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

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7252GEOMETRIÆ

COROLLARIVM.

_Q_Via verò oppoſitæ tangentes, AH, DF, MN, RQ, ductæ ſunt
vtcumque, angulos tamen æquales ad eandem partem cum homo-
logis lateribus continentes, ideò quaſcumq; duxerimus oppoſitas
tangentes in figuris rectilineis ſimilibus iuxta Euclidem, dummodo fa-
ciant angulos æquales ad eandem partem cum lateribus homologis, ea-
ſdem eſſe regulas homologarum ſimilium figurarum poterit probari.

THEOREMA XXV. PROPOS. XXVIII.

POſita infraſcripta definitione ſimilium portionum ſectio-
num coni, illi adiuncti, quod infra dicetur, ſequitur
pro ipſis etiam mea definitio generalis ſimilium planarum fi-
gurarum. Hoc autem dico pro ſpatijs ſub ipſis ſectionibus,
& rectis lineis contentis, non autem pro ipſis tanquam lineis,
licet crediderim Apolloniũ ipſarum ſimilium ſectionum tan-
quam linearum, non autem figurarum, quę fiunt ab ipſis, ſi-
militudinem attendiſſe, ego verò ipſam recipio tanquam ip-
ſarum figurarum ſimilitudini congruam, dum illi adiungitur,
quod in ipſa Propoſ. explicatur.

DEFINITIO.

SImiles portiones ſectionum coni ſunt, in quarum ſingulis ductis
lineis baſi parallelis numero æqualibus, ſunt ipſæ parallelæ, &
baſes ad abſciſſas diametrorum partes ſumptas à verticibus, in ijſdem
rationibus, tumabſciſſæ ipſæ ad abſciſſas: Apollonius lib. 6. Coni-
corum, vt refert Eutocius.

Sint ſimiles portiones ſectionum coni, DAF, QRK, in baſibus,
DF, QK, quarum diametri ſint ipſæ, AE, RG, ſecentur autem
ſimiliter ipſæ diametri in punctis, N, O; V, X; & ſit, D F, ad, E
A, vt, Q K, ad, G R, & , C H, ad, O A, vt, T L, ad, X R, & , P
M, ad, N A, vt, S P, ad, V R; has igitur Apollonius in ſupradicta
definitione ſimiles vocat, mihi autem hoc opus eſt illi adiungere. ſ.
quod anguli baſibus, & diametris, ad eandem partem contenti ſint
æquales, vt angulus, A E D, ipſi, R G Q, ſi. u. hoc non ponatur
poſſet contingere eſſe baſes, D F, Q K, æquales, & ipſas, A E, R
G, in quo caſu tot figuras ſimiles, & æquales, ex. gr. ipſi, A D

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