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

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10480 erunt ſimiles, at ſunt per verticem E ſimul adſcriptæ, vnde PEQ minorum
laterum inſcripta erit Hyperbolæ DEF maiorum laterum: & infra 115. Co-
roll. 19. h. applicata quacunque TVP; cum Hyperbolæ ABC, PEQ ſint congruentes,
& per diuerſos vertices ſimul adſcriptæ erit intercepta AX maior 2244. h. pta TP: cumque Hyperbolæ DEF, PEQ ſint ſimiles, ac per eundem verti-
cem ſimul adſcriptæ erit intercepta DX minor intercepta VP, vnde 3341. h. intercepta AD omnino erit maior reliqua intercepta TV; & hoc ſemper:
quare huiuſmodi Hyperbolæ ABC, DEF ſunt ad ſe propiùs accedentes.
Quod erat ſecundò, & c.

72[Figure 72]

Tandem, bifariam ſectis tranſuerſis lateribus GB, GE, RE, in Y, Z, K,
erit Y centrum Hyperbolæ ABC, Z verò centrum DEF, ac demum K cen-
trum PEQ: & cum ſit GB minor GE, erit dimidium GY minus dimidio GZ;
quare punctũ Z cadit infra Y: cumq; ſit EG maior ER, erit dimidiũ EZ maius
dimidio EK, vnde K punctum cadit infra Z. Si ergo ex Hyperbolarum cen-
tris Y, Z, ducantur earum aſymptoti Y 2, Z 3, K 4, erit Z 3, parallela 44Coroll.
41. huius. K 4, & Y 2 æquidiſtabit eidem K 4; quare aſymptoti omnes Y 2, Z 3, 55Coroll.
44. h. erunt inter ſe parallelæ: & cum Y 2 ſit aſymptotos ABC, & Z 3 ſit intra an-
gulum ab aſymptotis comprehenſum, ipſa ſectionem ABC ſecabit, vt in 66Coroll.
11. h. per quod ordinatim ducta recta 2 3 4, alias aſymptotos ſecantin 2 4, infra
ipſam applicetur quælibet alia TVP, ſingulas Hyperbolas ſecans in T, V, P.
Erit intercepta TP maior ſemper interuallo 2 4, ſed ablata intercepta 7744. h. eſt ſemper minor ablato interuallo 3 4, vnde reliqua intercepta TV 8841. h. datas ſectiones A B C, D E F, erit omnino maior reliquo interuallo 2 3,
quod inter datarum ſectionum parallelas aſymptotos eſt interceptum, ac
iuxta ordinatim ductis æquidiſtantes metitur. Quod erat vltimò demon-
ſtrandum.

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