Clavius, Christoph - In Sphaeram Ioannis de Sacro Bosco commentarius

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12891Ioan. de Sacro Boſco. tuor ſimul, poſterioribus quatuor ſimul æqualia: additis ergo communibus
A B, C D, fient ſex alte@a A E, E B, B A, C F, F D, D C, ſimul æqualia ſex late-
ribus A N, N B B A, C O, O D, D C, ſimul; ideoq́uetriangula A N B, C O D,
ſimul iſoperimetra erunt triangulis A E B, C F D, ſimul. Dico iam, quod & ſi-
milia inter ſe ſunt triangula A N B, C O D. Nam quoniam eſt, ut A B, ad O D,
ita G K, ad K H, hoc eſt, ita G L, ad K M, hoc eſt, ita A N, ad C O, & N B, ad
1115. quinti ad O D, erit permutando, vt A B, ad A N, ita C D, ad C O; & vt A N, ad N B,
ita C O; ad O D. Proportionalia ergo ſunt latera triangulorum A N B, COD;
ac proinde æquiangula inter ſe erunt, & idcireo ſimilia. Quare datis duobus
triangulis Iſoſcelibus, quorum baſes inæquales exiſtant. & c. conſtituim us. quod
225. ſexti. faciendum erat.

THEOR. 9. PROPOS. 11.

Dvo triangula Iſoſcelia ſimilia ſuper inæqualibus baſibus conſtitu-
33Triangulæ
duo Iſoſce-
lia ſimilia
maiora sũt
duobus Iſo
ſcelibus nõ
ſimilibus,
quæ illis
ſint Iſope-
rimetta, ba-
ſesque ha-
beant eaſ-
dem. ta, utraque ſimul maiora ſunt duobus triangulis Iſoſcelibus, utriuſque ſi-
mul, quę habeant eaſdem baſes cum prioribus, ſintq; disſimila quidem
inter ſe. at iſoperimetra prioribus duobus, nec non quatuor latera inter ſe
habeant æqualia.

Svper baſibus inæqualibus A C, C E, ſint duo triangula Iſoſcelia in-
ter ſe non ſimilia A B C, C D E, ita vt quatuor latera A B, B C, C D, D E,
inter ſe ſint æqualia. At-

29[Figure 29] que ſuper eiſdem baſibus
A C, C E, (per præceden-
tem propoſ.) conſtituan-
tur alia duo triãgula Iſo-
ſcelia A F C, C G E; ſimi-
lia inter ſe, & iſoperime-
tra ſimul prioribus trian-
gulis ſimul. Dico duo triã
gula A F C, C G E, ſimul
maiora eſſe duobus trian
gulis A B C, C D E, ſi-
mul. Ponantur enim A C,
C E, ſecundum lineam re
ctam vnam; ſitq́; A C, ba-
ſis maior baſe C E. Dein-
de ex F, per B, ducatur
recta F B K, ſecans rectam
A C, in puncto K; Item ex
D, per G, punctum duca
tur recta D C H, ſecans rectam C E, in H. Et quia latera A F, F B, triangu-
li A F B, æqualia ſunt lateribus C F, F B, trianguli C F B, & baſis A B, baſi
B C, æqualis, erit angulus A F B, angulo C F B, æqualis. ſurſus quia late-
@a A F, F K, trianguli A F K, æqualia ſunt lateribus C F, F K, trianguli,
448. primi.

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