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

Table of contents

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[261.] COROLLARIVM.
Page: 194 (174)
[262.] THEOREMA XXXII. PROPOS. XXXII.
Page: 195 (175)
[263.] COROLLARIVM.
Page: 196 (176)
[264.] THEOREMA XXXIII. PROPOS. XXXIII.
Page: 197 (177)
[265.] COROLLARIVM I.
Page: 198 (178)
[266.] COROLLARIVM II.
Page: 199 (179)
[267.] THEOREMA XXXIV. PROPOS. XXXIV.
Page: 199 (179)
[268.] COROLLARIVM I.
Page: 201 (181)
[269.] COROLLARIVM II.
Page: 201 (181)
[270.] COROLLARIVM III.
Page: 201 (181)
[271.] A. COROLLARII IV. GENERALIS. SECTIO I.
Page: 203 (183)
[272.] B. SECTIO II.
Page: 203 (183)
[273.] C. SECTIO III.
Page: 203 (183)
[274.] D. SECTIO IV.
Page: 204 (184)
[275.] E. SECTIO V.
Page: 204 (184)
[276.] F. SECTIO VI.
Page: 204 (184)
[277.] G. SECTIO VII.
Page: 204 (184)
[278.] H. SECTIO VIII.
Page: 204 (184)
[279.] I. SECTIO IX.
Page: 205 (185)
[280.] K. SECTIO X.
Page: 205 (185)
[281.] L. SECTIO XI.
Page: 206 (186)
[282.] M. SECTIO XII.
Page: 206 (186)
[283.] N. SECTIO XIII.
Page: 207 (187)
[284.] THEOREMA XXXV. PROPOS. XXXV.
Page: 207 (187)
[285.] SCHOLIV M.
Page: 208 (188)
[286.] THEOREMA XXXVI. PROPOS. XXXVI.
Page: 208 (188)
[287.] THEOREMA XXXVII. PROPOS. XXXVII.
Page: 209 (189)
[288.] COROLLARIVM.
Page: 210 (190)
[289.] THEOREMA XXXVIII. PROPOS. XXXVIII.
Page: 210 (190)
[290.] SCHOLIVM.
Page: 211 (191)
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            ſiue hoc ſit portio ſphæræ, vel ſphæroidis, ſiue tantum ſolidum ſi-
              <lb/>
            milare genitum ex portione, VCBFR, vtrectangulum, BAO, ſiue
              <lb/>
            quadratum, BA, ad rectangulum ſub, BM, & </s>
            <s xml:id="echoid-s6552" xml:space="preserve">ſub compoſita ex, M
              <lb/>
            O, OA, nam ſicut rectangulum, BAO, eſt tertia pars rectanguli
              <lb/>
              <note position="left" xlink:label="note-0282-01" xlink:href="note-0282-01a" xml:space="preserve">I. Propol.
                <lb/>
              24, lib. 2.</note>
            ſub, BA, & </s>
            <s xml:id="echoid-s6553" xml:space="preserve">tripla, AO, ita ſolidum ſimilare genitum ex triangulo,
              <lb/>
            BPN, eſt tertia pars ſolidi ſimilaris geniti ex, DN, vnde patet, &</s>
            <s xml:id="echoid-s6554" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6555" xml:space="preserve"/>
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        <div xml:id="echoid-div623" type="section" level="1" n="361">
          <head xml:id="echoid-head378" xml:space="preserve">COROLLARIVM III.</head>
          <p>
            <s xml:id="echoid-s6556" xml:space="preserve">IN Propoſit. </s>
            <s xml:id="echoid-s6557" xml:space="preserve">tertia colligitur, quam rationem habeat ſolidum ſi-
              <lb/>
            milare genitum ex, BF, ſiue ſit cylindrus, ſiue priſma, ſiue tan-
              <lb/>
            tum conicus, ad ſibi ſimilare genitum ex portione circuli, vel ellipſis,
              <lb/>
            ICFS, ſiue hoc ſit fruſtum ſphærę, vel ſphæroidis, ſiue tantum ſo-
              <lb/>
            lidum ſimilare genitum ex portione, ICFS, ſiue, AD, ſit a@is ſiue
              <lb/>
              <figure xlink:label="fig-0282-01" xlink:href="fig-0282-01a" number="174">
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            non, quę eadem eſt ei, quam habet re-
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            ctangulum, DRA, ad rectangulum
              <lb/>
            ſub, DR, & </s>
            <s xml:id="echoid-s6558" xml:space="preserve">ſub compoſita ex, {1/2}, R
              <lb/>
            M, & </s>
            <s xml:id="echoid-s6559" xml:space="preserve">ex, MA, vna cam rectangulo
              <lb/>
            ſub, RM, & </s>
            <s xml:id="echoid-s6560" xml:space="preserve">ſub compoſita ex, {1/6}, R
              <lb/>
            M, &</s>
            <s xml:id="echoid-s6561" xml:space="preserve">, {1/2}, MA. </s>
            <s xml:id="echoid-s6562" xml:space="preserve">Solidum autem ſimi-
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            lare genitum ex triangulo, MCF, ſiue
              <lb/>
            ſit conus, ſiue priſma, ſiue tantum co-
              <lb/>
            nicus, ad ſibi ſimilare genitum ex por-
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            tione, ICFS, ſiue hoc ſit fruſtum
              <lb/>
            ſphæræ, vel ſphæroidis, ſiue tantum
              <lb/>
            ſolidum ſimilare genitum ex tali por-
              <lb/>
            tione, ICFS, erit vt rectangulum,
              <lb/>
            DRA, ad rectangulum ſub compoſita ex, MD, DR, & </s>
            <s xml:id="echoid-s6563" xml:space="preserve">ſub ſex-
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            quialtera, MA, vna cum rectangulo ſub compoſita ex, MD, &</s>
            <s xml:id="echoid-s6564" xml:space="preserve">dupla, DR, & </s>
            <s xml:id="echoid-s6565" xml:space="preserve">ſub, {1/2}, MR, ſiue, AD, ſit axis, ſiue tantum dia-
              <lb/>
            meter, quę iuxta antecedẽtium declarationem facilè percipi poſſunt.</s>
            <s xml:id="echoid-s6566" xml:space="preserve"/>
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        <div xml:id="echoid-div625" type="section" level="1" n="362">
          <head xml:id="echoid-head379" xml:space="preserve">COROLLARIVM IV.</head>
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            <s xml:id="echoid-s6567" xml:space="preserve">IN Propof. </s>
            <s xml:id="echoid-s6568" xml:space="preserve">quarta patet ratio, quam habet ſolidum ſimilare ge-
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            nitum ex, GX, quod apparet in ſuperioris figura, ad ſibi ſimilare
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            genitum ex portione, ICFS, quæratio ibi conſpiciatur.</s>
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