Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

Table of contents

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[531.] COROLLARIVM XXVII.
[532.] SCHOLIV M.
[533.] Finis quarti Libri.
[534.] GEOMETRIÆ CAVALERII. LIBER QVINTVS. In quo de Hyperbola, Oppoſitis Sectionib us, ac ſolidis ab eiſdem genitis, babetur contemplatio. THEOREMA I. PROPOS. I.
[535.] THEOREMA II. PROPOS. II.
[536.] THEOREMA III. PROPOS. III.
[537.] THEOREMA IV. PROPOS. IV.
[538.] THEOREMA V. PROPOS. V.
[539.] PROBLEMA I. PROPOS. VI.
[540.] THEOREMA VI. PROPOS. VII.
[541.] THEOREMA VII. PROPOS. VIII.
[542.] THEOREMA VIII. PROPOS. IX.
[543.] THEOREMA IX. PROPOS. X.
[544.] THEOREMA X. PROPOS. XI.
[545.] THEOREMA XI. PROPOS. XII.
[546.] THEOREMA XII. PROPOS. XIII.
[547.] THEOREMA XIII, PROPOS. XIV.
[548.] SCHOLIVM.
[549.] THEOREMA XIV. PROPOS. XV.
[550.] THEOREMA XV. PROPOS. XVI.
[551.] COROLLARIVM.
[552.] THEOREMA XVI. PROPOS. XVII.
[553.] THE OREMA XVII. PROPOS. XVIII.
[554.] THEOREMA XVIII. PROPOS. XIX.
[555.] COROLLARIVM.
[556.] SCHOLIVM.
[557.] THEOREMA XIX. PROPOS. XX.
[558.] THEOREMA XX. PROPOS. XXI.
[559.] A@@ter ſupradictam rationem explicare.
[560.] COROLLARIVM:
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          <p>
            <s xml:id="echoid-s14060" xml:space="preserve">
              <pb o="539" file="0559" n="559" rhead="LIBER VII."/>
            percurremus. </s>
            <s xml:id="echoid-s14061" xml:space="preserve">Igitur circa Corollarium p. </s>
            <s xml:id="echoid-s14062" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14063" xml:space="preserve">nihil dicendum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s14064" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s14065" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14066" xml:space="preserve">autem reſtauratione non indiget. </s>
            <s xml:id="echoid-s14067" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s14068" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14069" xml:space="preserve">ſimiliter. </s>
            <s xml:id="echoid-s14070" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s14071" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14072" xml:space="preserve">
              <lb/>
            oſten detur eo modo, quo nos primam demonſtrauimus, Corolla-
              <lb/>
            riũ verò deducetur vt ibi, mutatis tamẽ ſepè dictis nominibus &</s>
            <s xml:id="echoid-s14073" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14074" xml:space="preserve">ex
              <lb/>
            hac autem oſtenſa facilè deducetur prop. </s>
            <s xml:id="echoid-s14075" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14076" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14077" xml:space="preserve">mutatis &</s>
            <s xml:id="echoid-s14078" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14079" xml:space="preserve">
              <lb/>
            vt etiam prop. </s>
            <s xml:id="echoid-s14080" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14081" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14082" xml:space="preserve">p. </s>
            <s xml:id="echoid-s14083" xml:space="preserve">7. </s>
            <s xml:id="echoid-s14084" xml:space="preserve">8. </s>
            <s xml:id="echoid-s14085" xml:space="preserve">cum dictis in Scholio. </s>
            <s xml:id="echoid-s14086" xml:space="preserve">Similiter
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s14087" xml:space="preserve">9. </s>
            <s xml:id="echoid-s14088" xml:space="preserve">10. </s>
            <s xml:id="echoid-s14089" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14090" xml:space="preserve">mutatis &</s>
            <s xml:id="echoid-s14091" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14092" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s14093" xml:space="preserve">11. </s>
            <s xml:id="echoid-s14094" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14095" xml:space="preserve">p. </s>
            <s xml:id="echoid-s14096" xml:space="preserve">12. </s>
            <s xml:id="echoid-s14097" xml:space="preserve">13. </s>
            <s xml:id="echoid-s14098" xml:space="preserve">14. </s>
            <s xml:id="echoid-s14099" xml:space="preserve">15. </s>
            <s xml:id="echoid-s14100" xml:space="preserve">
              <lb/>
            16. </s>
            <s xml:id="echoid-s14101" xml:space="preserve">17. </s>
            <s xml:id="echoid-s14102" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14103" xml:space="preserve">18. </s>
            <s xml:id="echoid-s14104" xml:space="preserve">19. </s>
