Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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cadat inter I, & </
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<
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portione
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IBF, per punctum E, Ellipſis alteri
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GEHD ſimilis inſcribi nũquam poterit, qualis ſemper inſcribi poteſt m
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triã-
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gulis IBF, MBL, &</
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patebit) illę omnino his minores erunt, cum verticibus ſint propiores; </
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id, quæ ad oppoſitas partes ibi inſcribuntur, erunt quidem _MAXIMAE_
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quæſitæ.</
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Parabolæ inſcripti, & </
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mutuò contingentes, ſunt inter ſe in ratione quadratorũ, diſparium
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numerorum ab vnitate incipientium.</
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<
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<
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xml:space
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e@ in-
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ſcripti, & </
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">à vertice ſucceſſiuè ſe mutuò contingentes ſint, quorum dia-
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metri BE, EF, FG, GH, &</
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punctum L, ter@ij O, quarti R, &</
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<
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quadrata numerorum diſparium ab vnitate incipientium, nempe 1. </
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<
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<
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O, R ordinatæ EI, FN, GQ, LM, OP, RS.</
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<
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<
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0146-01
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ſcriptibilium per verticẽ B, erit BE
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roll. 20. h.</
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lis recto lateri Parabolę, ſed EI eſt
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I. h.</
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proportionalis inter EB, & </
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hoc eſt inter æquales lineas, quare EI æ-
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qualis erit ipſi EB, quæ concipiatur, vt
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vnum; </
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<
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roll. 75. h.</
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eſt vt 1, & </
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roll. 13. h.</
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BM, ita BM ad BF, vel vt 1 ad 2, ita 2, ad
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4; </
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roll. 75 h.</
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FM, ſiue FN, ſiue FP erit pariter 2; </
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<
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detota BP erit 6; </
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<
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roll. 13. h.</
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4 ad 6, ita BP ad BG, & </
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<
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ſiue GQ, vel GS erit 3; </
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<
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12, ſed vt BG ad BS, vel vt 9 ad 12, ita BS
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ad BH, & </
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<
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BH, erit 16. </
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<
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eſt 4, BG, 9, & </
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<
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<
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rum differentijs EF, FG, GH, erunt, vt
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ſunt numeri 1, 3, 5, 7, qui ſunt numeri im-
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pares ab vnitate incipientes, ſed circuli
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ſunt, vt quadrata ſuorum diametrorum,
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ipſæque BF, EF, FG, GH ſunt inſcripto-
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rum circulorum diametri, quare hi </
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