337317LIBER IV.
THEOREMA XXIV. PROPOS. XXVI.
INeadem antecedentis figura oſtendemus omnia quadra-
ta portionis, BSF, ad rectangula ſub eadem portione,
BSF, & ſub figura, SEF, regula communi, BF, eſſe vt, B
F, ad, FE.
ta portionis, BSF, ad rectangula ſub eadem portione,
BSF, & ſub figura, SEF, regula communi, BF, eſſe vt, B
F, ad, FE.
Eſt enim quadratum, BF, ad rectangulum ſub, BF, FE, vt, B
F, ad, FE; ſimiliter ducta vtcunque, CD, parallela regulę, BF,
oſtendemus quadratum, CD, ad rectangulum, ſub, CD, DZ,
eſſe vt, CD, ad, DZ, eſt autem vt, BF, ad, FE, ita, CD, ad,
DZ, ergo quadratum, BF, ad rectangulum, BFE, erit vt qua-
dratum, CD, ad rectangulum, CDZ, ſic oſtendemus quamlibet
ductam intra portionem, BSF, parallelam regulę, BF, ad eiuſdem
11Corol.
4. 1. 2. portionem incluſam figura, SFE, eſſe vt quadratum, BF, ad re-
ctangulum ſub, BF, FE, ergo quadratum, BF, ad rectangulum
ſub, BF, FE, erit vt omnia quadrata portionis, BSF, ad rectan-
gula ſub portione, BSF, & ſub figura, SEF, vt autem quadratum,
BF, ad rectangulum ſub, BF, FE, ita, BF, ad, FE, ergo omnia
quadrata portionis, BSF, ad rectangula ſub portione, BSF, & fi-
gura, ESF, erunt vt, BF, ad, FE, quod oſtendere opus erat.
F, ad, FE; ſimiliter ducta vtcunque, CD, parallela regulę, BF,
oſtendemus quadratum, CD, ad rectangulum, ſub, CD, DZ,
eſſe vt, CD, ad, DZ, eſt autem vt, BF, ad, FE, ita, CD, ad,
DZ, ergo quadratum, BF, ad rectangulum, BFE, erit vt qua-
dratum, CD, ad rectangulum, CDZ, ſic oſtendemus quamlibet
ductam intra portionem, BSF, parallelam regulę, BF, ad eiuſdem
11Corol.
4. 1. 2. portionem incluſam figura, SFE, eſſe vt quadratum, BF, ad re-
ctangulum ſub, BF, FE, ergo quadratum, BF, ad rectangulum
ſub, BF, FE, erit vt omnia quadrata portionis, BSF, ad rectan-
gula ſub portione, BSF, & ſub figura, SEF, vt autem quadratum,
BF, ad rectangulum ſub, BF, FE, ita, BF, ad, FE, ergo omnia
quadrata portionis, BSF, ad rectangula ſub portione, BSF, & fi-
gura, ESF, erunt vt, BF, ad, FE, quod oſtendere opus erat.
THEOREMA XXV. PROPOS. XXVII.
SI intra curuam parabolæ duæ vtcunque ducantur rectæ
lineę in eandem @terminatæ, quarum vna rectè, altera
obliquè axim ſecet, ſint autem conſtitutarum ab eiſdem pa-
rabolarum diametri inter ſe æquales: Omnia quadrata pa-
rabolæ per eam, quæ rectè axim ſecat, conſtitutæ, regula
eadem, erunt æqualia rectangulis ſub parabola per obli-
quam ad axem conſtituta, regula eadem, & ſub figura di-
ſtantiarum eiuſdem parabolæ per obliquam ad axem con-
ſtitutæ.
lineę in eandem @terminatæ, quarum vna rectè, altera
obliquè axim ſecet, ſint autem conſtitutarum ab eiſdem pa-
rabolarum diametri inter ſe æquales: Omnia quadrata pa-
rabolæ per eam, quæ rectè axim ſecat, conſtitutæ, regula
eadem, erunt æqualia rectangulis ſub parabola per obli-
quam ad axem conſtituta, regula eadem, & ſub figura di-
ſtantiarum eiuſdem parabolæ per obliquam ad axem con-
ſtitutæ.
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