162142GEOMETRIÆ
QY, DEF, in recta, YM, ſuperſiciem, LDF, in linea, QM, ſu-
perficiem, ODF, in linea, TM, & figuram, CNX, in recta, ZI,
ſecet autem, QY, ipſam, BV, in puncto, ℟, & iungatur, A ℟, erit
ergo, ZI, ipſi, YK, æquidiſtans, eſt autem etiam, AK, æquidiſtans
ipſi, QY, ergo, YI, erit parallelogrammum, & ideò, IK, erit æ.
11Percõſtru
ctionem. qualis ipſi, ZY, & quia, AK, ad, KI, eſt vt, QY, ad, YT, . i. vt,
BH, ad, HC, . i vt, ℟ Y, ad, YZ, erit, AK, ad, KI, vt, ℟ Y, ad,
YZ, ſunt verò, IK, ZY, æquales, ergo & , AK, ℟ Y, erunt æqua-
les, & ſunt parallelæ, quia ambo ſunt parallelæ eidem, LE, ergo
eas iungentes, quæ ſunt, ℟ A, YK, erunt æquales, & parallelę, eſt
94[Figure 94]
autem, YK, pa-
rallela ipſi, Ε Ω,
& , Ε Ω, ipſi, VG,
ergo, ℟ A, erit pa-
rallela ipſi, VG.
Similiterautẽ pro-
cedemus in reli-
quis, quę per pun-
cta lineę, CX, ipſi,
LE, ducuntur æ-
quidiſtantes, do-
nec occurrant ſu-
perſiciei, LDF,
& plano, DEF,
harum autem patet nihil extra ſuperficiem, LDF, manere, ex iam
dictis, ſint ergo omnium earum termini ex vna parte in linea, BAG,
ex alia in linea, Η Κ Ω, veluti ergo oſtenſum eſt, A ℟, eſſe paralle-
lam ipſi, GV, ſic oſtendemus reliquas, quę iungunt puncta, quibus
iam ductæ occurrunt lineæ, BG, cum punctis, in quibus plana per
dictas lineas ducta, ipſi, LEF, æquidiſtantia, ſecant ipſam, BV, eſſe
ipſi, VG, paralſelas ergo omnes erunt in eodem plano, in eo ſcili-
cet quod tranſit per, BV, VG, omnes . n. dictæ parallelæ tranſeunt
per puncta rectæ lineæ, BV, ſunt igiturd cta occurſuum puncta, &
in ſuperficie, LDF, & in plano, BVG, erunt ergo in eorum com-
muni ſectione, linea ergo, BAG, eſt communis ſectio plani per, B
V, VG, tranſeuntis, & ſuperficiei, LDF; habemus ergo ſolidum,
Β Ω, in cuius ambiente ſuperficie ſunt duæ figuræ planæ inuicem pa-
rallelæ, BVG, Η Ε Ω, in quarum circuitu ſumptis vtcunque duo-
bus punctis, V, E, & iuncta, VE, cæteræ iungentes quælibet aliæ
22Def. Cy-
lindrici
confor-
miter. duo puncta earundem circuitus eidem ſemper, VE, parallelę reper-
tæ ſunt æquales, ergo, Β Ω erit cylindricus, cu@us oppoſitæ baſes
ipſæ, BVG, Η Ε Ω, hoc autem ſecatur plano eildem oppoſit@s
perficiem, ODF, in linea, TM, & figuram, CNX, in recta, ZI,
ſecet autem, QY, ipſam, BV, in puncto, ℟, & iungatur, A ℟, erit
ergo, ZI, ipſi, YK, æquidiſtans, eſt autem etiam, AK, æquidiſtans
ipſi, QY, ergo, YI, erit parallelogrammum, & ideò, IK, erit æ.
11Percõſtru
ctionem. qualis ipſi, ZY, & quia, AK, ad, KI, eſt vt, QY, ad, YT, . i. vt,
BH, ad, HC, . i vt, ℟ Y, ad, YZ, erit, AK, ad, KI, vt, ℟ Y, ad,
YZ, ſunt verò, IK, ZY, æquales, ergo & , AK, ℟ Y, erunt æqua-
les, & ſunt parallelæ, quia ambo ſunt parallelæ eidem, LE, ergo
eas iungentes, quæ ſunt, ℟ A, YK, erunt æquales, & parallelę, eſt
rallela ipſi, Ε Ω,
& , Ε Ω, ipſi, VG,
ergo, ℟ A, erit pa-
rallela ipſi, VG.
Similiterautẽ pro-
cedemus in reli-
quis, quę per pun-
cta lineę, CX, ipſi,
LE, ducuntur æ-
quidiſtantes, do-
nec occurrant ſu-
perſiciei, LDF,
& plano, DEF,
harum autem patet nihil extra ſuperficiem, LDF, manere, ex iam
dictis, ſint ergo omnium earum termini ex vna parte in linea, BAG,
ex alia in linea, Η Κ Ω, veluti ergo oſtenſum eſt, A ℟, eſſe paralle-
lam ipſi, GV, ſic oſtendemus reliquas, quę iungunt puncta, quibus
iam ductæ occurrunt lineæ, BG, cum punctis, in quibus plana per
dictas lineas ducta, ipſi, LEF, æquidiſtantia, ſecant ipſam, BV, eſſe
ipſi, VG, paralſelas ergo omnes erunt in eodem plano, in eo ſcili-
cet quod tranſit per, BV, VG, omnes . n. dictæ parallelæ tranſeunt
per puncta rectæ lineæ, BV, ſunt igiturd cta occurſuum puncta, &
in ſuperficie, LDF, & in plano, BVG, erunt ergo in eorum com-
muni ſectione, linea ergo, BAG, eſt communis ſectio plani per, B
V, VG, tranſeuntis, & ſuperficiei, LDF; habemus ergo ſolidum,
Β Ω, in cuius ambiente ſuperficie ſunt duæ figuræ planæ inuicem pa-
rallelæ, BVG, Η Ε Ω, in quarum circuitu ſumptis vtcunque duo-
bus punctis, V, E, & iuncta, VE, cæteræ iungentes quælibet aliæ
22Def. Cy-
lindrici
confor-
miter. duo puncta earundem circuitus eidem ſemper, VE, parallelę reper-
tæ ſunt æquales, ergo, Β Ω erit cylindricus, cu@us oppoſitæ baſes
ipſæ, BVG, Η Ε Ω, hoc autem ſecatur plano eildem oppoſit@s