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

Table of contents

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[231.] THEOR. VIII. PROP. XII.
[232.] THEOR. IX. PROP. XIII.
[233.] THEOR. X. PROP. XIV.
[234.] THEOR. XI. PROP. XV.
[235.] LEMMA V. PROP. XVI.
[236.] COROLL.
[237.] THEOR. XII. PROP. XVII.
[238.] THEOR. XIII. PROP. XVIII.
[239.] THEOR. XIV. PROP. XIX.
[240.] PROBL. I. PROP. XX.
[241.] MONITVM.
[242.] THEOR. XV. PROP. XXI.
[243.] PROBL. II. PROP. XXII.
[244.] PROBL. III. PROP. XXIII.
[245.] MONITVM.
[246.] THEOR. XVI. PROP. XXIV.
[247.] THEOR. XVII. PROP. XXV.
[248.] COROLL.
[249.] THEOR. XIIX. PROP. XXVI.
[250.] COROLL. I.
[251.] COROLL. II.
[252.] SCHOLIVM.
[253.] LEMMA VI. PROP. XXVII.
[254.] LEMMA VII. PROP. XXVIII.
[255.] LEMMA VIII. PROP. XXIX.
[256.] THEOR. XIX. PROP. XXX.
[257.] SCHOLIVM.
[258.] COROLL.
[259.] LEMMA IX. PROP. XXXI.
[260.] THEOR. XX. PROP. XXXII
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          <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"/>
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        <div xml:id="echoid-div905" type="section" level="1" n="361">
          <head xml:id="echoid-head370" xml:space="preserve">THEOR. LXI. PROP. LXXXXI.</head>
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            <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>
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          <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>
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          </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>
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