Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRI Æ byperbolam hic babentur, circa ſectiones oppoſitas, quirum communes
ſunt dictæ paſſiones, quoq; intelligi poſſe. Eadem verò nedum in dictis
integris ſolidis, ſed etiam in eorum portionibus, ſiue in portionibus ſe-
ctionum coni abſciſſis per line as ad earum axim, vel diametrum ordina-
tim ductas, pariter verificari manifeſtum eſt.

142. LEMMA.

PRopoſitis duabus quibuſcumq; ſimilibus figuris, duæ quæuis re-
ctæ lineæ earum homologę poterunt eſſe incidentes, vel in ipſis
productis reperientur ſaltem earum incidentes, & oppoſitarum tan-
gentium, quibus ipſæ incidunt ad eundem angulum ex eadem parte,
erunt autem dictæ homologæ ſemper inuentarum incidentium par-
tes proportionales.

Sint duæ quæcunq; ſimiles figuræ planæ, IQsP, 487R, in eiſ-
que duæ quælibet homologę, Is, 47. Dico has eſſe vel incidentes,
vel in eiſdem productis reperiri poſſe incidentes prædictarum figura-
rum, & oppoſitarum tangentium, quibus occurrant ipſæ homolo-
gæ, productæ, ad eundem angulum ex eadem parte, quales ſint, D
L, dO; pu, g Y. Ducantur autem vlterius oppoſitę tangentes, quę
ſunt regulæ homologarum,
ls, 47, ipſæ, Ad, Co; F
g, KZ, quarum, & dicta-
rum figurarum incidentes
ſint, AC, FK, parallelæ
ipſis, DL, pu, hoc . n. fieri
poteſt; erunt autem etiam
ipſæ, d O, g Y, regulæ ho-
mologarum, cum faciant
angulos æquales cum regu-
lis, dA, gF, vt ſuppono,
& inueniri poterunt earum,
& dictarum figurarum inci-
dentes parallelæ eiſdem, A
d, Fg, ſint ipſę, LO, uY,
tales incidentes: Vel ergo
homologæ datæ, ls, 47,
terminantur ad oppofitas
tangentes, DL, dO; pu,
gY, velnon, & tunc producantur, & ipſis incidant in punctis, E,
f; ℟, & , & vlterius productæ vſque ad, AC, FK, ſecent ipſas in
punctis, B, G. Vlterius vel, Ho, XZ, tangunt ſetotis, vel aliqua

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer