Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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atque ex N agatur N P O ipſi G L parallela, ex O verò recta O Q R paral-
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lela ad L N, & </
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<
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buerit: </
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<
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">patet, ſi per puncta I, P, S, interſectionum ipſarum diagona-
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lium cum diametro, agantur applicatæ T V, X Y, Z K, &</
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<
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xml:space
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ſegmenta F M, M Q, Q D, &</
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<
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xml:space
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">per extrema prædictarum applicatarum
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deſcribantur Ellipſes T F V M, X M Y Q, Z Q K D, has omnes eſſe Para-
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bolæ A B C inſcriptas, & </
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<
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gentes. </
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<
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rationem habere, ac numeri quadrati diſparium numerorum ab vnitate: </
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mirum eſſe in progreſſione numerorum 1. </
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<
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">Quoniam igitur eſt M B ad B I, vt B I
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roll. 13. h.</
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B F, erit diuidédo M I ad I B, vt I F ad F B,
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ſed eſt I F æqualis F B, ex conſtructione,
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quare M I ipſi I B æqualis erit, ac ideo in
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Ellipſi T F V M, erit quadratum T I ad re-
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ctangulum M I F, hoc eſt rectum eius
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mi Conic.</
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ad tranſuerſum, vt idem quadratum T I, vel
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rectangulum ſub I B, & </
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<
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1. huius.</
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gulum ſub eadem I B, & </
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linea B E ad I F, (cum ſit I B communis re-
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ctangulorum altitudo) vel ad ei æqualem B
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F, nempe vt rectum ad tranſuerſum Ellipſis
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BF: </
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<
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ſimilis, ſed vnaqueque aliarum inſcriptarum
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Ellipſium circ? </
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D, &</
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<
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">eidem T F V M eſt ſimilis, vt ſupra
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monuimus, quare omnes huiuſm odi inſcri
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ptæ Ellipſes erunt ſimiles inter ſe. </
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M I ęqualis I B, & </
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ta M B quadrupla B F. </
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piatur vt vnum, erit B I vt 2, & </
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atque M I vt 2, & </
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ob æquidiſtantes applicatas M N, F G; </
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ob parallelas diagonales N P, G I, erunt reliqui ad N, G pariter æquales,
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ſiue ipſa triangula inter ſe ſimilia, vnde latus N M ad M P erit, vt latus G F
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ad F I, & </
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G F, ſiue recta M B ad B F; </
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mi Conic.</
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dratum F I; </
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M P dupla F I, ſiue dupla ad B F, ſed B F ponitur vt vnum, ergo M P erit
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2; </
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roll. 13. h.</
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Q, quare B Q erit vt 9, ſed B M eſt vt 4, ergo M Q erit 5. </
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dem ratione, ac ſupra, oſtendetur triangulum R Q S ſimile triangulo G F I,
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& </
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<
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mi Conic.</
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tum R Q nonuplum quadrati G F, cum ſit recta Q B nonupla B F, vt mo-
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dò oſtendimus, ergo, & </
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<
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quadrati B F, hoc eſt linea Q S tripla B F, quare tota B S erit vt 12; </
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