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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            ſunt æquales, quando verò recti Canones, ſiue portiones de eodem
              <note symbol="a" position="left" xlink:label="note-0312-01" xlink:href="note-0312-01a" xml:space="preserve">84. h.</note>
            lo, vel de eadem coni-ſectione, quæ ſolidum procreat æquales ſunt, inter
              <lb/>
            ipſarum altitudines _MAXIM A_ eſt ea illius portionis, cuius diameter
              <note symbol="b" position="left" xlink:label="note-0312-02" xlink:href="note-0312-02a" xml:space="preserve">Schol.
                <lb/>
              poſt 51. h.
                <lb/>
              ad nu. 3.</note>
            ſegmentum maioris axis, & </s>
            <s xml:id="echoid-s8666" xml:space="preserve">_MINIMA_, cuius diameter ſit ſegmentum mi-
              <lb/>
            noris; </s>
            <s xml:id="echoid-s8667" xml:space="preserve">atque altitudines, & </s>
            <s xml:id="echoid-s8668" xml:space="preserve">diametri rectorum Canonum, ſiue planarum
              <lb/>
            portionum eædem ſunt, ac altitudines, & </s>
            <s xml:id="echoid-s8669" xml:space="preserve">axes ſolidarum, ergo, & </s>
            <s xml:id="echoid-s8670" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-0312-03" xlink:href="note-0312-03a" xml:space="preserve">3. Schol.
                <lb/>
              69. h.</note>
            portiones eiuſdem Coni recti, vel Conoidis, aut Sphæroidis ſunt æquales,
              <lb/>
            inter earum altitudines _MAXIM A_ erit ea illius portionis, cuius axis ſit ſe-
              <lb/>
            gmentum maioris axis genitricis ſolidi, cuius eſt portio, & </s>
            <s xml:id="echoid-s8671" xml:space="preserve">_MINIM A_ eius,
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            cuius axis ſit ſegmentum minoris. </s>
            <s xml:id="echoid-s8672" xml:space="preserve">Itaque ſi primò altitudines omnium ha-
              <lb/>
            rum æqualium portionum, (dempta ea circa _MAXIM AM_ altitudinem)
              <lb/>
            producantur, & </s>
            <s xml:id="echoid-s8673" xml:space="preserve">huic _MINIM AE_ altitudini æquales fiant, atque ex interſe-
              <lb/>
            ctionum punctis ducantur plana portionum baſibus æquidiſtantia, abſcin-
              <lb/>
            dentur ab ipſis portiones ſolidæ æqualium altitudinum, & </s>
            <s xml:id="echoid-s8674" xml:space="preserve">vnaquæque ma-
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            ior erit quacunque æqualium portionum (nam totum ſua parte maius eſt)
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            vnde, & </s>
            <s xml:id="echoid-s8675" xml:space="preserve">maior ea portione, cuius altitudini, vel cui portioni nihil additum
              <lb/>
            fuit, quæ ea eſt, cuius axis conuenit cum maiori axe genitricis ſectionis dati
              <lb/>
            ſolidi. </s>
            <s xml:id="echoid-s8676" xml:space="preserve">Si ergo omnes aliæ portiones æqualium altitudinum hane portio-
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            nem excedunt, erit è contra hæc ipſa portio, cuius axis congruit cum maio-
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            ri axe genitricis ſectionis dati ſolidi aliarum portionum æqualium altitudi-
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            num _MINIM A_.</s>
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          <p>
            <s xml:id="echoid-s8678" xml:space="preserve">PRo Sphæroide autem, ſi altitudines omnium prædictarum æqualium
              <lb/>
            portionum (dempta ea circa _MINIM AM_ altitudinem, quæ iam ea eſt
              <lb/>
            circa minorem axem Ellipſis Sphæroidis genitricis) ę quales ſecentur eidem
              <lb/>
            _MINIM AE_ altitudini, atque per puncta ſectionum, plana ſolidarum por-
              <lb/>
            tionum baſibus æquidiſtantia ducantur, hæc à portionibus auferent portio-
              <lb/>
            nes ſolidas æqualium altitudinum, ſed vnaquæque ipſarum minor erit
              <lb/>
            quacunque æqualium portionum (eò quod pars ſuo toto ſit minor) quapro-
              <lb/>
            pter & </s>
            <s xml:id="echoid-s8679" xml:space="preserve">minor ea portione a cuius altitudine, vel à qua portione nihil dem-
              <lb/>
            ptum fuit, quæ quidem eſt ea, cuius axis congruit cum minori axe Ellipſis
              <lb/>
            datum Sphæroides procreantis: </s>
            <s xml:id="echoid-s8680" xml:space="preserve">ſi igitur omnes portiones æqualium altitu-
              <lb/>
            dinum hac portione ſunt minores, erit ex aduerſo hæc eadem portio, cuius
              <lb/>
            axis conuenit cum minori axe genitricis Ellipſis dati Sphæroidis earundem
              <lb/>
            omnium portionum, æqualium altitudinum, _MAXIMA_. </s>
            <s xml:id="echoid-s8681" xml:space="preserve">Quod tandem ſu-
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            pererat demonſtrandum.</s>
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        <div xml:id="echoid-div907" type="section" level="1" n="362">
          <head xml:id="echoid-head371" xml:space="preserve">SCHOLIV M.</head>
          <p>
            <s xml:id="echoid-s8683" xml:space="preserve">HVc etiam, prout expoſuimus in Scholio poſt 51. </s>
            <s xml:id="echoid-s8684" xml:space="preserve">huius, hæc tria ſunt
              <lb/>
            animaduertenda. </s>
            <s xml:id="echoid-s8685" xml:space="preserve">Videlicet.</s>
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          </p>
          <p>
            <s xml:id="echoid-s8687" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8688" xml:space="preserve">I Nter axes æqualium portionum eiuſdem Coni recti, vel Conoidis Hy-
              <lb/>
            perbolici, aut cuiuſcunque Sphæroidis, _MINIMV S_ eſt is eius portionis,
              <lb/>
            cuius axis congruat cum axe, & </s>
            <s xml:id="echoid-s8689" xml:space="preserve">pro Sphæroide, cum minori axe genitricis
              <lb/>
            ſectionis dati ſolidi, & </s>
            <s xml:id="echoid-s8690" xml:space="preserve">in Sphæroide _MAXIMV S_ eius portionis, cuius axis
              <lb/>
            congruat cum maiori axe eiuſdem genitricis ſectionis.</s>
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