Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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10682 occurrat in P, O; quoniam datæ ſectiones ſunt ſimiles, erit HB ad BI, vt LE
ad EM, ſuntque anguli ad B, E æquales, (cum ſectiones ſint ſimul adſcriptæ)
quare triangula HBI, LEM æquiangula erunt, ideoque regula HIP æquidi-
ſtabit regulæ LMO; & triangula LNO, HNP inter ſe ſimilia.

Iam cum ſit GE æqualis ipſi GL, & ablata GB æqualis ablatæ GH, erit
reliqua BE, reliquæ HL æqualis, ſed eſt EN minor HN, quare BE ad EN
maiorem habet rationem, quàm LH ad HN, & componendo BN ad NE,
maiorem item rationem quàm LN ad NH, vel quàm ON ad NP, ergo re-
ctangulum ſub extremis BN, NP, ſiue quadratum applicatæ AN, 11Coroll.
1. huius. erit rectangulo ſub medijs EN, NO, ſiue quadrato applicatę DN, hoc 2217. ſept.
Pappi.33Coroll.
1. huius. ipſa AN maior DN, ac propterea punctum D cadit intra Hyperbolen ABC,
idemque de quolibet alio puncto ſectionis DEF: vnde ipſa DEF inſcripta
erit ipſi ABC, vel erunt nunquam ſimul coeuntes. Quod erat primò, & c.

74[Figure 74]

Ampliùs applicata infra ADT qualibet alia QRS, & Hyperbolę DEF per
eundem verticem E adſcripta Hyperbola ETV, quæ ſit æqualium laterum,
ſiue congruens Hyperbolæ ABC, applicatas ſecans in T, V: cum duæ Hy-
perbolæ EDR, ETV, ſint ſimiles, & per eundem verticem ſimul adſcriptæ
erit ETV, cuius latera æqualia ſunt ipſis lateribus HB, BI, inſcripta 445. Co-
roll. 19. h. ni EDR, cuius maiora ſunt latera LE, EM: ſed erunt ſimul ſemper 5541. h. tes; quare intercepta DT minor erit intercepta RV, eſt autem tota AT 6644. h. ior tota QV; quapropter reliqua AD erit omnino maior reliqua QR; & hoc
ſemper: Vnde ſimiles concentricæ Hyperbolæ per diuerſos vertices ſimul
adſcriptæ, ſunt ad ſe propiùs accedentes. Quod ſecundò erat, & c.

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