508488GEOMETRIÆ
autem figuræ, vt ſupra innuimus, dicatur æqualiter analogæ, &
ſi
opus erit, iuxta regulas lineas parallelas, ſeu plana parallela, AD,
Y4.
opus erit, iuxta regulas lineas parallelas, ſeu plana parallela, AD,
Y4.
SCHOLIVM.
_C_Vm antecedens Prop.
maximi ſit momenti, vt in ſequentibus
apparebit, aliuſq; modus priorem partem demonſtrandi, ſtylo
Archimedeo haud abſimilis, menti ſuccurrerit, idipſum ne pereatin
Lemmata diſtributum hic ſubiungere placuit.
apparebit, aliuſq; modus priorem partem demonſtrandi, ſtylo
Archimedeo haud abſimilis, menti ſuccurrerit, idipſum ne pereatin
Lemmata diſtributum hic ſubiungere placuit.
LEMMA PRIMVM.
SI in eadem, vel æqualibus baſibus, &
in eiſdem paral-
lelis figuræ planę æqualiter analogę iuxta eaſdem ba-
ſes fuerint conſtitutæ, itatamen, vt quæcunq; æquidiſtã-
tium baſibus linearum portiones in eiſdem conceptæ figu-
ris integræ ſint, ac eidem baſi, vel baſibus æquales, ipſæ
pariter figuræ inter ſe æquales erunt.
lelis figuræ planę æqualiter analogę iuxta eaſdem ba-
ſes fuerint conſtitutæ, itatamen, vt quæcunq; æquidiſtã-
tium baſibus linearum portiones in eiſdem conceptæ figu-
ris integræ ſint, ac eidem baſi, vel baſibus æquales, ipſæ
pariter figuræ inter ſe æquales erunt.
Sint in eadem baſi, GH, ſeu in æqualibus baſibus, &
in eiſdem
parallelis, AF, PQ, figuræ planæ, AGHB, EGHF, æqualiter ana-
340[Figure 340]
logę iux-
ta eandẽ
baſem, G
H, ſeu ba
ſes ęqua-
les iã di-
ctas, ex-
tenſa ve-
ro qua-
cunq; ip-
ſis, PQ, A
F, parallela, SR, eiuſdem portiones captæ in præfatis figuris, vt,
ST, NO, integræ ſint, ac æquales baſi, GH, ſeu dictis æqualibus
baſibus. Dico etiam præfatas figuras inter ſe æquales eſſe. In ea-
dem enim baſi, GH, ſeu in altera dictarum æqualium baſium ſit
conſtitutum, & in eiſdem parallelis, AF, PQ, quodcunq; paralle-
logrammum, CH, in quo portio concepta ipſius, SR, ſit, LM, quę
erit æqualis ipſi, GH, & conſequenter ipſi, NO, vnde addita cõ-
muni, MN, fiet, LN, æqualis, MO. Eodem modo autem oſten-
demus, CE, eſſe æqualem, DE, & reliquas huiu ſmodi
parallelis, AF, PQ, figuræ planæ, AGHB, EGHF, æqualiter ana-
ta eandẽ
baſem, G
H, ſeu ba
ſes ęqua-
les iã di-
ctas, ex-
tenſa ve-
ro qua-
cunq; ip-
ſis, PQ, A
F, parallela, SR, eiuſdem portiones captæ in præfatis figuris, vt,
ST, NO, integræ ſint, ac æquales baſi, GH, ſeu dictis æqualibus
baſibus. Dico etiam præfatas figuras inter ſe æquales eſſe. In ea-
dem enim baſi, GH, ſeu in altera dictarum æqualium baſium ſit
conſtitutum, & in eiſdem parallelis, AF, PQ, quodcunq; paralle-
logrammum, CH, in quo portio concepta ipſius, SR, ſit, LM, quę
erit æqualis ipſi, GH, & conſequenter ipſi, NO, vnde addita cõ-
muni, MN, fiet, LN, æqualis, MO. Eodem modo autem oſten-
demus, CE, eſſe æqualem, DE, & reliquas huiu ſmodi