451429LIBER VI.
ſunt circulorum, à quibus abſcinduntur partes proportionales, ipſi au-
tem circuli ſunt, vt diametrorum quadrata.
tem circuli ſunt, vt diametrorum quadrata.
THEOREMA IV. PROPOS. IV.
DAti circuli, necnon ſimiles fectores inter ſe ſunt, vt
omnes eorundem circumferentiæ.
omnes eorundem circumferentiæ.
Sint in eadem antecedentis figura circuli quinque, BADC,
FXZ, deſcripti ſuper eodem centro, E, & abijſdem intelligantur
310[Figure 310]
abſciſſi ſimiles ſectores, D
ED, XEZ. Dico circulos,
DABC, FZX, necnon ſe-
ctores, DEC, XEZ, inter ſe
eſſe, vt omnes iplorum cir-
cumferentiæ. Sit denuò
expoſitũ triãgulum, HOM,
cuius ſit angulus rectus, H
MO, latus, HM, æquale ra-
dio, ED, & , MO, circum-
ferentiæ, DCBA, abſciſſa
autem, HR, æqualr ipſi,
EX, & per, R, ducta paral-
lela ipſi, OM, quæ ſit, SR, intercepta lateribus, HO, HM, patet,
vt dicebatur in Corol. 2. ant. Propoſ. quod circumferentia, FZX,
æquatur ipſi, SR, eodem modo abſcindentes ab ipſis, HM, ED,
verſus, H, E, puncta æquales quaſcunque rectas lineas, & per ea-
rum terminos ducentes parallelam quidem ipſi, OM, in triangulo,
& circumfer entiam iuper cenrro, E, in circulo, ABCD, manife-
ſtum erit prædictam circumferentiam æquari prædictæ parallelæ,
lateribus, HO, HM, interceptæ, & vnicuique circumferentiæ in
circulo, ABCD, fic deſcriptæ reſpondere ſuam parallelam in triã-
gulo, HOM, cum ſint rectę, HM, ED, æquales, igitur conclude-
mus omnes circumferentias circuli, DABC, æquari omnibus li-
neis trianguli, HOM, regula, OM, ſicut etiam omnes circumfe-
rentias circuli, FZX, æquari omnibus lineis trianguli, HSR, regu-
la eadem, OM, quapropter, vt omnes lineæ trianguli, HOM, ad
omnes lineas trianguli, HSR, ideſi vt triãgulum, HOM, ad, HSR,
113. l. 2. ideſt vt circulus, DABC, ad circulum, FZX, ita omnes circumfe-
rentiæ circuli, ABCD, erunt ad omnes circumfarentias circuli
ciuidem, FZX; quod & fimuli methodo de ſectoribus ex. g.
FXZ, deſcripti ſuper eodem centro, E, & abijſdem intelligantur
ED, XEZ. Dico circulos,
DABC, FZX, necnon ſe-
ctores, DEC, XEZ, inter ſe
eſſe, vt omnes iplorum cir-
cumferentiæ. Sit denuò
expoſitũ triãgulum, HOM,
cuius ſit angulus rectus, H
MO, latus, HM, æquale ra-
dio, ED, & , MO, circum-
ferentiæ, DCBA, abſciſſa
autem, HR, æqualr ipſi,
EX, & per, R, ducta paral-
lela ipſi, OM, quæ ſit, SR, intercepta lateribus, HO, HM, patet,
vt dicebatur in Corol. 2. ant. Propoſ. quod circumferentia, FZX,
æquatur ipſi, SR, eodem modo abſcindentes ab ipſis, HM, ED,
verſus, H, E, puncta æquales quaſcunque rectas lineas, & per ea-
rum terminos ducentes parallelam quidem ipſi, OM, in triangulo,
& circumfer entiam iuper cenrro, E, in circulo, ABCD, manife-
ſtum erit prædictam circumferentiam æquari prædictæ parallelæ,
lateribus, HO, HM, interceptæ, & vnicuique circumferentiæ in
circulo, ABCD, fic deſcriptæ reſpondere ſuam parallelam in triã-
gulo, HOM, cum ſint rectę, HM, ED, æquales, igitur conclude-
mus omnes circumferentias circuli, DABC, æquari omnibus li-
neis trianguli, HOM, regula, OM, ſicut etiam omnes circumfe-
rentias circuli, FZX, æquari omnibus lineis trianguli, HSR, regu-
la eadem, OM, quapropter, vt omnes lineæ trianguli, HOM, ad
omnes lineas trianguli, HSR, ideſi vt triãgulum, HOM, ad, HSR,
113. l. 2. ideſt vt circulus, DABC, ad circulum, FZX, ita omnes circumfe-
rentiæ circuli, ABCD, erunt ad omnes circumfarentias circuli
ciuidem, FZX; quod & fimuli methodo de ſectoribus ex. g.
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