Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si in angulo A B C applicatæ ſint duæ rectæ lineæ D E, A
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C, quæ ab eadem recta B G per verticem B ducta proportio-
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naliter ſecentur, ita vt ſit A G ad G C, homologè, vt D F ad
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F E. </
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applicata A H, ſecans B G in I: </
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(ob parallelas) A I ad I H, vt D F ad F E; </
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ob hypotheſim, vt A G ad G C, ergo in trian-
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gulo A C H erit I G parallela ad H C, ſed ipſæ
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conueniunt in B. </
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D E parallela, quàm A C. </
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ſum Pro-
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p. 45. h.</
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quacunque coni- ſectione, vel circulo abſciſſarum, eandem in-
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ſcriptam eiuſdem nominis ſectionem ſimilem, & </
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ad puncta media contingunt.</
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">SInt de angulo rectilineo, vt in prima figura, vel de qualibet alia coni- ſe-
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ctione, vel circulo, vt in ſecunda, abſciſſæ duæ æquales portiones A
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B C, D E F, quarum baſes A C, D F ſint bifariam ſectæ in G, H, & </
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inſcribatur eiuſdem nominis ſectio ſimilis, & </
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conic &
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5 6.7. p. h.</
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quæ ſit I G H. </
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ſim quoque D F eandem ſectionem contingere in H.</
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bolæ I G H (cum ſit B eius centrum) bifariam ſecans omnes in ea applica-
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tas, quæ ſi vſque ad aſymptotos producantur, erunt, & </
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inter aſymptotos, & </
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conic.</
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concipiantur addita æqualibus ſemi- applicatis in ſectione eis in directum
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poſitis, prouenient totæ applicatæ in angulo A B E biſariam ſectæ à dia-
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metro B G producta, ſed ponitur quoque applicata A C bifariam ſecta in
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G, quare A C ipſis applicatis in ſectione æquidiſtabit, ac ideò
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I G H continget in G.</
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mi conic.</
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ex G diameter G B, quæ vtriuſque ſectionis A B E, I G H erit communis
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diameter (cumipſæ ponantur ſectiones concentricæ, &</
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