8262GEOMETRIÆ
punctis, P, O, occurrentes, ductis autem duobus planis quomodo-
cumque baſibus parallelis, & ſecantibus altitudines, FC, PO, ſimi-
liter ad eandem partem in punctis, Λ Γ, eadem ſecent latera homo-
loga ex. gr. IH, QS, in punctis, Π Z. Dico in eiſdem ſecari ſimi-
liter ad eandem partem. Producantur ergo, HI, SQ, hinc inde,
ita vt (niſi hocipſis contingat abſque eo, quod producantur) ad pla-
na baſium, DAB, KMN, & eiſdem æquidiſtantia plana per ver-
tices, F, P, ducta, terminentur, vt in punctis, L, T, G, R, à pun-
ctis verò, G, R, demittantur ad plana dictarum baſium perpendicu-
lares, GE, RX, illis incidentes in, E, X, & iungantur, L, E, TX.
Sìmiliter à verticibus, F, P, ad puncta baſium, B, N, ducantur, F
B, PN, & iungantur, BC, NO. Quoniam ergo latera homolo-
ga, HI, SQ, continent cumhomologis lateribus ſimilium trian-
gulorum, AID, MQK, ad eandem partem baſibus, DAB, KM
N, inclinatorum (quia, IADB, QMNK, eſſent ſimiles pyrami-
des) angulos ęquales, & producta incidunt in plana dictarum baſium
11Ex Lem.
5. in, L, T, erunt eiſdem æqualiter inclinata, ergo anguli, GLE, R
43[Figure 43]
TX, erunt ęquales,
& , GEL, RXT,
ſunt recti, ergo triã-
gula, GLE, RT
X, ſimilia erunt, er-
go, GL, ad, RT,
erit vt, GE, ad, R
X, ideſt vt, FC, ad
PO. Vlterius ſi iun-
geremus, FA, FD,
PM, PK, fierent
ſimiles pyramides,
FDAB, PKMN, vnde pateret, FB, PN, eſſe ad plana baſium,
22Ex Lem.
4. DAB, KMN, ſimiliter inclinata, & ſubinde angulos, FBC, P
NO, eſſe ęquales, & cum ſint recti, FCB, PNO, triangula, FB
C, PNO, eſſe æquiangula, & vt, FC, ad, PO, ita eſſe, FB, ad,
PN, etiam manifeſtum eſſet, ſed vt, FC, ad, PO, ita eſt, GL, ad,
RT, & vt, FB, ad, PN, ita, BD, ad, NK, & ita quodcunque
latus in ſolido, FHB, ad latus ſibi homologum in ſolido, PSN,
ideſt ita, IH, ad, QS, ergo vt, GL, ad, RT, ita, HI, ad, SQ,
3319. Quin.
Elem.& ita compoſitum ex reſiduis, LH, IG, ad compoſitum ex reſiduis,
TS, QR, ſunt autem, LH, TS, latera homologa ſimilium pyra-
44Ex Lem.
5. midum, HLAD, STMK, ergo vt, HA, ad, SM, velvt, HI,
ad, SQ, ita, HL, ad, ST, ergo etiam reliqua, IG, ad reliquam,
QR, eſt vt, HI, ad, SQ, vel vt altitudo, FC, ad, PO, vel vt,
cumque baſibus parallelis, & ſecantibus altitudines, FC, PO, ſimi-
liter ad eandem partem in punctis, Λ Γ, eadem ſecent latera homo-
loga ex. gr. IH, QS, in punctis, Π Z. Dico in eiſdem ſecari ſimi-
liter ad eandem partem. Producantur ergo, HI, SQ, hinc inde,
ita vt (niſi hocipſis contingat abſque eo, quod producantur) ad pla-
na baſium, DAB, KMN, & eiſdem æquidiſtantia plana per ver-
tices, F, P, ducta, terminentur, vt in punctis, L, T, G, R, à pun-
ctis verò, G, R, demittantur ad plana dictarum baſium perpendicu-
lares, GE, RX, illis incidentes in, E, X, & iungantur, L, E, TX.
Sìmiliter à verticibus, F, P, ad puncta baſium, B, N, ducantur, F
B, PN, & iungantur, BC, NO. Quoniam ergo latera homolo-
ga, HI, SQ, continent cumhomologis lateribus ſimilium trian-
gulorum, AID, MQK, ad eandem partem baſibus, DAB, KM
N, inclinatorum (quia, IADB, QMNK, eſſent ſimiles pyrami-
des) angulos ęquales, & producta incidunt in plana dictarum baſium
11Ex Lem.
5. in, L, T, erunt eiſdem æqualiter inclinata, ergo anguli, GLE, R
& , GEL, RXT,
ſunt recti, ergo triã-
gula, GLE, RT
X, ſimilia erunt, er-
go, GL, ad, RT,
erit vt, GE, ad, R
X, ideſt vt, FC, ad
PO. Vlterius ſi iun-
geremus, FA, FD,
PM, PK, fierent
ſimiles pyramides,
FDAB, PKMN, vnde pateret, FB, PN, eſſe ad plana baſium,
22Ex Lem.
4. DAB, KMN, ſimiliter inclinata, & ſubinde angulos, FBC, P
NO, eſſe ęquales, & cum ſint recti, FCB, PNO, triangula, FB
C, PNO, eſſe æquiangula, & vt, FC, ad, PO, ita eſſe, FB, ad,
PN, etiam manifeſtum eſſet, ſed vt, FC, ad, PO, ita eſt, GL, ad,
RT, & vt, FB, ad, PN, ita, BD, ad, NK, & ita quodcunque
latus in ſolido, FHB, ad latus ſibi homologum in ſolido, PSN,
ideſt ita, IH, ad, QS, ergo vt, GL, ad, RT, ita, HI, ad, SQ,
3319. Quin.
Elem.& ita compoſitum ex reſiduis, LH, IG, ad compoſitum ex reſiduis,
TS, QR, ſunt autem, LH, TS, latera homologa ſimilium pyra-
44Ex Lem.
5. midum, HLAD, STMK, ergo vt, HA, ad, SM, velvt, HI,
ad, SQ, ita, HL, ad, ST, ergo etiam reliqua, IG, ad reliquam,
QR, eſt vt, HI, ad, SQ, vel vt altitudo, FC, ad, PO, vel vt,