ducantur rectæ BI & BD &longs;ecantes circulum CE in F & E: <lb/> Radium B excedunt exce&longs;&longs;ibus FI & ED, qui ex 8. lib.
3. in­<lb/> æquales &longs;unt, & ma­<lb/> <figure id="id.017.01.363.1.jpg" xlink:href="casat_mecha_017_la_1684/017-01-figures/017.01.363.1.jpg"/><lb/> jor e&longs;t ED quàm FI <lb/> differentiâ KD. </s>
<s id="s.002647">Ar­<lb/> cuum &longs;ubten&longs;æ CI <lb/> & ID æquales &longs;unt, <lb/> &longs;inuum IH & DG <lb/> differentia e&longs;t LD. <!-- KEEP S--></s>
<lb/>
<s id="s.002648">Dico majorem Ra­<lb/> tionem e&longs;&longs;e HI ad IF, quàm LD ad DK. <!-- KEEP S--></s>
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<s id="s.002649">Primò ducantur rectæ EF, KI: EF autem producatur ita, <lb/> ut occurrat rectæ DI productæ in O. <!-- KEEP S--></s>
<s id="s.002650">Quia triangula BFE & <lb/> BIK &longs;unt i&longs;o&longs;celia, & angulus BEF æqualis e&longs;t angulo BKI, <lb/> rectæ EO & KI ex 28.lib.1. &longs;unt parallelæ: igitur ex 2 lib.
6. <lb/> in triangulo DOE ut DI ad IO, ita DK ad KE: Atqui DI <lb/> major e&longs;t quàm IO, ergo etiam DK major quàm KE. </s>
<s id="s.002651">Proba­<lb/> tur autem DI majorem e&longs;&longs;e quàm IO; quia DI æqualis e&longs;t <lb/> ip&longs;i CI ex hypothe&longs;i; punctum verò O e&longs;t extra circulum CE, <lb/> quem linea EFO &longs;ecat: ergo linea EF producta occurrit li­<lb/> neæ IC citrà punctum C in S. <!-- KEEP S--></s>
<s id="s.002652">Sed quoniam angulus BEF e&longs;t <lb/> acutus, qui e&longs;t illi deinceps DEO e&longs;t obtu&longs;us; ergo per 16. <lb/> lib.1. externus DOS multo magis e&longs;t obtu&longs;us: ergo per 19 <lb/> lib.1. major e&longs;t IS quàm IO, ergo multò major e&longs;t IC quàm <lb/> IO, hoc e&longs;t ID major e&longs;t quàm IO. <!-- KEEP S--></s>
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<s id="s.002653">Deinde angulus MCI major e&longs;t angulo NID, majori enim <lb/> arcui MDI ille in&longs;i&longs;tit, hic autem minori ND ex 33. lib.
6: <lb/> triangula verò HIC & LDI rectangula æquales habent hy­<lb/> pothenu&longs;as, hoc e&longs;t Radios CI & ID, ergo majoris anguli <lb/> HCI major e&longs;t &longs;inus HI; minoris verò anguli LID minor e&longs;t <lb/> &longs;inus LD. <!-- KEEP S--></s>
<s id="s.002654">Igitur ex 8. lib.5. HI major ad KE, hoc e&longs;t ad IF, <lb/> habet majorem Rationem quàm ad eandem KE habeat LD <lb/> minor: & eadem LD habet minorem Rationem ad DK ma­<lb/> jorem quàm ad KE minorem: Ergo HI ad IF majorem habet <lb/> Rationem, quàm LD ad DK.
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