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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          <head xml:id="echoid-head361" xml:space="preserve">THEOR. LIV. PROP. LXXXIV.</head>
          <p>
            <s xml:id="echoid-s8497" xml:space="preserve">Æquales portiones de eodem ſolido, quodcunque ſit ex ſæ-
              <lb/>
              <note position="left" xlink:label="note-0306-01" xlink:href="note-0306-01a" xml:space="preserve">Conuerſ.
                <lb/>
              Prop. 78.
                <lb/>
              huius.</note>
            pius memoratis, habent Canones rectos, in ipſis interceptos,
              <lb/>
            inter ſe æquales.</s>
            <s xml:id="echoid-s8498" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8499" xml:space="preserve">ETenim huiuſmodi portiones ſolidæ æquales, habent axes, vel
              <note symbol="a" position="left" xlink:label="note-0306-02" xlink:href="note-0306-02a" xml:space="preserve">83. h.</note>
            ſe æquales, vel proprijs ſemi-diametris proportionales, vel ad idem
              <lb/>
            Conoides ſimile concentricum, & </s>
            <s xml:id="echoid-s8500" xml:space="preserve">inſcriptum pertingentes, ſed ijdem
              <lb/>
            axes ſunt quoque diametri prædictorum Canonum, & </s>
            <s xml:id="echoid-s8501" xml:space="preserve">quando hæ
              <note symbol="b" position="left" xlink:label="note-0306-03" xlink:href="note-0306-03a" xml:space="preserve">3. Schol.
                <lb/>
              prop. 69.
                <lb/>
              huius.</note>
            metri habuerint conditiones huiuſmodi, ipſi Canones recti ſunt æqua- les, ergo ſolidæ portiones æquales, habebunt rectos Canones inter ſe
              <lb/>
              <note symbol="c" position="left" xlink:label="note-0306-04" xlink:href="note-0306-04a" xml:space="preserve">40. h. &
                <lb/>
              ex 45. h.</note>
            æquales. </s>
            <s xml:id="echoid-s8502" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s8503" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8504" xml:space="preserve"/>
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        <div xml:id="echoid-div885" type="section" level="1" n="353">
          <head xml:id="echoid-head362" xml:space="preserve">THEOR. LV. PROP. LXXXV.</head>
          <p>
            <s xml:id="echoid-s8505" xml:space="preserve">Baſes æqualium portionum ex eodem quocunque prædicto-
              <lb/>
            rum ſolidorum, ſuperſiciem eiuſdem ſimilis inſcripti ſolidi con-
              <lb/>
              <note position="left" xlink:label="note-0306-05" xlink:href="note-0306-05a" xml:space="preserve">Conuerſ.
                <lb/>
              Prop. 80.
                <lb/>
              huius.</note>
            centrici ad earum centra contingunt.</s>
            <s xml:id="echoid-s8506" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8507" xml:space="preserve">POrtiones enim æquales eiuſdem ſolidi habent rectos Canones in ipſis
              <lb/>
            interceptos inter ſe æquales, ſed quando huiuſmodi Canones ſunt æquales (ſi concipiantur translati ſuper eandem ſectionem ſolidi geni-
              <lb/>
              <note symbol="d" position="left" xlink:label="note-0306-06" xlink:href="note-0306-06a" xml:space="preserve">84. h.</note>
            tricem) ipſorum baſes ad puncta media, eandem concentricam, inſcri-
              <lb/>
            ptam, & </s>
            <s xml:id="echoid-s8508" xml:space="preserve">ſimilem ſectionem contingunt, & </s>
            <s xml:id="echoid-s8509" xml:space="preserve">baſes ſolidarum
              <note symbol="e" position="left" xlink:label="note-0306-07" xlink:href="note-0306-07a" xml:space="preserve">68. h.</note>
            tranſeunt per has baſes rectorum Canonum, atque ad eos ſunt erectæ, nem-
              <lb/>
            pe ad planum per axem dati ſolidi, quare eędem baſes ſolidarum portionum
              <lb/>
            contingent ſuperſiciem interioris ſolidi concentrici ab inſcripta concentri-
              <lb/>
            ca ſectioni geniti (dum hæc circa axim conuertatur) ad eadem puncta,
              <note symbol="f" position="left" xlink:label="note-0306-08" xlink:href="note-0306-08a" xml:space="preserve">55. h.</note>
            quibus baſes planarum, ſectionem interiorem contingunt, quę puncta ſunt
              <lb/>
            centra axium, vel baſium ſolidarum portionum ex Archimede, & </s>
            <s xml:id="echoid-s8510" xml:space="preserve">ex iam à
              <lb/>
            nobis animaduerſis.</s>
            <s xml:id="echoid-s8511" xml:space="preserve"/>
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          <head xml:id="echoid-head363" xml:space="preserve">THEOR. LVI. PROP. LXXXVI.</head>
          <p>
            <s xml:id="echoid-s8512" xml:space="preserve">Solidæ portiones eiuſdem Coni recti, vel Conoidis, ſiue Sphæ-
              <lb/>
            ræ, aut Sphæroidis, quarum axes (pro Cono recto) pertingant ad
              <lb/>
            idem inſcriptum concentricum Conoides Hyperbolicum (vel pro
              <lb/>
            Conoide Parabolico) ſint æquales (ſiue pro reliquis) ad proprias
              <lb/>
            ſemi - diametros eandem habeant rationem, habent baſes altitu-
              <lb/>
            dinibus reciprocè proportionales.</s>
            <s xml:id="echoid-s8513" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8514" xml:space="preserve">Eſto vt ponitur dico, &</s>
            <s xml:id="echoid-s8515" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8516" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8517" xml:space="preserve">ETenim cum axibus huiuſmodi ſolidarum portionum inſint prædictæ
              <lb/>
            conditiones, ipſæ portiones ſolidæ æquales erunt, pariterque
              <note symbol="g" position="left" xlink:label="note-0306-09" xlink:href="note-0306-09a" xml:space="preserve">Prop. 79.
                <lb/>
              huius.</note>
            </s>
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