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

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

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8464GEOMETRIÆ plana figurarum, oOS, spf, in rectis, BC, QR, quibus occur-
rant, Oo, fs, productæ vt in punctis, B, Q, & iungantur, SB, p
Q, eſto autem, quod plana figurarum, LHMP, YVZd, diuiſe-
rint plana figurarum, oOS, sfp, producta in rectis, KN, ug, quę
ab ipſis, BS, Qp, BO, Qf, ſecentur in, I, X, Ku, & iungantur,
LK, PI, Yu, dX. Quoniam ergo plana figurarum, HMPL, V

44[Figure 44] ZdY, prędictas altitudines ſi-
militer ad eandem partem di-
uidentia, ſecant latera homo-
loga, ao, Ts, ſimiliter ad
eandem partem in punctis, L,
11Ex Lem.
ant. Y, vt etiam, AG, T8, in, H
V, erunt figurę, ALH, TY
V, ad eandem partem ſecan-
22Ex Lem,
3. tium, HL, VY, conſtitutæ
inter ſe ſimiles, & earum late-
ra homologa ipſę, HL, VY;
eodem modo oſtendemus ſi-
miles eſſe ipſas, EALP, lT
Yd, & earum latera homolo-
ga ipſas, LP, Yd, ſunt autem
figuræ, AEPL, ALH, in-
uicem ad eandem partem æ.
què inclinatæ, acipſæ, Tld
Y, TYV, cum ſint in planis
33Ex Lem.
1. ſimilium figurarum, AESo,
Tlps, AGOo, T8fs, quę
44Ex Lem.
2. ſunt inuicem ad eandem par-
tem æquè inclinatę, ergo an-
guli, HLP, VYd, homolo-
gis lateribus contenti eruntę-
quales, & circa eoſdem latera
erunt proportionalia. Eodem
modo oſtedemus cæteros an-
gulos, LPM, YdZ, interſe,
necnon, PMH, dZV, ac,
MHL, ZVY, æquales eſ-
ſe, & circa æquales angulos
latera exiſtere proportionalia,
ergo figuræ, LHMP, YVZd, ſimiles erunt iuxta Euclidem, er-
55Defin. 1.
Sex. El. go etiam ſimiles erunt iuxta definit. 10. huius.

Reliquum eſt, vt demonſtremus earum homologas duabus

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