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

Table of contents

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[311.] THEOR. XLII. PROP. LXVIII.
Page: 274 (88)
[312.] COROLL. I.
Page: 276 (90)
[313.] COROLL. II.
Page: 276 (90)
[314.] MONITVM.
Page: 276 (90)
[315.] DEFINITIONES. I.
Page: 278 (92)
[316.] II.
Page: 278 (92)
[317.] III.
Page: 279 (93)
[318.] IIII.
Page: 279 (93)
[319.] PROBL. XIV. PROP. LXIX.
Page: 280 (94)
[320.] SCHOLIVM I.
Page: 282 (96)
[321.] COROLL. I.
Page: 282 (96)
[322.] SCHOLIVM II.
Page: 282 (96)
[323.] COROLL. II.
Page: 282 (96)
[324.] SCHOLIVM III.
Page: 283 (97)
[325.] COROLL. III.
Page: 283 (97)
[326.] THEOR. XLIII. PROP. LXX.
Page: 284 (98)
[327.] COROLL.
Page: 286 (100)
[328.] THEOR. XLIV. PROP. LXXI.
Page: 286 (100)
[329.] COROLL.
Page: 287 (101)
[330.] THEOR. XLV. PROP. LXXII.
Page: 288 (102)
[331.] SCHOLIVM.
Page: 288 (102)
[332.] THEOR. XLVI. PROP. LXXIII.
Page: 288 (102)
[333.] THEOR. XLVII. PROP. LXXIV.
Page: 288 (102)
[334.] MONITVM.
Page: 290 (104)
[335.] LEMMA XIV. PROP. LXXV.
Page: 290 (104)
[336.] SCHOLIVM.
Page: 291 (105)
[337.] LEMMA XV. PROP. LXXVI.
Page: 292 (106)
[338.] THEOR. XLVIII. PROP. LXXVII.
Page: 292 (106)
[339.] MONITVM.
Page: 293 (107)
[340.] THEOR. IL. PROP. LXXVIII.
Page: 294 (108)
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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
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            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
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            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
              <lb/>
            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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