Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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occurrat in P, O; </
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">quoniam datæ ſectiones ſunt ſimiles, erit HB ad BI, vt LE
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ad EM, ſuntque anguli ad B, E æquales, (cum ſectiones ſint ſimul adſcriptæ)
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quare triangula HBI, LEM æquiangula erunt, ideoque regula HIP æquidi-
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ſtabit regulæ LMO; </
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">& </
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<
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<
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">Iam cum ſit GE æqualis ipſi GL, & </
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">ablata GB æqualis ablatæ GH, erit
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reliqua BE, reliquæ HL æqualis, ſed eſt EN minor HN, quare BE ad EN
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maiorem habet rationem, quàm LH ad HN, & </
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<
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">componendo BN ad NE,
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maiorem item rationem quàm LN ad NH, vel quàm ON ad NP, ergo re-
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ctangulum ſub extremis BN, NP, ſiue quadratum applicatæ AN,
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1. huius.</
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erit rectangulo ſub medijs EN, NO, ſiue quadrato applicatę DN, hoc
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Pappi.</
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1. huius.</
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ipſa AN maior DN, ac propterea punctum D cadit intra Hyperbolen ABC,
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idemque de quolibet alio puncto ſectionis DEF: </
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erit ipſi ABC, vel erunt nunquam ſimul coeuntes. </
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">Quod erat primò, &</
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">Ampliùs applicata infra ADT qualibet alia QRS, & </
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">Hyperbolę DEF per
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eundem verticem E adſcripta Hyperbola ETV, quæ ſit æqualium laterum,
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ſiue congruens Hyperbolæ ABC, applicatas ſecans in T, V: </
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perbolæ EDR, ETV, ſint ſimiles, & </
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erit ETV, cuius latera æqualia ſunt ipſis lateribus HB, BI, inſcripta
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roll. 19. h.</
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ni EDR, cuius maiora ſunt latera LE, EM: </
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tes; </
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">quare intercepta DT minor erit intercepta RV, eſt autem tota AT
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ior tota QV; </
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ſemper: </
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adſcriptæ, ſunt ad ſe propiùs accedentes. </
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