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

Table of contents

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[341.] ALITER.
Page: 295 (109)
[342.] COROLL. I.
Page: 297 (111)
[343.] COROLL. II.
Page: 297 (111)
[344.] THEOR. L. PROP. LXXIX.
Page: 297 (111)
[345.] THEOR. LI. PROP. LXXX.
Page: 298 (112)
[346.] SCHOLIVM.
Page: 299 (113)
[347.] THEOR. LII. PROP. LXXXI.
Page: 299 (113)
[348.] SCHOLIVM.
Page: 302 (116)
[349.] PROBL. XV. PROP. LXXXII.
Page: 302 (116)
[350.] COROLL.
Page: 304 (118)
[351.] THEOR. LIII. PROP. LXXXIII.
Page: 304 (118)
[352.] THEOR. LIV. PROP. LXXXIV.
Page: 306 (120)
[353.] THEOR. LV. PROP. LXXXV.
Page: 306 (120)
[354.] THEOR. LVI. PROP. LXXXVI.
Page: 306 (120)
[355.] THEOR. LVII. PROP. LXXXVII.
Page: 307 (121)
[356.] THEOR. LVIII. PROP. LXXXVIII.
Page: 308 (122)
[357.] THEOR. LIX. PROP. LXXXIX.
Page: 309 (123)
[358.] THEOR. LX. PROP. LXXXX.
Page: 310 (124)
[359.] COROLL.
Page: 311 (125)
[360.] SCHOLIV M.
Page: 311 (125)
[361.] THEOR. LXI. PROP. LXXXXI.
Page: 311 (125)
[362.] SCHOLIV M.
Page: 312 (126)
[363.] MONIT V M.
Page: 313 (127)
[364.] LEMMA XVI. PROP. XCII.
Page: 313 (127)
[365.] PROBL. XVI. PROP. XCIII.
Page: 314 (128)
[366.] SCHOLIVM.
Page: 316 (130)
[367.] PROBL. XVII. PROP. XCIV.
Page: 317 (131)
[368.] PROBL. XVIII. PROP. XCV.
Page: 318 (132)
[369.] PROBL. XIX. PROP. XCVI.
Page: 319 (123)
[370.] COROLL.
Page: 320 (134)
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            <s xml:id="echoid-s8692" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8693" xml:space="preserve">INter baſes æqualium portionum de eodem Cono recto, aut de quocun-
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            que Conoide, aut Sphæroide _MINIM A_ eſt ea illius portionis, cuius axis
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            ſit ſegmentum axis, & </s>
            <s xml:id="echoid-s8694" xml:space="preserve">pro Sphæroide ſit ſegmen tum maioris axis genitricis
              <lb/>
            ſectionis dati ſolidi. </s>
            <s xml:id="echoid-s8695" xml:space="preserve">_MAXIM A_ verò eius, cuius axis ſit ſegmentum mino-
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            ris axis eiuſdem ſectionis genitricis.</s>
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            <s xml:id="echoid-s8697" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8698" xml:space="preserve">INter altitudines æqualium portionum de eodem Cono recto, ſiue de quo-
              <lb/>
            libet Conoide, aut Sphæroide, _MAXIMA_ eſt ea illius portionis, cuius
              <lb/>
            axis congruat cum maiori axe genitricis ſectionis dati ſolidi, & </s>
            <s xml:id="echoid-s8699" xml:space="preserve">in Sphæroi-
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            de _MINIM A_ eius, cuius axis cum minori axe eiuſdem genitricis ſectionis
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            conueniat.</s>
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            <s xml:id="echoid-s8701" xml:space="preserve">Quæ omnia, ex hucuſque demonſtratis, paucis oſtendentur (vti factum
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            fuit in præfato Scholio, & </s>
            <s xml:id="echoid-s8702" xml:space="preserve">ſuper eaſdem figuras 51. </s>
            <s xml:id="echoid-s8703" xml:space="preserve">h.) </s>
            <s xml:id="echoid-s8704" xml:space="preserve">conſimilibus, ac ibi
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            argumentis, veruntamen circa ſolidas portiones verſantibus, è quibus de-
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            nique vniuſcuiuſque trium proximè præcedentium propoſitionum veritas
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            iterum eluceſcet. </s>
            <s xml:id="echoid-s8705" xml:space="preserve">Sed de his hactenus.</s>
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          <head xml:id="echoid-head372" xml:space="preserve">MONIT V M.</head>
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            <s xml:id="echoid-s8707" xml:space="preserve">PLacuit SERENO, Antinſ enſi Philoſopho, in quibuslibet Conis
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            terminatis MAXIMV M, & </s>
            <s xml:id="echoid-s8708" xml:space="preserve">MINIMV M triangulum
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            per verticem ductum inquirere, liceat nobis tanti Geometræ
              <lb/>
            veſtigia inſequentibus in Cono pariter terminato quocunque
              <lb/>
            MAXIMAM, & </s>
            <s xml:id="echoid-s8709" xml:space="preserve">MINIMAM Paraboæ portionem aſsignare, pro
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            cuius indigatione nonnulla circa plana, nec præter ſuſceptam materiam,
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            nec ſcitu iniucunda occurrunt afferenda.</s>
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          <head xml:id="echoid-head373" xml:space="preserve">LEMMA XVI. PROP. XCII.</head>
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            <s xml:id="echoid-s8711" xml:space="preserve">Si duo triangula habuerint latus lateri æquale, atque alterum
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            adiacentium angulorum in vno triangulo, alteri adiacentium in
              <lb/>
            reliquo æqualem, ſitque reliquus angulus adiacentium in primo,
              <lb/>
            maior reliquo adiacentium in altero, & </s>
            <s xml:id="echoid-s8712" xml:space="preserve">latus illi oppoſitum, late-
              <lb/>
            re huic oppoſito maius erit.</s>
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          <p>
            <s xml:id="echoid-s8714" xml:space="preserve">SInt duo triangula A B C, D E F, quo-
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            rum latera B C, E F ſint æqualia, & </s>
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            anguli pariter A B C, D E F æquales, an-
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            gulus verò A C B maior ſit angulo D F E.
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            <s xml:id="echoid-s8716" xml:space="preserve">Dico, & </s>
            <s xml:id="echoid-s8717" xml:space="preserve">latus A B maiori angulo oppoſitũ,
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            maius eſſe latere D E oppoſitum minori.</s>
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            <s xml:id="echoid-s8719" xml:space="preserve">Fiat angulus B C G æqualis ipſi E F D.</s>
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