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Show QVO N1.A M Apollonius omnia feré conicorfi demonfh‘a:a Con 1111: 1.131211 281 TERTIVS. (11111 plano hyperbolarum communes {cé‘cioncs per 111. pfié‘tum cites 84 vtrinq;contln1utzelincz r mm s. Q19 fict,vt punaa 1- s.in quibus diétx lineg coincidunt lincis bafim conicum tangécib11528; pfiéh 1311. tnngcnnlxus 51t0fimrumlocutu1'i filcienms.3unt enim Non tmné'fisn in quib. hypcrbolcs parifcria occurrit perifcrix bafis conici : 11ccn_on punétum k. in (1110 lmfis hyperbolcs fiuc ordinam P q.lccnt diamcrrum a c.11qc inquam quinque punéh lintin vna rcéh r p k q s. qua: communis fcé‘tio ell plnni facicntis ' hyperlaolns tum bafi conico. hoc idem intellige per rcliqua W1 lines. qubd cf‘t igitur ndfi Oflcndc . pofim hyperbole. contra (lu 1' mac lines: II: 11111103111 in ccntro Epofitnmm hvpcrbolag; {Sc-'11."; & Vtrmquefempcr magis acnmgis in infinitum Parifcrijs 5p .~;.»:}- cs contrapoin pumSh) m. quodquc m r. m 5.111112121111117 Non tangent y w Cf]: 1‘11 Flanum rcdigctegmriquioribus ingcniofior; nélylcé"q co 11'01'11m'dcfc1'3p11011c‘, 84 aliund: quarcn; nrgunlcnm CGn'lt11v?,c~7;no onfc111'111s 8(1 . Ii‘cfle demonllsmrc 1d , qubd contcm1.1::an1loFlgl11l/x [1:511rally-6111921211191pertius 6: brcuius demonl‘tmturld :105 fccim11s in 4' 130.11.11115 pm‘cedcntis capiri conclulionibus : Icicm 1 unc dc No mqntfssmunquim verb coincimnrcsfit ob id Non mngeures fill-9N6 Commdcntc;1ppcllatm:de quibus Apollonius in 2° cogicoruln loéu- (us eitl‘los 1311111l1111'ul1nodilincarfi proprietares demonlh‘ntun luoc Erxfipnnuraduns hyperbolas in duobus reé‘tis conis fié‘tas ac (Emili111 mangulls per vcrticcs conorum Lluéhs :equidiflantes lhfiilcs elliv: 11.1.60 conicorum lib.o{lcnlum elendc omni probolitx l1v Acrbol; $1331: ac etjiilimilés)? (qualis collocari potefi 111 31111110 reélg com, 11 cm [1.11 1tur. 1 cm cm '0' ' ' ' (1 ficétinuam {ccat per mqualia diametrfi l n.conrmpol‘1mrfi prius hoc fitnrumziplhmc'lur: 111.ccntl'um ell: Seéfionum. Lcmm.1.Sed k: Cd. odclnpl punc'lzo vno ab lint lemma olfcndcndum eitDurelincae ntur C 5;. 86 ab carum termini: 3113 ad 1111115 mumb rcflcflza d fig 3.1% inuicczn in punéh) hAECantcsDicmq; ratio c d --d a.componitur cx rationibus c f He c f~fLItcm€1-, ficut g h --h mlic g ("flu Igitur & c Fflfg. 8: {g ~ft. - ._ triammli D , C u i p la num , vcrticali ratio cd-d a.C0mponctur ex rationib. C f--fg.& g h~»--l1 a. bal1sgx1c11111§1 b overtf‘x {In quo hyperbole r l s.propofit:e fimilis 1‘5: zqualxs : ‘cu1us diameter tranlherl‘a‘ k l m n o. Ita vt In. {11: d1amctcr commums 1pfius r 1 S- 36 {um contl'apofitx inter earum vcrriccs l n anrumflano E‘qulldifit‘t triangulum 1: fl). cuius balis b 1 ad macs. ' ' . ‘ {ccatacmametrum bafis coniczr bafim ' A" f‘ c.Vndc rec'ht' d 1 ml b S - taunt-t (I, 3 ud a l)GP" ' 1. 1111619 0" es cuculum _ flxmhm Puao concqrret ‘ Cl. ' 86 P ht P ad Ide punélum cum ca '1groduaa pc‘rlndc V - _ ,qu01{ pun&11m mm Planu1p{u1n,in quo fimt d l) s. b Elmer, (11mm planum,in (1110 {11m d1 r.if.linc<; tanocr conum.&. tales contacflus fient filpcr latcratéo nica b £1 £56 communis (can) tégcnrium plan01'11m,q11:£ linca rcfla cfi, ibit per vcrticcm f. Eomcfi eat,fitc'1-,d fm.occurrens diametro l n. ppollt‘grgm apud m. punfium. C111 diametro xqumlfias agatur a h g.conicg fi1pc1‘ficic-ifipofine occurrens in punélo g.& 1111.111] cl {.[cczms 1n Bunc'lzo h.Eruntc'1;linczz d 1 ml b s.mngéfcs ballm conicam apud ilnpunc'h c665 fec'tloncs planorum tangentium cum 1plo bafis plano. Slnt dcmum tangentium eorundLm 1112111015" Cum Scd ratio c {-4}. c6ponimr ex rationib. dcrc per cétrum 51101113111111 géglélu'flilglmC-"INO" range" "5 Inceu'm ""1981?" {angu' I llypcxbolc; scquldll'tat. kilo 10fangulo conus F5743: g 11 -- l1 .1. a. Duca rur enim ipfi Ll fixquidifians a t.Eritl1',,fic'Lit C d-d quod ell propofitum. Std pet céclufioncm 13" antcprqmilfi capilcut c d--d a. fic c e-c a. 8: propter xquidiflantiam li- emcéponerur nearum .1 g.c fific cfl & c fwf'g. Igi‘ ratio c e- elf,vt g h. ex rationibus c 6-:(1 a.& g l1_._h a. @316 nccelfe l n.Er1t & lm. l1 alint xqualcs: C11méuc a g.a:quidiftct ipfi zqualis 11311 m n.Q1Larc 111.1111nch1m erit 1w wmfim NW"- cenrrum 1'Eéliom1 m contmpollmrum . smtiumé' centri- Supcrclt nun: ollcndcrc, qubd radix 111 L111 slum Non {angri- tes dichrfi lEftionum: céplcxz fcilicct .mgulfi xqualé angulo ifb. Nipcr 165* I 1.Eucl.lima: 1 f. {blunt xquidil‘tétes lip 105 ciufl E,:1n;311l11s i f l). ncis 1' 111.111 5.1;}; x‘gldilfitiiplanoMEt ideo 111.611". per 111:1111‘1lccimr. xqualis ell angulo r m 5.8: linguli p lincas‘k cam l 11. qua: per pi D1103 ergo ipfi 1‘ s. ccquidfllmtcm &_1pl1b11.lm p l q. in 171111610 l. nem C(mclulioncnx anrc prxmi‘ffi cap. range: fec'kio fic 1n l~-l u. S'ir. b. fc-c t Igz'ylicu b. {C A" E11111; A'C‘m l 11.:squ'2111‘7l lxcut ftf-c 1). 11.85 l-»~l m ergo 1P1? l minglal 1;. E1131; :1 l--l}.l1:ut Sub1un~ A HoxAklm 7 DELINEm . 736 A072 tzmgmtzéw COfltVdPOfl‘ZflVMWLJ. C4. 0". -:-%:-§'r-="s- .r > 28o |