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

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

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6848GEOMETRIÆ eadem parallela plana eſſe æqualiter ad eandem partem inclinata.
11Defin. 3.
Vndec. El. Siigitur, AG, KY, eſſent dictis planis parallelis perpendiculares,
2218. Vnde-
cimi El. manifeſtum eſt, quod anguli, AGV, Κ Υ Λ, eſſent æquales, ideſt
recti, & plana, AV, Κ Λ, eiſdem planis parallelis erecta; ſed non
ſint perpendiculares, & à punctis, A, K, demittanturipſę, AE, K

34[Figure 34] T, quæ eiſdem
ſint perpẽdicu-
lares, incidant
autem ſubiectis
planis in pun-
ctis, E, T; de-
inde à puncto,
A, ad, HG, V
G, productas,
ducantur per-
pendiculares, A
F, quidem ipſi;
HG, & AP,
33Vide di-
cta lib. 7.
annot. ipſi, VG, inci-
dentes in pun-
44Prop. 3. ctis, V, P, niſi
fortè, AG, eſſet
alteri earũ per-
pendicularis, vt
contingere po-
teſt, & iungan-
tur, EP, EG,
EF; ſimiliter in
alia figura ca-
dant à puncto,
K, perpendicu-
lariter ſuper ip-
ſas, & Y, Λ Υ,
productas, ſi o-
pus ſit, ipſæ, K
Z, KX, & iun-
5547. Primi
Elem. gantur ſimiliter, TX, TY, & , TZ. Quoniam ergo anguli, AF
G, KZY, ſunt recti, ideò quadratum, AG, erit æquales duobus
quadratis, AF, FG, ſicut quadratum, KY, æquale duobus, KZ,
ZY, eſt autem etiam quadratum, AF, ęquale duobus quadratis, A
E, EF, quia angulus, AEF. rectus eſt, & quadratum, KZ, pari-
teræquale quadratis, KT, TZ, ergo quadratum, AG, ideſt

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