            <s xml:id="echoid-s14105" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14106" xml:space="preserve">20. </s>
            <s xml:id="echoid-s14107" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14108" xml:space="preserve">reſtaurationem mi-
              <lb/>
            nimè poſtulant, cum a methodo in diuiſibilium non dependeant.</s>
            <s xml:id="echoid-s14109" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1243" type="section" level="1" n="751">
          <head xml:id="echoid-head784" xml:space="preserve">THEOREMA XXIV. PROPOS. XXIV.</head>
          <p>
            <s xml:id="echoid-s14110" xml:space="preserve">EXpoſito denuò Schemate prop. </s>
            <s xml:id="echoid-s14111" xml:space="preserve">21. </s>
            <s xml:id="echoid-s14112" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s14113" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14114" xml:space="preserve">regu-
              <lb/>
            la eadem, VF, retenta, oſtendemus quadratum ſolidũ,
              <lb/>
            AF, duplum eſſe quadrati ſolidi parabolæ, VEF, & </s>
            <s xml:id="echoid-s14115" xml:space="preserve">hoc eſſe
              <lb/>
            ſexquialterum quadrati ſolidi trianguli, VEF.</s>
            <s xml:id="echoid-s14116" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14117" xml:space="preserve">Eſtò quòd, ND, ſecet, EF, in, I, igitur rectangulum, DNI, eſt æ-
              <lb/>
            quale quadrato, NO, quod & </s>
            <s xml:id="echoid-s14118" xml:space="preserve">circa quaſcumq; </s>
            <s xml:id="echoid-s14119" xml:space="preserve">applicatas con-
              <lb/>
              <note position="right" xlink:label="note-0559-01" xlink:href="note-0559-01a" xml:space="preserve">13 l. 4.</note>
              <figure xlink:label="fig-0559-01" xlink:href="fig-0559-01a" number="366">
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            tingere concludemus, ergo rectan-
              <lb/>
            gulum ſolidum ſub parallelogram-
              <lb/>
            mo, CM, & </s>
            <s xml:id="echoid-s14120" xml:space="preserve">triangulo, EMF, erit æ-
              <lb/>
            qualiter analogum quadrato ſolido
              <lb/>
            ſemiparabolæ, EMF, quadratum
              <lb/>
            ſolidum autem, CM, ad rectangulũ
              <lb/>
            ſolidum ſub eodem parallelogram-
              <lb/>
            mo, CM, & </s>
            <s xml:id="echoid-s14121" xml:space="preserve">ſub triangulo, EMF, eſt
              <lb/>
            vt, CM, ad EMF, ideſt duplum, ergo quadratum ſolidum, CM, du-
              <lb/>
              <note position="right" xlink:label="note-0559-02" xlink:href="note-0559-02a" xml:space="preserve">Cor. 1. 13.
                <lb/>
              huius.</note>
            plum erit quadrati ſolidi, EMF, & </s>
            <s xml:id="echoid-s14122" xml:space="preserve">conſequenter quadratum ſoli-
              <lb/>
            dum, AF, duplum etiam erit quadrati ſolidi parabolæ, VEF, vnde
              <lb/>
            & </s>
            <s xml:id="echoid-s14123" xml:space="preserve">quadratum ſolidum, VEF, ſexquialterum erit quadrati ſolidi, E
              <lb/>
            VF, quod &</s>
            <s xml:id="echoid-s14124" xml:space="preserve">c.</s>
            <s xml:id="echoid-s14125" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1245" type="section" level="1" n="752">
          <head xml:id="echoid-head785" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s14126" xml:space="preserve">PEr ſuprapoſitam prop. </s>
            <s xml:id="echoid-s14127" xml:space="preserve">ſuppletur prop. </s>
            <s xml:id="echoid-s14128" xml:space="preserve">21. </s>
            <s xml:id="echoid-s14129" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s14130" xml:space="preserve">22. </s>
            <s xml:id="echoid-s14131" xml:space="preserve">verò dedu-
              <lb/>
            cetur eodem modo mutatis nominibus &</s>
            <s xml:id="echoid-s14132" xml:space="preserve">c.</s>
            <s xml:id="echoid-s14133" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1246" type="section" level="1" n="753">
          <head xml:id="echoid-head786" xml:space="preserve">THEOREMA XXV. PROPOS. XXV.</head>
          <p>
            <s xml:id="echoid-s14134" xml:space="preserve">ASſumpta ex Schemate prop. </s>
            <s xml:id="echoid-s14135" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14136" xml:space="preserve">ſemiparabola, NOH,
              <lb/>
            cum fruſto, MROH, & </s>
            <s xml:id="echoid-s14137" xml:space="preserve">parallelogrammo, VO, ac </s>
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