Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſtans. </
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<
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">Iungatur CS, quæ producta ſectioni occurret, per ſecundam partem 8.
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<
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ſectioni occurret, vt in X.</
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<
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">Præterea, cum quæcunque contingenti æquidiſtans GI ſupra RX, inter
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aſymptoton, & </
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<
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">ſectionem intercepta, maior ſit ipſa RX, ſiue ipſa GZ, pun-
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ctum Z cadet extra ſectionem, & </
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<
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contra cum quælibet intercepta LY infra RX, parallela ad DB, minor ſit ip-
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ſa RX, ſiue LF, punctum F cadet intra ſectionem, idemque de quolibet alio
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puncto rectæ XF: </
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<
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">vnde recta STX ab ipſo occurſu X cum ſectione, ad partes
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verticis tota cadit extra, ad oppoſitas verò partes tota cadit intra ſectionem;
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ſit, vel in ipſa ſectione, vel intra, pariter in vno tantùm puncto ſe-
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ctioni occurrere, eamque ſecare.</
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<
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">Nam recta XS ex puncto X, quod cſt in Hyperbola, vel recta FS ex pun-
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cto F, quod eſt intra, æquidiſtanter ducta aſymptoto CD, ſi ad partes cen-
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tri C producatur, alteri aſymptoto CE omnino occurrit, (quoniam EC, ſe-
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cans DC vnam parallelarum ſecat quoque alteram CE) vnde aliqua pars,
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ipſius rectæ XS, vel FS cadit in loco ab aſymptotis, & </
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ac ideo ex his, quæ ſuperius oſtendimus, ipſa linea in vno tantùm puncto ſe-
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ctioni occurret, ac Hyperbolen ſecabit.</
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ducta ex puncto, quod ſit in angulo ab aſymptotis facto, in vno tantùm pun-
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cto Hyperbolæ occurrit, atque eam ſecat.</
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