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

Table of contents

< >
[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)
< >
page |< < (125) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div899" type="section" level="1" n="358">
          <pb o="125" file="0311" n="311" rhead=""/>
          <p>
            <s xml:id="echoid-s8627" xml:space="preserve">QVod autem in quolibet Sphæroide, inter portiones eius dimidio mi-
              <lb/>
            nores, & </s>
            <s xml:id="echoid-s8628" xml:space="preserve">æqualium baſium, _MINIMA_ ſit ea, cuius axis ſit ſegmen-
              <lb/>
            tum minoris axis Ellipſis datum Sphæroides procreantis, id con-
              <lb/>
            ſimili conſtructione, atque argumentis oſtendetur, vti factum fuit in ſecun-
              <lb/>
            da parte Prop. </s>
            <s xml:id="echoid-s8629" xml:space="preserve">50. </s>
            <s xml:id="echoid-s8630" xml:space="preserve">huius, ſi tamen ſuper tertia figura lineæ rectæ, & </s>
            <s xml:id="echoid-s8631" xml:space="preserve">Ellipſes
              <lb/>
            ibi animaduerſæ, concipiantur tanquam baſes ſolidarum portionum, & </s>
            <s xml:id="echoid-s8632" xml:space="preserve">ve-
              <lb/>
            luti Sphæroidalia ſolida, &</s>
            <s xml:id="echoid-s8633" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8634" xml:space="preserve">Quod fuit, &</s>
            <s xml:id="echoid-s8635" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8636" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div901" type="section" level="1" n="359">
          <head xml:id="echoid-head368" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s8637" xml:space="preserve">HInc conſtat _MINIM AM_ portionum ſemi- Sphæroide maiorum, & </s>
            <s xml:id="echoid-s8638" xml:space="preserve">
              <lb/>
            quarum baſes ſint æquales, eam eſſe, cuius axis ſit ſegmentum maio-
              <lb/>
            ris axis Ellipſis genitrics; </s>
            <s xml:id="echoid-s8639" xml:space="preserve">_MAXIM AM_ autem, cuius axis ſit ſegmentum
              <lb/>
            minoris.</s>
            <s xml:id="echoid-s8640" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div902" type="section" level="1" n="360">
          <head xml:id="echoid-head369" xml:space="preserve">SCHOLIV M.</head>
          <p>
            <s xml:id="echoid-s8641" xml:space="preserve">QVod ſuperius promiſſimus abſoluetur ſic, ſuper figuras prædictæ 50. </s>
            <s xml:id="echoid-s8642" xml:space="preserve">h.
              <lb/>
            </s>
            <s xml:id="echoid-s8643" xml:space="preserve">Cum ibi ſit A C minor H I, erit quoque dimidium D C minus di-
              <lb/>
            midio F I. </s>
            <s xml:id="echoid-s8644" xml:space="preserve">Detrahatur ergo F P, quę ſit media proportionalis
              <lb/>
            inter F I, D C; </s>
            <s xml:id="echoid-s8645" xml:space="preserve">agatur P R diametro F O æquidiſtans, & </s>
            <s xml:id="echoid-s8646" xml:space="preserve">ſectioni occur-
              <lb/>
            rensin R, atque ex R applicetur R Q S, & </s>
            <s xml:id="echoid-s8647" xml:space="preserve">facta figurarum reuolutione
              <lb/>
            circa axim B D, concipiantur deſcribiſolida, &</s>
            <s xml:id="echoid-s8648" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8649" xml:space="preserve">èquibus cum planis per
              <lb/>
            rectas A C, H I, S R ductis, & </s>
            <s xml:id="echoid-s8650" xml:space="preserve">ad eaſdem genitrices ſectiones erectis, ab-
              <lb/>
            ſcindentur portiones ſolidæ A B C, H O I inter ſe æquales, & </s>
            <s xml:id="echoid-s8651" xml:space="preserve">portio S
              <note symbol="a" position="right" xlink:label="note-0311-01" xlink:href="note-0311-01a" xml:space="preserve">80. h.</note>
            R. </s>
            <s xml:id="echoid-s8652" xml:space="preserve">Dico huius baſim per S R ductam, æqualem eſſe baſi per A C.</s>
            <s xml:id="echoid-s8653" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8654" xml:space="preserve">Nam baſis per H I ad baſim per A C, eſt vt recta H I ad rectam A
              <note symbol="b" position="right" xlink:label="note-0311-02" xlink:href="note-0311-02a" xml:space="preserve">2. Co-
                <lb/>
              78. h.</note>
            vel ſumptis dimidijs, vt F I ad D C, vel vt quadratum F I, ad quadratum
              <lb/>
            F P, ſiue ad quadratum Q R, vel ſumptis quadruplis, vt quadratum H I ad
              <lb/>
            quadratum S R, ſed etiam baſis per H I ad baſim per S R, eſt vt quadra-
              <lb/>
            tum H I ad quadratum S R, cum ob planorum æquidiſtantiam ſint
              <note symbol="c" position="right" xlink:label="note-0311-03" xlink:href="note-0311-03a" xml:space="preserve">Coroll.
                <lb/>
              15. Arch.
                <lb/>
              de Co-
                <lb/>
              noid.</note>
            nes ſimiles, ergo baſis per H I ad baſim per A C, erit vt eadem baſis per H
              <lb/>
            I ad baſim per S R: </s>
            <s xml:id="echoid-s8655" xml:space="preserve">vnde baſis per S R æqualis eſt baſi per A C, &</s>
            <s xml:id="echoid-s8656" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8657" xml:space="preserve">Quod
              <lb/>
            facere oportebat.</s>
            <s xml:id="echoid-s8658" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div905" type="section" level="1" n="361">
          <head xml:id="echoid-head370" xml:space="preserve">THEOR. LXI. PROP. LXXXXI.</head>
          <p>
            <s xml:id="echoid-s8659" xml:space="preserve">MINIMA portionum de eodem Cono recto, vel de quocunque
              <lb/>
            Conoide, aut Sphæroide, & </s>
            <s xml:id="echoid-s8660" xml:space="preserve">quarum altitudines ſint æquales ea
              <lb/>
            eſt, cuius axis congruat cum maiori axe genitricis ſectionis dati
              <lb/>
            ſolidi.</s>
            <s xml:id="echoid-s8661" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8662" xml:space="preserve">In Sphæroide, MAXIMA eſt, cuius axis cum minori axe eiuſ-
              <lb/>
            dem genitricis ſectionis conueniat.</s>
            <s xml:id="echoid-s8663" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8664" xml:space="preserve">NAm quando portiones de eodem Cono recto, vel Conoide, aut Sphę-
              <lb/>
            roide quocunque ſunt æquales, & </s>
            <s xml:id="echoid-s8665" xml:space="preserve">ipſarum recti Canones inter </s>
          </p>
        </div>
      </text>
    </echo>
Impressum