264244GEOMETRIÆ
THEOREMA XXIV. PROPOS. XXV.
IN figura circuli, &
ellipſis eiuſdem Theor.
21.
oſtenden-
dum eſt, ibi appoſitis retentis, ſumpta tamen vtcunque
portione minori, RFV, & regula diametro eiuſdem portio-
nis. ſ. FM; omnia quadrata parallelogrammi, Δ V, ad omnia
quadrata portionis, RFV, eſſe vt quadratum, FM, ad ſpa-
tium, quod remanet, dempto rectangulo ſub, IM, & ſub, F
M, (ad quam, FM, ſit, vt, Δ V, ad portionem, RFV,) à re-
ctangulo ſub, FM, & ſub, {2/3}, ipſius, MH.
dum eſt, ibi appoſitis retentis, ſumpta tamen vtcunque
portione minori, RFV, & regula diametro eiuſdem portio-
nis. ſ. FM; omnia quadrata parallelogrammi, Δ V, ad omnia
quadrata portionis, RFV, eſſe vt quadratum, FM, ad ſpa-
tium, quod remanet, dempto rectangulo ſub, IM, & ſub, F
M, (ad quam, FM, ſit, vt, Δ V, ad portionem, RFV,) à re-
ctangulo ſub, FM, & ſub, {2/3}, ipſius, MH.
Sit igitur vt, Δ V, ad, RFV, ita, FM, ad, MI;
omnia ergo qua-
drata, Δ V, adrectangula ſub, Δ V, VT, ſunt vt quadratum, FM,
ad rectangulum, FMI, rectangula inſuper ſub, Δ V, VT, ad re-
1114. Lib. 2. ctangula ſub portione, RFV, & ſub, VT, ſunt vt, Δ V, ad portionem,
163[Figure 163]
RFV, .
i.
vt, FM, ad, MT, .
i.
ſumpta, MI,
22Coroll. 1.
26. lib. 2. communi altitudine, vt rectangulum, F
MI, ad rectangulum, r MI, ergo ex æ-
33@. Lib. 2. quali omnia quadrata, Δ V, ad rectangu-
la ſub portione, RFV, & ſub, VT, erunt
vt quadratum, FM, ad rectangulum,
Γ Μ Ι, quod ſerua.
drata, Δ V, adrectangula ſub, Δ V, VT, ſunt vt quadratum, FM,
ad rectangulum, FMI, rectangula inſuper ſub, Δ V, VT, ad re-
1114. Lib. 2. ctangula ſub portione, RFV, & ſub, VT, ſunt vt, Δ V, ad portionem,
22Coroll. 1.
26. lib. 2. communi altitudine, vt rectangulum, F
MI, ad rectangulum, r MI, ergo ex æ-
33@. Lib. 2. quali omnia quadrata, Δ V, ad rectangu-
la ſub portione, RFV, & ſub, VT, erunt
vt quadratum, FM, ad rectangulum,
Γ Μ Ι, quod ſerua.
Vlterius omnia quadrata, ΔV, ad om-
44@. Lib. 2. nia quadrata, VII, ſunt vt quadratum, F
M, ad quadratum, MO, vel ad quadra-
tum, RV, . i. ad quatuor rectangula ſub,
R M, MV: Omnia inſuper quadrata,
V II, ad rectangula ſub portione, RFV,
& quadrilineo, RTHY V, ſunt vt ſex
quadrata, CE, ad quadratũ, FH, nam in
circulo omnia quadrata, RZ, ſunt ſex-
55Elicitur
èx 21.hu-
ius. cupla rectangulorum ſub portione, RF
V, & quadrilineo, RTHYV, & ideo ſunt
ad illa, vt ſex quadrata, CE, ad quadra-
tum, CE, vel ad quadratum, FH, in ellipſi
verò omnia quadrata, RZ, ſunt ad re-
ctangula ſub portione, RFV, & quadrilineo, RTHYV, vt ſex quadra-
ta, CE, ad quadratum, FH, quod elicitur ex Prop. 21. huius. Quia
vero rectangulum, RMV, ad rectangulum, FMH, (tum in cir-
6617. 3. Con.
44@. Lib. 2. nia quadrata, VII, ſunt vt quadratum, F
M, ad quadratum, MO, vel ad quadra-
tum, RV, . i. ad quatuor rectangula ſub,
R M, MV: Omnia inſuper quadrata,
V II, ad rectangula ſub portione, RFV,
& quadrilineo, RTHY V, ſunt vt ſex
quadrata, CE, ad quadratũ, FH, nam in
circulo omnia quadrata, RZ, ſunt ſex-
55Elicitur
èx 21.hu-
ius. cupla rectangulorum ſub portione, RF
V, & quadrilineo, RTHYV, & ideo ſunt
ad illa, vt ſex quadrata, CE, ad quadra-
tum, CE, vel ad quadratum, FH, in ellipſi
verò omnia quadrata, RZ, ſunt ad re-
ctangula ſub portione, RFV, & quadrilineo, RTHYV, vt ſex quadra-
ta, CE, ad quadratum, FH, quod elicitur ex Prop. 21. huius. Quia
vero rectangulum, RMV, ad rectangulum, FMH, (tum in cir-
6617. 3. Con.
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