Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
22 KSiNIKOT d'. aTto xov B TtaQcc rrjv TIO dyo^svrj i]^£c dia tmv K, A. di 8L yag ^rj, rjtOL dia tov ivog avtcov elev^staL ^ ovdstSQOv. 5 sQ%sc^(o Slcc ^ovov tov K. s0tLV aQa, ag rj ZzJ TtQog z/H, rj ZX TtQog XH' ojtSQ atOTtov. ovx, aQa 7] ajto rov B TtaQO, tr^v 110 ayo^svri dLo, ^ovov tov K ilsvCstaL' di a^cpotsQCJV aQa. 10 Tav avtdov ovtcov sav to z/ arjfistov snl ^i&g J tc5v ddv^Tttatov , xal rj ^sv /d E ts^vr] tr]v to^rjv Tcata dvo ^rj^sta, 7] ds ^H ocatd /xovov to H jtaQdXXrjXog ov6a tij stsQa tcov davfiTttcotov, xal ysvrjtaL, 6g 7} JE TtQog z/0, ^ EK TtQog K&, tfi ds JH l'
CONICORUM LIBER IV. 23 contingens ducatur ^B. dico, rectam a B rectae ITO parallelam ductam per K, A cadere. nam si per minus, aut alterutrum eorum cadet aut per neutrum. cadat per K solum. itaque [III, 35] cadet ergo per utrumque cadet. quod absurdum est. ergo recta a B rectae 770 parallela ducta per K solum non XIV. lisdem positis si punctum A in alterutra asymptotarum positum est, et ziE sectionem in duobus punctis secat, z/77" autem alteri asymptotarum parallela in 77 solo, et fit EK:K® = AE: z/@, poniturque in JH producta HA = JH, recta per Kj A puncta ducta et asymptotae parallela erit et cum sectione concurret, rectaque a puncto concursus ad z/ ducta sectionem continget. nam eodem modo, quo in praecedenti, ducta ZlB contingenti dico, rectam a jB asymptotae 770 parallelam ductam per puncta K, A cadere. si igitur per K solum cadit, non erit AH =^ HA [III, 34]-, quod absurdum est. sin per A solum cadit, non erit EA : K® [III, 35]. sin neque z/0 = EK : per K neque per A cadit, ergo per utrumque cadet! utrobique absurdum eueniet.
- Page 63 and 64: PROLEGOMENA. LVII Cap. II. Q,uo mod
- Page 65 and 66: PROLEGOMENA. LIX Pappi lemma
- Page 67 and 68: PROLEGOMENA. LXI monstratione recep
- Page 69 and 70: PROLEGOMENA. LXIII praeter hos loco
- Page 71 and 72: PROLEGOMENA. LXV Bignificare uidetn
- Page 73 and 74: PROLEGOMENA. LXVII I p. 104, 4 JE]
- Page 75 and 76: ; PROLEGOMENA. LXIX Gtiq^rjg 7toXv7
- Page 77 and 78: PROLEGOMENA. LXXI fatione ornatae c
- Page 79 and 80: PROLEGOMENA. LXXIII 18 TtXdTog —
- Page 81 and 82: . PROLEGOMENA. LXXV ipsius scctioni
- Page 83 and 84: PROLEGOMENA. LXXVII caput linee mun
- Page 85 and 86: PKOLEGOMENA. LXXIX aut extra eam, c
- Page 87 and 88: PROLEGOMENA. LXXXI lun. 1428). qui
- Page 89 and 90: PROLEGOMENA. • LXXXIII de prets d
- Page 91: PROLEGOMENA. LXXXV notis commemorau
- Page 94 and 95: KiiNIKi^N 8'. IIqoxbqov ^ev i^ed^Tj
- Page 96 and 97: 4 KSiNIK^N d'. ysvij tovtOLs ccTtlc
- Page 98 and 99: 6 KSiNIKS^N d'. yiivYi av^ela Sdts
- Page 100 and 101: 8 K2NIKQN S'. P'- Tavta fihv xocvwg
- Page 102 and 103: 10 KSiNIK^N S'. 66j;o0av avTLxeC^ev
- Page 104 and 105: 12 K^NIK^JN 8\ lirj yccQ, c(XX% el
- Page 106 and 107: 14 KSJNIK^N d'. Tciv avtcav ovrcov
- Page 108 and 109: 16 KSiNIKSiN d'. ixrbg aTCoXa^Pavo^
- Page 110 and 111: 18 KSiNIKSiN d\ L . TaZta iikv xoiv
- Page 112 and 113: 20 KS^NIKSiN 8\ TtQos AH, deLKtaov,
- Page 116 and 117: 24 KSiNlKSiN 8'. dh iirixs dicc tov
- Page 118 and 119: 26 KS^NIKSiN d'. ccXla dLcc xov H.
