6141LIBERI.
vt incidentes) ynde etiam figuræ eſſent æquales, &
ſi minores, etiam
ipſa figura, TDF, eſſet minor figura, BVO, contra ſuppoſitum,
eſtigitur, DC, maior ipſa, BR, eſt autem, vt, DC, ad, BR, ita,
PH, ad, NK, nam vt, DG, ad, BM, itaeſt, PH, ad, NK, &
11A. Defin.
10. etiamita, CG, ad, RM, ergo reliqua, DC, ad reliquam, BR,
erit vt, PH, ad, NK, ſic etiam eſſe oſtendemus, EF, ad, IO, vt,
PH, ad, NK, & quia, DC, eſt maior ipſa, BR, vel, EF, ipſa,
IO, ideò, HP, erit maior, KN, ſi igitur iunxerimus puncta, PN,
HK, ipſæ, PN, HK, ſi producantur ad partes ipſius, NK, con-
current, vt in, A. Dico, A, eſſe verticem conici, cuius eſt baſis ipſa,
30[Figure 30]
TDF, &
explano ipſi,
TDF, ęquidiſtanter du-
cto eſt in ipſo concepta
figura, VBO. Quia er-
224. Sexti
Elem. go, NK, eſt parallela
ipſi, PH, erunt triangu-
la, ANK, APH, ęqui-
angula, & circa æquales
angulos latera propor-
tionalia, igitur, HP, ad,
PA, erit vt, KN, ad, N
A, & , permutando, H
P, ad, NK, erit vt, PA,
ad, AN, vt autem, PH,
ad, NK, ita eſt, PG, ad, NM, nam ipſa, HP, KN, ſimiliter
ſunt diuiſæ in punctis, G, M, ergo, PA, ad, AN, erit vt, PG,
ad, NM, & ſunt parallelæ ipſæ, PG, NM, ergo puncta, G, M,
A, erunt in vna recta linea, ſit illa, AG, igitur, vt, PG, ad, NM,
33Ex Lem-
mate leq. vel, PH, ad, NK, ita erit, GA, ad, AM, eſt autem, PH, ad,
NK, vt, FG, ad, OM, & vt, EG, ad, IM, & tandem, vt, D
G, ad, BM, ergo, vt, GA, ad, AM, ita erit, FG, ad, OM; E
G, ad, IM; CG, ad, RM; & , DG, ad, BM, ergo, cum ſint
parallelæ, erunt tum puncta, AOF, tum, AIE, ARC, tum etiam,
ABD, in vna recta linea, extendantur ergo dictæ rectæ lineæ, quę
44Ex Lem-
mate leq. erunt, AF, AE, AD, AC. Eodem modo, ſi per duas quaslibet
homologas figurarum, VBO, TDF, planum extendamus, fiet in
cæteris demonſtratio; igitur ſi ſumantur in ambitu figurę, TDF,
quęcumq; puncta, quę iungantur cum puncto, A, ſemper iungen-
tes tranſibunt per circuitum figuræ, VBO, ergo figurę, TDF, & ,
VBO, erunt fruſti conici oppoſitę baſes, quod à conico, ATDF,
55Defin. 4. abſcinditur per figuram, VBO, quod erat demonſtrandum.
ipſa figura, TDF, eſſet minor figura, BVO, contra ſuppoſitum,
eſtigitur, DC, maior ipſa, BR, eſt autem, vt, DC, ad, BR, ita,
PH, ad, NK, nam vt, DG, ad, BM, itaeſt, PH, ad, NK, &
11A. Defin.
10. etiamita, CG, ad, RM, ergo reliqua, DC, ad reliquam, BR,
erit vt, PH, ad, NK, ſic etiam eſſe oſtendemus, EF, ad, IO, vt,
PH, ad, NK, & quia, DC, eſt maior ipſa, BR, vel, EF, ipſa,
IO, ideò, HP, erit maior, KN, ſi igitur iunxerimus puncta, PN,
HK, ipſæ, PN, HK, ſi producantur ad partes ipſius, NK, con-
current, vt in, A. Dico, A, eſſe verticem conici, cuius eſt baſis ipſa,
TDF, ęquidiſtanter du-
cto eſt in ipſo concepta
figura, VBO. Quia er-
224. Sexti
Elem. go, NK, eſt parallela
ipſi, PH, erunt triangu-
la, ANK, APH, ęqui-
angula, & circa æquales
angulos latera propor-
tionalia, igitur, HP, ad,
PA, erit vt, KN, ad, N
A, & , permutando, H
P, ad, NK, erit vt, PA,
ad, AN, vt autem, PH,
ad, NK, ita eſt, PG, ad, NM, nam ipſa, HP, KN, ſimiliter
ſunt diuiſæ in punctis, G, M, ergo, PA, ad, AN, erit vt, PG,
ad, NM, & ſunt parallelæ ipſæ, PG, NM, ergo puncta, G, M,
A, erunt in vna recta linea, ſit illa, AG, igitur, vt, PG, ad, NM,
33Ex Lem-
mate leq. vel, PH, ad, NK, ita erit, GA, ad, AM, eſt autem, PH, ad,
NK, vt, FG, ad, OM, & vt, EG, ad, IM, & tandem, vt, D
G, ad, BM, ergo, vt, GA, ad, AM, ita erit, FG, ad, OM; E
G, ad, IM; CG, ad, RM; & , DG, ad, BM, ergo, cum ſint
parallelæ, erunt tum puncta, AOF, tum, AIE, ARC, tum etiam,
ABD, in vna recta linea, extendantur ergo dictæ rectæ lineæ, quę
44Ex Lem-
mate leq. erunt, AF, AE, AD, AC. Eodem modo, ſi per duas quaslibet
homologas figurarum, VBO, TDF, planum extendamus, fiet in
cæteris demonſtratio; igitur ſi ſumantur in ambitu figurę, TDF,
quęcumq; puncta, quę iungantur cum puncto, A, ſemper iungen-
tes tranſibunt per circuitum figuræ, VBO, ergo figurę, TDF, & ,
VBO, erunt fruſti conici oppoſitę baſes, quod à conico, ATDF,
55Defin. 4. abſcinditur per figuram, VBO, quod erat demonſtrandum.