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

Table of contents

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[301.] PROBL. X. PROP. LIX.
Page: 261 (77)
[302.] PROBL. XI. PROP. LX.
Page: 262 (78)
[303.] PROBL. XII. PROP. LXI.
Page: 262 (78)
[304.] PROBL. XIII. PROP. LXII.
Page: 265 (79)
[305.] MONITVM.
Page: 268 (82)
[306.] THEOR. XXXVIII. PROP. LXIII.
Page: 268 (82)
[307.] THEOR. XXXIX. PROP. LXIV.
Page: 270 (84)
[308.] THEOR. XL. PROP. LXV.
Page: 271 (85)
[309.] THEOR. XLI. PROP. LXVI.
Page: 273 (87)
[310.] LEMMA XIII. PROP. LXVII.
Page: 274 (88)
[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)
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            recti Canones erunt æquales (eo quod ijdem ſint axes ſolidarum, &</s>
            <s xml:id="echoid-s8518" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-0307-01" xlink:href="note-0307-01a" xml:space="preserve">84. h.</note>
            diametri Canonum) ac propterea ipſorum baſes altitudinibus erunt
              <note symbol="b" position="right" xlink:label="note-0307-02" xlink:href="note-0307-02a" xml:space="preserve">3. Schol.
                <lb/>
              69. h.</note>
            procè proportionales, ſed in æqualibus portionibus de eodem ſolido, vt
              <lb/>
              <note symbol="c" position="right" xlink:label="note-0307-03" xlink:href="note-0307-03a" xml:space="preserve">65. h.</note>
            ſunt baſes rectorum Canonum ita ſunt baſes ſolidarum portionum, & </s>
            <s xml:id="echoid-s8519" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-0307-04" xlink:href="note-0307-04a" xml:space="preserve">2. Co-
                <lb/>
              roll. 78. h.</note>
            titudines tùm portionum, tùm Canonum ſunt eædem, ergo in datis
              <note symbol="e" position="right" xlink:label="note-0307-05" xlink:href="note-0307-05a" xml:space="preserve">3. Schol.
                <lb/>
              69. h.</note>
            tionibus, quibus inſunt prædictæ conditiones, erunt quoque baſes altitudi-
              <lb/>
            nibus reciprocè proportionales. </s>
            <s xml:id="echoid-s8520" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s8521" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8522" xml:space="preserve"/>
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        <div xml:id="echoid-div890" type="section" level="1" n="355">
          <head xml:id="echoid-head364" xml:space="preserve">THEOR. LVII. PROP. LXXXVII.</head>
          <p>
            <s xml:id="echoid-s8523" xml:space="preserve">Æquales portiones ſolidæ de eodem Conoide, vel Sphæra, aut
              <lb/>
            quocunque Sphæroide, vel etiam de Cono recto, habent baſes al-
              <lb/>
            titudinibus reciprocè proportionales: </s>
            <s xml:id="echoid-s8524" xml:space="preserve">& </s>
            <s xml:id="echoid-s8525" xml:space="preserve">è conuerſo.</s>
            <s xml:id="echoid-s8526" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8527" xml:space="preserve">Si baſes portionum de eodem ſolido fuerint altitudinibus reci-
              <lb/>
            procè proportionales, ipſæ portiones æquales erunt.</s>
            <s xml:id="echoid-s8528" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8529" xml:space="preserve">QVando enim huiuſmodi portiones ſolidæ ſunt æquales, neceſſariò ea-
              <lb/>
            rum axes (ſi portiones fuerint de eodem Conoide Parabolico) erunt
              <lb/>
            æquales (ſi de eodem Hyperbolico, aut Sphæra, aut Sphæ-
              <lb/>
            roide) erunt proprijs ſemi - diametris proportionales; </s>
            <s xml:id="echoid-s8530" xml:space="preserve">ſed in his
              <note symbol="f" position="right" xlink:label="note-0307-06" xlink:href="note-0307-06a" xml:space="preserve">83. h.</note>
            eædem portiones ſolidæ habent baſes altitudinibus proportionales,
              <note symbol="g" position="right" xlink:label="note-0307-07" xlink:href="note-0307-07a" xml:space="preserve">86. h.</note>
            & </s>
            <s xml:id="echoid-s8531" xml:space="preserve">cum portiones de eodem quocunque prædictorum ſolidorum fuerint
              <lb/>
            æquales, ipſarum baſes altitudinibus reciprocabuntur.</s>
            <s xml:id="echoid-s8532" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8533" xml:space="preserve">De portionibus autem æqualibus eiuſdem, vel etiam diuerſi Coni recti,
              <lb/>
            aut obliqui, iam id oſtenſum fuit à Commandino in Comment. </s>
            <s xml:id="echoid-s8534" xml:space="preserve">ſuper Ar-
              <lb/>
            chim. </s>
            <s xml:id="echoid-s8535" xml:space="preserve">de Conoid. </s>
            <s xml:id="echoid-s8536" xml:space="preserve">&</s>
            <s xml:id="echoid-s8537" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8538" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s8539" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8540" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8541" xml:space="preserve">PRæterea ſint duæ ſolidæ portiones A B C, D E F de eodem ſolido,
              <lb/>
            quodcunque ſit ex prædictis (quæ tamen in Sphæroide non excedant
              <lb/>
            eius dimidium) quarum axes ſint B G, E H, & </s>
            <s xml:id="echoid-s8542" xml:space="preserve">baſes A I C, D K F, alti-
              <lb/>
            tudines verò B L, E M, & </s>
            <s xml:id="echoid-s8543" xml:space="preserve">ſit
              <lb/>
            baſis A I C ad D K F reci-
              <lb/>
              <figure xlink:label="fig-0307-01" xlink:href="fig-0307-01a" number="248">
                <image file="0307-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0307-01"/>
              </figure>
            procè, vt altitudo E M ad B
              <lb/>
            L. </s>
            <s xml:id="echoid-s8544" xml:space="preserve">Dico has portiones inter
              <lb/>
            ſe æquales eſſe.</s>
            <s xml:id="echoid-s8545" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8546" xml:space="preserve">Concipiantur ipſarum ſoli-
              <lb/>
            darum portionum recti Ca-
              <lb/>
            nones A B C, D E F, quo-
              <lb/>
            rum diametri, & </s>
            <s xml:id="echoid-s8547" xml:space="preserve">altitudines
              <lb/>
            eædem erunt atque axes, &</s>
            <s xml:id="echoid-s8548" xml:space="preserve">
              <note symbol="h" position="right" xlink:label="note-0307-08" xlink:href="note-0307-08a" xml:space="preserve">3. Schol.
                <lb/>
              69. h.</note>
            altitudines ſolidarum portio-
              <lb/>
            num.</s>
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          <p>
            <s xml:id="echoid-s8550" xml:space="preserve">Iam, ſi huiuſmodi Cano-
              <lb/>
            nes ſunt æquales, & </s>
            <s xml:id="echoid-s8551" xml:space="preserve">portiones ſolidæ æquales erunt. </s>
            <s xml:id="echoid-s8552" xml:space="preserve">At ſi dicatur
              <note symbol="i" position="right" xlink:label="note-0307-09" xlink:href="note-0307-09a" xml:space="preserve">78. h.</note>
            inæquales eſſet alter ipſorum, vt puta A B C, altero D E F maior erit: </s>
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