Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

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, maius erit rectangulo ſub medijs EN, NO, ſiue quadrato applicatę DN, hoc eſt 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.

117.1.

Coroll.
1. huius.
17. ſept.
Pappi.
Coroll.
1. huius.
0106-01

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 ſectio- ni EDR, cuius maiora ſunt latera LE, EM: ſed erunt ſimul ſemper receden- tes; quare intercepta DT minor erit intercepta RV, eſt autem tota AT ma- 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.

117.1.

5. Co-
roll. 19. h.
41. h.
44. h.

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