Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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8969LIBER I. incidentes, ac oppoſitarum tangentium, HK, MN, Vu, Zg, ip-
ſas, KN, ug, ſi. n. iungeremus, MK, Zu, probaretur, MH, ad,
HK, eſſe vt, ZV, ad, Vu, (ſunt. n. ſimiles figuræ, HMPL, V
ZdY, necnon, LPK, Ydu, circumſtant autem latera proportio-
nalia angulos æquales, MHK, ZVu, & ideò oſtenderemus trian-
gula, MHK, ZVu, eſſe ſimilia, vnde pateret angulos, HKM,
VuZ, eſſe æquales, ſed etiam, HKN, Vug, ſunt ęquales, ergo
116. Sex. El. pateret angulos, MKN, Zug, eſſe æquales, ſunt autem etiam æ-
quales, MNK, Zgu, ergo triangula, MKN, Zug, eſſent æ-
quiangula, vnde, MN, ad, Zg, eſſet vt, KN, ad, ug, incidunt
autem, KN, ug, oppoſitis tangentibus, HK, MN, Vu, Zg, ad
eundem angulum ex eadem parte, ergo ipſarum tangentium, ac fi-
2224. huius. gurarum ſunt incidentes, KN, ug, cum verò, KN, ad, ug, ſit vt,
MK, ad, Zu, ideſt vt, MH, ad, ZV, vel vt quoduis ſolidorum
latus homologum ad quoduis latus homologum, ideſt vt, GO, ad,
8f, ideſt vt, OD, ad, f℟; OD, autem ad, f℟, ſit vt, Bo, ad, Qf,
ideò, KN, ad, ug, erit vt, BO, ad, Qf, & diuidunt ſimiliter ad
eandem partem ipſas, BO, Qf, in punctis, Ku, quæ incidunt ip-
ſis, BC, OD, Qf, R℟, ad eundem angulum ex eadem parte, ſunt
. n. anguli, BOD, Qf℟, æquales, quod & de cæteris incidentibus
probabitur, ergo figurę, BODC, Qf℟R, quę capiunt omnes di-
33Deſio. 10.
huius. ctas incidentes, ſunt ſimiles, & arum homologę ipſę incidentes, qua-
rum omnium regulæ ſunt, OD, f℟, & ſunt ipſę figurę, BD, Q℟,
æquè ad eandem partem ipſis baſibus inclinatę, cum ſint in planis fi-
44Lem. 1. gurarum, oOS, sfp, ergo dicta ſolida ſunt etiam ſimilia iuxta de-
fin. 11. huius. quod ſi plana, GOo, 8fs, non eſſent in ambitu ſi-
milium dictorum ſolidorum, facilè tamen oſtenderemus portiones
ſolidorum vltra eadem plana exiſtentes eſſe ſimiles, ac ipſarum, &
oppoſitorum tangentium planorum iam dictorum incidentes repe-
riri in planis figurarum, BD, Q℟, cum eiſdem integrantes figuras
incidentes integrorum ſimilium ſolidorum, ac dictorum oppoſito-
rum tangentium, quod ſpeculanti facilè innoteſcet, hoc autem erat
oſtendendum.

LEMMA.

CIrculi omnes, necnon femicirculi ſunt ſimiles iuxta meam deſi-
nitionem ſimilium planarum figurarum, & eorum, & tangen-
tium oppoſitarum, quæ ab extremitatibus diamertrorum ducuntur,
incidentes ſunt ipſi diametri.

Sint circuli, ABCD, ONQ, quorum diametri, AC, OQ, per
quorum extrema ducantur tangentes, FA, GC, HO, LQ.

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