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.
THEOREMA IV. PROPOS. IV.
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.
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