Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of handwritten notes

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            iuxta regulam B C: </s>
            <s xml:id="echoid-s8911" xml:space="preserve">quare Parabolica portio G E F, aliarum, iuxta ean-
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            dem regulam B C progenitarum, eſt _MAXIMA._ </s>
            <s xml:id="echoid-s8912" xml:space="preserve">Quod inuenire propoſi-
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            tum fuerat.</s>
            <s xml:id="echoid-s8913" xml:space="preserve"/>
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        <div xml:id="echoid-div928" type="section" level="1" n="370">
          <head xml:id="echoid-head379" xml:space="preserve">COROLL.</head>
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            <s xml:id="echoid-s8914" xml:space="preserve">HInc eſt, quod _MAXIMAE_ Parabolæ iuxta quæuis Coni latera genitæ,
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            habent baſes æquales: </s>
            <s xml:id="echoid-s8915" xml:space="preserve">nam ipſæ baſes, vti conſtat ex ſuperiori con-
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            ſtructione æqualiter diſtant à centro circuli (qui eſt baſis Coni) ſiue per
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            quadrantem ſui ipſius diametri, ac propterea inter ſe ſunt æquales.</s>
            <s xml:id="echoid-s8916" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div929" type="section" level="1" n="371">
          <head xml:id="echoid-head380" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s8917" xml:space="preserve">SI hinc inde à _MAXIMA_ inuenta Parabolica ſectione, quærantur binæ
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            æquales, id facili negotio conſequetur, & </s>
            <s xml:id="echoid-s8918" xml:space="preserve">conſimilibus argumentis, ac
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            ſupra demonſtrabitur, eas nimirum æquales eſſe inter ſe, quæ ductæ ſint ex
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            punctis in circuli diametro A C, hinc inde à puncto D æqualia rectangula
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            præſtantibus.</s>
            <s xml:id="echoid-s8919" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s8920" xml:space="preserve">Si autem quæratur inter has _MAXIMAS_ Parabolicas ſectiones, iuxta in-
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            finita Conilatera genitas, quæ ſit _MAXIMA_, quæue _MINIMA_, hoc, non-
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            nullis præmiſſis, proximo Problemate venabimur, ſed tantummodò in Co-
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            no Scaleno, nam in recto, ſatis ſuperque patet, omnes huiuſmodi _MAXI-_
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            _MAS_ inter ſe æquales eſſe, cùm omnia triangula per axem Coni recti, ſint
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            ad baſim erecta, æqualia, æquicruria, & </s>
            <s xml:id="echoid-s8921" xml:space="preserve">æqualium laterum, &</s>
            <s xml:id="echoid-s8922" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8923" xml:space="preserve"/>
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        <div xml:id="echoid-div930" type="section" level="1" n="372">
          <head xml:id="echoid-head381" xml:space="preserve">THEOR. LXII. PROP. XCVII.</head>
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            <s xml:id="echoid-s8924" xml:space="preserve">In plano dati circuli, perpendicularium à puncto dato, quod
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            non ſit centrum, ſuper rectas eiuſdem circuli peripheriam contin-
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            gentes ducibilium, MAXIMA eſt ea, in qua centrum, MINIMA
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            verò, ſi punctum fuerit intra circulum, eſt reliquum diametri ſe-
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            gmentum; </s>
            <s xml:id="echoid-s8925" xml:space="preserve">ſi autem datum punctum fuerit in ipſa peripheria, vel
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            extra, tunc non datur MINIMA.</s>
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            <s xml:id="echoid-s8927" xml:space="preserve">ESto circulus A B, cuius centrum C, & </s>
            <s xml:id="echoid-s8928" xml:space="preserve">datum punctum vbicunque ſit
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            D præter in centro, & </s>
            <s xml:id="echoid-s8929" xml:space="preserve">iuncta D C, ac producta vſque ad peripheriam
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            in A, B punctis, è quibus ductis contingentibus A E, B L (quæ diametro
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            A B perpendiculares erunt) & </s>
            <s xml:id="echoid-s8930" xml:space="preserve">ex quolibet alio peripheriæ puncto F, ducta
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            item contingente F H, ſuper qua ex dato puncto D demiſſa ſit perpendicu-
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            laris D H, &</s>
            <s xml:id="echoid-s8931" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8932" xml:space="preserve">Dico huiuſmodi perpendicularium _MAXIMAM_ eſſe D A,
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            in qua eſt centrum C, & </s>
            <s xml:id="echoid-s8933" xml:space="preserve">in prima figura, in qua punctum cadit intra, _MI-_
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            _NIMAM_ eſſe D B: </s>
            <s xml:id="echoid-s8934" xml:space="preserve">ſi verò datum punctum D cadat in ipſam peripheriam,
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            vt in B, vel extra, vt in ſecunda figura, tunc dico non dari _MINIMAM._</s>
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