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

Table of contents

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[271.] THEOR. XXIII. PROP. XXXX.
Page: 235 (51)
[272.] COROLL. I.
Page: 237 (53)
[273.] COROLL. II.
Page: 237 (53)
[274.] COROLL. III.
Page: 237 (53)
[275.] PROBL. VI. PROP. XXXXI.
Page: 238 (54)
[276.] PROBL. VII. PROP. XXXXII.
Page: 238 (54)
[277.] COROLL.
Page: 239 (55)
[278.] THEOR. XXIV. PROP. XXXXIII.
Page: 240 (56)
[279.] THEOR. XXV. PROP. XXXXIV.
Page: 240 (56)
[280.] SCHOLIVM.
Page: 242 (58)
[281.] THEOR. XXVI. PROP. XLV.
Page: 242 (58)
[282.] COROLL.
Page: 243 (59)
[283.] THEOR. XXVII. PROP. XLVI.
Page: 243 (59)
[284.] COROLL. I.
Page: 245 (61)
[285.] COROLL. II.
Page: 245 (61)
[286.] THEOR. XXVIII. PROP. XLVII.
Page: 245 (61)
[287.] THEOR. XXIX. PROP. XLVIII.
Page: 247 (63)
[288.] THEOR. XXX. PROP. XLIX.
Page: 248 (64)
[289.] THEOR. XXXI. PROP. L.
Page: 249 (65)
[290.] COROLL.
Page: 250 (66)
[291.] THEOR. XXXII. PROP. LI.
Page: 251 (67)
[292.] SCHOLIVM.
Page: 252 (68)
[293.] THEOR. XXXIII. PROP. LII.
Page: 253 (69)
[294.] THEOR. XXXIV. PROP. LIII.
Page: 253 (69)
[295.] ALITER.
Page: 254 (70)
[296.] THEOR. XXXV. PROP. LIV.
Page: 255 (71)
[297.] THEOR. XXXIV. PROP. LV.
Page: 256 (72)
[298.] THEOR. XXXVII. PROP. LVI.
Page: 257 (73)
[299.] PROBL. VIII. PROP. LVII.
Page: 259 (75)
[300.] PROBL. IX. PROP. LVIII.
Page: 260 (76)
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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"/>
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        <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>
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        <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>
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          <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-
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            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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