- Page 120 and 121: 28 KS^NIKSiN d\ XeyG), (ki, rj ano
- Page 122 and 123: 30 KSiNIKSiN 8'. TCQog 6v^7ts6SitaL
- Page 124 and 125: 32 K^NIKSiN S' 'Eccv ds To Xrig^d^s
- Page 126 and 127: 34 KSiNIKSiN S\ kiyco^ oxL 7} dta x
- Page 128 and 129: 36 KSiNIKSiN 8'. ovx ^6taL, c)g rj
- Page 130 and 131: 38 KSiNIKQN 8'. oTCeQ aroTtov' tj t
- Page 132 and 133: 40 KSiNIKSiN d'. Xoyov 7] AA JtQog
- Page 134 and 135: 42 KSiNIKSiN S'. 7C
- Page 136 and 137: 44 KSiNIKSiN S'. iccv ds inl xijg i
- Page 138 and 139: 46 K
- Page 140 and 141: 48 KSiNIKSiN 8'. i7t£^€vj(^d-co
- Page 142 and 143: 50 KSiNIKi^N 3'. M^ TCQog ^ A xal X
- Page 144 and 145: 52 KSiNIKSiN d'. aTts^svx^c^ ^V ^^^
- Page 146 and 147: 54 KSiNIKSlN 8\ «TTo rcov A, B i(p
- Page 148 and 149: 56 KSiNlKS^N $'. £6tco0av avtLKSL^
- Page 150 and 151: 58 KQNIKJJN S'. Xr,'. Kcovov roft^
- Page 152 and 153: 60 KS^NIKS^N d'. itpdtl^srccL Kata
- Page 154 and 155: 62 KSiNIKSiN d'. dia tr^v ABF vtcsq
- Page 156 and 157: ' 64 KiiNIKiiN d\ xa KVQtd, 7] dvTL
- Page 158 and 159: QQ KiiNIKSiN 8', 'Eav vTtsQ^oXrj ^t
- Page 160 and 161: 68 K£iNIK
- Page 162 and 163: 5. at] p, om. V. 13. ON] ONP Y; cor
22 KSiNIKOT d'.<br />
aTto xov B TtaQcc rrjv TIO dyo^svrj i]^£c dia tmv<br />
K, A.<br />
di<br />
8L yag ^rj, rjtOL dia tov ivog avtcov elev^staL ^<br />
ovdstSQOv.<br />
5 sQ%sc^(o Slcc ^ovov tov K. s0tLV aQa, ag rj ZzJ<br />
TtQog z/H, rj ZX TtQog XH' ojtSQ atOTtov. ovx, aQa<br />
7] ajto rov B TtaQO, tr^v 110 ayo^svri dLo, ^ovov tov K<br />
ilsvCstaL' di a^cpotsQCJV aQa.<br />
10 Tav avtdov ovtcov sav to z/ arjfistov snl ^i&g J<br />
tc5v ddv^Tttatov , xal rj ^sv /d E ts^vr] tr]v to^rjv<br />
Tcata dvo ^rj^sta, 7] ds ^H ocatd /xovov to H jtaQdXXrjXog<br />
ov6a tij stsQa tcov davfiTttcotov, xal ysvrjtaL,<br />
6g 7} JE TtQog z/0, ^ EK TtQog K&, tfi ds JH l'