223203LIBER III.
ctangula triplicata, rectangulum autem ſub, DR, &
ſub compoſi-
111. 2. elem. ta ex, {1/2}, RM, & , MA, diuiditur in rectangula ſub, DR, & , {1/2}, R
M, & ſub, DR, & , MA, triplicetur rectangulum ſub, DR, & ,
221. 2. elem. {1/2}, RM, fit rectangulum ſub tripla, DR, & ſub, {1/2}, RM, cui ſi ad-
datur rectangulum ſub, MR, & , {1/2}, RM, fit rectangulum ſub com-
poſita ex tripla, RD, & ex, RM, . ſ. ſub compoſita ex, MD, &
dupla, RD, & ſub, {1/2}, RM, quod ſerua: Remanent rectangula ad-
337. Lib. 2. huc ſub, DR, MA, & ſub, MR, & , {1/2}, MA, triplicanda, quod
ſic fiet; rectangulum ſub, DR, MA, æquatur rectangulo ſub dupla,
441. 2. ele@. DR, & , {1/2}, MA, cui ſi addatur rectangulum ſub, {1/2}, MA, & ſub,
MR, fiet rectangulum ſub, {1/2}, MA, & ſub compoſita ex, MR, &
dupla, RD, . ſ. ſub compoſita ex, MD, DR, quod triplicatum fit
rectangulum ſub compoſita ex, MD, DR, & ſub ſexquialtera, M
A, quod ſimul cum rectangulo ſub compoſita ex, MD, & dupla, D
R, & ſub, {1/2}, MR, ad rectangulum, DRA, conuertendo, habe-
bit eandem rationem, quam omnia quadrata portionis, ICFS, ad
omnia quadrata trianguli, CMF; quod etiam verificabitur, ſi di-
55Ex 9. & @.
Coroll.
22. lib. 2@ ctum parallelogrammum, & triangulum, ſint quidem in eadem baſi
cum portione, ſed non circa eundem axim, vel diametrum cum ea-
dem portione, vt ſupra patere poteſt in antecedentibus, quod erat
oſtendendum.
111. 2. elem. ta ex, {1/2}, RM, & , MA, diuiditur in rectangula ſub, DR, & , {1/2}, R
M, & ſub, DR, & , MA, triplicetur rectangulum ſub, DR, & ,
221. 2. elem. {1/2}, RM, fit rectangulum ſub tripla, DR, & ſub, {1/2}, RM, cui ſi ad-
datur rectangulum ſub, MR, & , {1/2}, RM, fit rectangulum ſub com-
poſita ex tripla, RD, & ex, RM, . ſ. ſub compoſita ex, MD, &
dupla, RD, & ſub, {1/2}, RM, quod ſerua: Remanent rectangula ad-
337. Lib. 2. huc ſub, DR, MA, & ſub, MR, & , {1/2}, MA, triplicanda, quod
ſic fiet; rectangulum ſub, DR, MA, æquatur rectangulo ſub dupla,
441. 2. ele@. DR, & , {1/2}, MA, cui ſi addatur rectangulum ſub, {1/2}, MA, & ſub,
MR, fiet rectangulum ſub, {1/2}, MA, & ſub compoſita ex, MR, &
dupla, RD, . ſ. ſub compoſita ex, MD, DR, quod triplicatum fit
rectangulum ſub compoſita ex, MD, DR, & ſub ſexquialtera, M
A, quod ſimul cum rectangulo ſub compoſita ex, MD, & dupla, D
R, & ſub, {1/2}, MR, ad rectangulum, DRA, conuertendo, habe-
bit eandem rationem, quam omnia quadrata portionis, ICFS, ad
omnia quadrata trianguli, CMF; quod etiam verificabitur, ſi di-
55Ex 9. & @.
Coroll.
22. lib. 2@ ctum parallelogrammum, & triangulum, ſint quidem in eadem baſi
cum portione, ſed non circa eundem axim, vel diametrum cum ea-
dem portione, vt ſupra patere poteſt in antecedentibus, quod erat
oſtendendum.
IN eadem antecedentis figura ſi parallelogrammum ſit
quidem in eadem altitudine cum portione, ſed in baſi æ-
quali ſecundæ diametro; omnia quadrata dicti parallelo-
grammiad omnia quadrata dictę portionis erunt, vt quadra-
tum dimidijaxis, vel diametri eorumdem ad eadem conſe-
quentia rectangula, retenta eadem regula.
quidem in eadem altitudine cum portione, ſed in baſi æ-
quali ſecundæ diametro; omnia quadrata dicti parallelo-
grammiad omnia quadrata dictę portionis erunt, vt quadra-
tum dimidijaxis, vel diametri eorumdem ad eadem conſe-
quentia rectangula, retenta eadem regula.
Exponatur denuò antece@entis figura,
136[Figure 136]&
producatur, CF, ita vt, V @, ſit æqua-
lis ſecundæ diametro, quæ ſit, EH, & ,
VR, æqualis, RX, & in, VX, baſi ſit
conſtructum parallelogrammum, GX,
in altitudine eadem cum portione, ICF
S, ſit etiam circa eandem axim, vel dia-
metrum, MR, cum portione, IECFH
S: Omnia ergo quadrata parallelogram-
mi, GR, ad omnia quadrata parallelogrammi, BR, (regula, CF,)
669. Lib. 2.
lis ſecundæ diametro, quæ ſit, EH, & ,
VR, æqualis, RX, & in, VX, baſi ſit
conſtructum parallelogrammum, GX,
in altitudine eadem cum portione, ICF
S, ſit etiam circa eandem axim, vel dia-
metrum, MR, cum portione, IECFH
S: Omnia ergo quadrata parallelogram-
mi, GR, ad omnia quadrata parallelogrammi, BR, (regula, CF,)
669. Lib. 2.