Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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<
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xml:space
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">Si verò, in ſecunda figura, datum punctum G fuerit in maiori ſemi-
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axe, at diſtet à vertice B per interuallum G B non maius dimidio recti
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B F, ipſa G D, in qua centrum, erit _MAXIMA_, & </
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<
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ad nu. 1. 2.</
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<
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xml:space
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axe E B, ſed diſter à vertice B per interuallum maius dimidio recti B F
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(nam ſemi-axis maior E B, eſt ſemper maior ſemi-recto B F, cum totus
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axis B D ſit maior toto recto B F) _MAXIMA_ erit GD, in qua centrum:</
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_MINIMA_ verò venabitur ſic.</
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<
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<
s
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xml:space
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">Cum ſit B G maior ſemi-recto B F, habebit E B ad B G minorem ra-
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tionem, quàm E B ad ſemi-rectum B F, vel ſumptis duplis, quàm tranſ-
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uerſum D B ad rectum B F, ſuntque hæ rationes maioris inæqualitatis:
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</
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<
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xml:space
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">Itaque diuidatur B G in H, ita vt E H ad H G ſit vt D B ad B F, & </
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<
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<
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xml:space
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H applicetur I H K, & </
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<
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">iungantur G I, G K: </
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">nam ipſæ, quæ ſunt ęquales,
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erunt _MINIMAE_.</
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<
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</
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<
s
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xml:space
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">Quoniam ducta I L contingente, hæc axi occurret in L: </
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">& </
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mi conic.</
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E H ad H G, vt tranſuerſum D B ad rectum B F, ſumpta communi altitu-
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dine H L, erit rectangulum E H L ad G H L, vt tranſuerſum ad rectum,
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ſed eſt quoque rectangulum E H L ad quadratum H I, vt
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">37. ibid.</
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ad rectum, ergo rectangulum E H L ad G H L, eſt vt idem E H L ad qua-
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dratum H I, quare rectangulum G H L æquale eſt quadrato H I: </
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<
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H I ipſi G L perpendicularis, ergo angulus G I L rectus erit, & </
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<
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nem contingit in I, à quo ducta eſt I G perpendicularis, & </
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<
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occurrens, quapropter G I erit _MINIMA_, eſtque G K æqualis G I. </
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<
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<
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de in hoc caſu duæ erunt _MINIMAE_, & </
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<
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<
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xml:space
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diſtantia G B ſit non minor dimidio recti lateris B E: </
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<
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maior erit ſemi-axe B E, vt ad finem 9. </
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">huius monuimus) tunc ipſa G B
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erit _MAXIMA_, & </
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ad num. 3.</
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pra inter D, & </
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">Nam ſi caderet in ipſo puncto D (dummodo D B ſit
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vt ponitur, nempe non minor dimidio recti) ipſa D B eſſet _MAXIMA_,
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nec daretur _MINIMA_, cum hæc in punctum euaneſcat.</
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<
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<
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">Verùm, ſi datum punctum G ſit in axe minori, ſed diſtet à vertice B
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per interuallum minus dimidio recti B E, & </
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<
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inter E, & </
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<
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G B minor ſemi-recto, & </
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<
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">E B æqualis ſemi-tranſuerſo B D, habebit G B
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ad B E minorem rationem, quàm ſemi-rectum ad ſemi-tranſuerſum, vel
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quàm rectum F B ad tranſuerſum B D. </
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<
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G H ad H E, ſit vt rectum F B ad B D tranſuerſum, & </
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<
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dinata H I, & </
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<
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turque G I. </
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<
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<
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<
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ne H L erit rectangulum G H L ad E H L, vt F B ad B D, vel vt
<
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conic.</
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dratum G
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I
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H ad idem rectangulum E H L, quare rectangulum G H L æ-
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quale eſt quadrato G H, eſtque H I perpendicularis ad G L; </
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<
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lus G I L rectus erit, eſtque I L ſectionem contingens in L, à quo ducta
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eſt I G perpendicularis, & </
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<
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<
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_MAXIMA_, & </
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<
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