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

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THEOR. IV. PROP. XXXIII.
Ductis enim regulis F O, G P, & applicatis vbi-
56[Figure 56] cunque duabus ADH, IL M;
quæ productę ſecent
regulas
in P, O, N, R;
manifeſtum iam eſt ex 1. h.
has regulas inter ſe æquidiſtare: & cum ſit vt qua-
dratum
I M ad M L, ita recta R M ad M N, vel vt 116. Co-
rol
. 19. h.
H ad H P, vel vt quadratum A H ad H D, erit etiam
recta
IM ad ML, vt AH ad H D, &
per conuerſionẽ
rationis
, &
permutando I M ad A H, vt I L ad A D,
2232. h. ſed eſt IM maior AH, quare, &
IL erit maior AD. Quod ſecundò, & c.
_HV_C Franciſcum Barocium ſubaudiet fortaſſe aliquis admurmurantem,
nos
, qui de aſymptoticis lineis mutuam acceſsionem, vel receſsionem
perpendendam
ſuſcepimus, æquidiſtantium linearum ſegmentis, inter
conuergentes
, ac diuergentes aſymptotos interceptis vſos fuiſſe, veluti
in
præcedenti, vbi iuxta lineas, ſiue portiones A D, I L ex ordinatim
app
licatis ad communem diametrum, datarum ſectionum diſtantias commetimur;
dum tamen ipſæ à breuiſsimis, ſeu MINIMIS lineis ſint determinandæ, atque

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