
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ſe inaiorem peripheria circuli propter demonſtrationem Archimedis, cumnihil
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vnquam in contrarium à quo quam ſit allatum, vt ſupra diximus.</
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demonſtrauimus nos in libr. </
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hic aliter demonſtrabimus ex Pappo, hoc modo. </
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<
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EFGH, quorum diametri AC, EG. </
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cumferentiam ad circumferentiam, vt eſt diameter
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ad diametrum. </
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culum, vt quadratum diametri ad quadratum dia-
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metri. </
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E F G H, ita eſt quadruplum circuli ad quadru-
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plam circuli. </
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circuli A B C D, ad quadruplum circuli E F-
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G H, vt quadratum diametri A C, ad quad atum
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diametri EG. </
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ABCD, ſit æqualis, comprehenſum, quadruplũ eſt circuli ABCD; </
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lum ſub diametro E G, & </
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