207187LIBER II.
ſe extendit, quot ſunt figurarum planarum variationes, quæ nulto aſſi-
gnato coarctantur numero, cuius modi demonſtrationis vniuerſalitatem
in alijs figuris quoque in poſterum conſiderandis proſequemur, vt am-
plius infra patebit.
gnato coarctantur numero, cuius modi demonſtrationis vniuerſalitatem
in alijs figuris quoque in poſterum conſiderandis proſequemur, vt am-
plius infra patebit.
N. SECTIO XIII.
_I_N Prop.
29.
&
eius Corollario tandem edocemur ſolida ſimilaria
genita ex parallelogrammo, vel triangulo eodem, iuxta duas regu-
las latera angulum continentia, ideſt cylindricos ab eodem parallelo-
grammo, & conicos ab eodem triangulo genitos, iuxta dictas regulas,
eſſe inter ſe, vt eaſdem regulas.
genita ex parallelogrammo, vel triangulo eodem, iuxta duas regu-
las latera angulum continentia, ideſt cylindricos ab eodem parallelo-
grammo, & conicos ab eodem triangulo genitos, iuxta dictas regulas,
eſſe inter ſe, vt eaſdem regulas.
THEOREMA XXXV. PROPOS. XXXV.
PArallelepipedum ſub baſi rectangulo quodam, altitu-
dine autem quadam recta linea æquatur parallelepipe-
dis ſub baſi eodem rectangulo, & ſub quotcumq; paitibus,
in quas altitudo vtcumq; diuidui poteſt. Et ſi rectangulum,
quod eſt baſis, intelligatur vtcumq; diuiſum in quotcumq;
rectangula, dictum parallelepipedum æquatur parallelepi-
pedis ſub ſingulis partibus altitudinis, & ſingulis partibus
bafis.
dine autem quadam recta linea æquatur parallelepipe-
dis ſub baſi eodem rectangulo, & ſub quotcumq; paitibus,
in quas altitudo vtcumq; diuidui poteſt. Et ſi rectangulum,
quod eſt baſis, intelligatur vtcumq; diuiſum in quotcumq;
rectangula, dictum parallelepipedum æquatur parallelepi-
pedis ſub ſingulis partibus altitudinis, & ſingulis partibus
bafis.
Sit parallelepipedum rectangulum, AP, cuius baſis rectangulum,
TH, ſupponatur pro nunc indiuiſa, & altitudo, DT, diuiſa vtcum-
quein quotcumq; partes, DS, ST. Dico parallelepipedum, AP,
æquari parallelepipedis ſub, DS, TH, & ſub, ST, TH. Duca-
tur per, S, planum æquidiſtans baſi, TH, quodin eo producet re-
11Corol. 12.
lib. I. ctangulum, vt, SG, ſuntigitur, AM, NP, parallelepipeda, & , A
M, eſt ſub, DS, SG, vel, IH, (quia, SG, TH, ſunt figuræ ſi-
22Corol. 12.
lib. I. mdes, & æquales) NP, vero ſub, ST, TH, continetur, eit autem
parallelepipedum, AP, contentum ſub, DT, TH, æquale paral-
lelepipedis, AM, NP, ſuis partibus ſimul ſumptis, ergo parallele-
pipedum ſub, DT, TH, æquatur parallelepipedis ſub, DS, TH,
& ſub, ST, TH.
TH, ſupponatur pro nunc indiuiſa, & altitudo, DT, diuiſa vtcum-
quein quotcumq; partes, DS, ST. Dico parallelepipedum, AP,
æquari parallelepipedis ſub, DS, TH, & ſub, ST, TH. Duca-
tur per, S, planum æquidiſtans baſi, TH, quodin eo producet re-
11Corol. 12.
lib. I. ctangulum, vt, SG, ſuntigitur, AM, NP, parallelepipeda, & , A
M, eſt ſub, DS, SG, vel, IH, (quia, SG, TH, ſunt figuræ ſi-
22Corol. 12.
lib. I. mdes, & æquales) NP, vero ſub, ST, TH, continetur, eit autem
parallelepipedum, AP, contentum ſub, DT, TH, æquale paral-
lelepipedis, AM, NP, ſuis partibus ſimul ſumptis, ergo parallele-
pipedum ſub, DT, TH, æquatur parallelepipedis ſub, DS, TH,
& ſub, ST, TH.
Sit nunc bafis, TH, diuiſa vtcumque in quotcumque rectangula,
TV, VP. Dico parallelepipedum ſub, DT, TH, æquari paral-
lelepipedis ſub, DS, TV, ſub, DS, VP, ſub, ST, TV, & ſub,
ST, VP. Ducatur per rectam, QV, planum æquidiſtans
TV, VP. Dico parallelepipedum ſub, DT, TH, æquari paral-
lelepipedis ſub, DS, TV, ſub, DS, VP, ſub, ST, TV, & ſub,
ST, VP. Ducatur per rectam, QV, planum æquidiſtans
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib