Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ctionem, & </
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">cum ſit FH ad HE, vt FA ad EB, vel vt FD ad EC, vel vt FI ad
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IE, erit diuidendo FE ad EH, vt FE ad EI, quare EH, & </
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hoc eſt productę AB, DC in eodem pun-
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cto H cum diametro conueniunt, & </
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ctio fuerit Hyperbola infra
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conic.</
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ab aſymptotis factum; </
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<
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poterunt Hyperbolen contingentes.</
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<
s
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">Iam, ſi ductæ HL, HM ſectionem non
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contingunt, ducatur ex H contingens HO
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ad aliud punctũ quàm L, vt ad O, & </
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<
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applicetur OPN; </
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<
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xml:space
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">erit ergo AP ad PB,
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conic.</
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AH ad HB, ſed AH ad HB, eſt vt AF ad
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BE, vel ad EC, vel vt FG ad GE (ob ſimi-
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litudinem triangulorum AFG, CEG) vel
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vt AR ad RB, ergo AP ad PB erit vt AR
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ad RB: </
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<
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">quod eſt falſum. </
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uenit quàm L, & </
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nem contingunt. </
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quam circa tranſuerſum latus, & </
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">per extrema applicatæ, quæ per pũ-
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ctum inter ſectionis diagonalis eiuſdem menſalis cum diametro, ordinatim
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ducitur, Ellipſis deſcribatur, ipſa, menſalis latera in eiuſdem applicatæ ex-
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tremis omnino continget, nempe ei erit inſcripta.</
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<
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<
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circuli cuius baſis AD, maior ſit baſi BC, oſtendimus AH ad HB eſſe vt AR
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ad RB, ergo & </
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<
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cum tranſuerſo EF, & </
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<
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R, Q, vel à rectis HL, HM in punctis L, M contingetur; </
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vti nuper oſtendimus in ijſdem punctis ſectionem quoque contingunt: </
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re huiuſmodi Ellipſis, & </
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ijſdem applicatæ extremis contiget, ac ipſi menſali, erit inſcripta, cum etiam
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AD, BC ex diametri terminis F, E ordinatim ductis æquidiſtantes eandem
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Ellipſim contingant.</
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<
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">At pro menſali coni-ſectionis ALBCMD, ſi ipſa fuerit menſalis Elliptica,
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vel circularis, cuius oppoſita latera AD, BC ſint æqualia, erunt quoque eo-
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rum dimidia AF, EC æqualia, ac ideo etiam FG æqualis GE, hoc eſt G cen-
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trũ erit Ellipſis, quæ per ELFM deſcribitur cum tranſuerſo EF; </
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LM erit eius diameter coniugata. </
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EF vtriuſque ſectionis æquidiſtantes ducentur vtranque ſectionem
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mi conic.</
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gent, quàm contingunt quoque applicatæ AD, DC: </
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quæ per E, L, F, Q deſcribitur eidem menſali Ellipticæ, vel circulari
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inſcripta.</
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