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276 COMMENTARIA ANTIQUA. Br, rj EJ TCQos ^Z, xal dC%a tsr^i]0&(D rj EZ' drilov dri, on, sl ^sv r} AB rfj BF £0tiv l'6rj Kal 7] E^ tfj z/Z, dixotofiia s6tai r^g EZ t6 ^, sl ds i] AB tijg BF ^sl^cov xal rj EA tfjg ^Z, rj 8L%oto^ia 5 xat(otSQ(o s6tl tov ^, st ds rj AB trjg BF skci66(ov, dvcotsQCO. s6tcj ds vvv tS(og ^atatSQC} wg to H, xal zsvtgcj ta H diaatriiiiati ta HZ nvTikog ysyQcitpd^cD' dst di] di,a td5v A, B ^rj^sCav ri^siv r/ sGcatsQCJ r] s^cjtSQCo. 10 Kal sl [isv dicc tc5v A, B ^rj^sicov SQ%oito, ysyovbg av sl'rj tb ijtitax^sv vjtSQTtiTttstco ds ra A, B, xal SKpXrjd^staa s
EUTOCII COIVIMENTARIA IN CONICA. 277 dicularis ducatur E^Z, et fiat EJ : ^Z = AB: BF, seceturque EZ m duas partes aequales; manifestum igitur, si AB == BF Qi EJ = AZ, punctum z/ esse medium rectae EZ, sin AB>Br et EJ>JZ, punctum medium infra A positum esse, sin AB ^ BF, supra A. nunc autem infra sit positum ut if, et centro H radio HZ circulus describatur; is igitur aut per puncta A, B ueniet aut intra ea aut extra. iam si per puncta A, B uenerit, effectum erit, quod propositum est; cadat uero extra Aj B, et AB ad utramque partem producta cum ambitu in @, K concurrat, ducanturque Z0, &Ej EKy KZj per B autem rectae ZK parallela ducatur MB, rectae KE autem parallela BAj ducanturque MA, AA\ eae igitur et ipsae rectis Z®y ®E parallelae erunt, quia AA = AB, A® = z/iT, et ZAE ad &K perpendicularis [Eucl. T, 4]. et quoniam angulus ad K positus rectus est, et MB, BA rectis ZK, KE parallelae, erit etiam angulus ad B positus rectus; eadem de causa etiam angulus ad A positus rectus est. quare circulus circum MA descriptus per A, B ueniet [Eucl. III, 31]. describatur ut MAAB, et quoniam MB, ZK parallelae sunt, erit [Eucl. YI, 4] ZA : modo erit K^ : AM= = EA : KA : AB EA:AZ^AA: AM= AB : zJB. iam eodem AA^) et permutando BT. 1) Post JA lin. 25 excidisse uidentur haec fere: Eativ ccqcc, ag ri Zd nQog z/M, 7] Ez/ TiQog JA. Wp, corr. Comm. 23. MAAB] MAAB Wp, corr. Comm. 25. JB] B e corr. m. 1 W. JA] AA Wj^, corr. Comm.
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(D s APOLLONIl PERGAEI QUAE GEAECE
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PEAEFATIO. Praeter librum lY Conico
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AB PRAEFATIO. V 3. cod. Paris. Gr.
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