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

Table of contents

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[461.] B. SECTIO II.
Page: 344 (324)
[462.] C. SECTIO III.
Page: 344 (324)
[463.] D. SECTIO IV.
Page: 344 (324)
[464.] E. SECTIO V.
Page: 345 (325)
[465.] THEOREMA XXIX. PROPOS. XXXI.
Page: 345 (325)
[466.] THEOREMA XXX. PROPOS. XXXII.
Page: 346 (326)
[467.] COROLLARIVM.
Page: 347 (327)
[468.] THEOREMA XXXI. PROPOS. XXXIII.
Page: 347 (327)
[469.] THEOREMA XXXII. PROPOS. XXXIV.
Page: 348 (328)
[470.] COROLLARIVM.
Page: 349 (329)
[471.] THEOREMA XXXIII. PROPOS. XXXV.
Page: 349 (329)
[472.] COROLLARIVM.
Page: 350 (330)
[473.] THEOREMA XXXIV. PROPOS. XXXVI.
Page: 351 (331)
[474.] THEOREMA XXXV. PROPOS. XXXVII.
Page: 352 (332)
[475.] THEOREMA XXXVI. PROP. XXXVIII.
Page: 353 (333)
[476.] THEOREMA XXXVII. PROP. XXXIX.
Page: 354 (334)
[477.] THEOREMA XXXVIII. PROP. XL.
Page: 354 (334)
[478.] COROLLARIVM.
Page: 354 (334)
[479.] THEOREMA XXXIX. PROPOS. XLI
Page: 355 (335)
[480.] THEOREMA XL. PROPOS. XLII.
Page: 356 (336)
[481.] THEOREMA XLI. PROPOS. XLIII.
Page: 357 (337)
[482.] THEOREMA XLII. PROPOS. XLIV.
Page: 358 (338)
[483.] THEOREMA XLIII. PROP. XLV.
Page: 358 (338)
[484.] THEOREMA XLIV. PROP. XLVI.
Page: 359 (339)
[485.] THEOREMA XLV. PROP. XLVII.
Page: 360 (340)
[486.] THEOREMA XLVI. PROPOS. XLVIII.
Page: 361 (341)
[487.] THEOREMA XLVII. PROPOS. XLIX.
Page: 362 (342)
[488.] THEOREMA XLVIII. PROPOS. L.
Page: 364 (344)
[489.] THEOREMA XLIX. PROPOS. LI.
Page: 365 (345)
[490.] SCHOLIVM.
Page: 365 (345)
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            ſcripta ſequuntur Corollaria, in quibus exempla adbibebimus, veluti
              <lb/>
            Lib. </s>
            <s xml:id="echoid-s8701" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8702" xml:space="preserve">effectum eſt, aſſumptis nempè omnibus figuris ſimilibus genitri-
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            cium figurarum, quæ ſint circuli, diametros in ipſis genitricibus figu-
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            ris, quibus ſunt erecti, ſitos babentes, quæ per reuolutionem figuraram
              <lb/>
            circa ſuos axes deſcribi facilè appræbendi poſsũt, propter quod in exẽ-
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            plis tantũmodò axes aſſumemus congruenter ipſarũ genitrium figurarũ
              <lb/>
            reuolutioni, licet exempla etiam aſſumptis diametris confiici poſſent
              <lb/>
            per deſcriptionem omnium ſimilium figurarum haud tamen per reuolu-
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            tionem factam. </s>
            <s xml:id="echoid-s8703" xml:space="preserve">Liceat autem Prop. </s>
            <s xml:id="echoid-s8704" xml:space="preserve">antecedentium reaſſamptas figu-
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            ras ſub ampliori forma quandoque proponere, bel ſub auguſtiori, pro-
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            ut expedire comperietur, ſeruata ſemper earundem ſimilitudine.</s>
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        <div xml:id="echoid-div830" type="section" level="1" n="491">
          <head xml:id="echoid-head511" xml:space="preserve">COROLLARIVM I.</head>
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            <s xml:id="echoid-s8706" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s8707" xml:space="preserve">21. </s>
            <s xml:id="echoid-s8708" xml:space="preserve">ergo ſi intelligantur tres figuræ, nempè parallelo-
              <lb/>
            grammum, AF, triangulus, EVF, & </s>
            <s xml:id="echoid-s8709" xml:space="preserve">parabola, VEF, circa com-
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            munem axem reuolui, qui ſuppona-
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            tur eſſe, EM, fiet ex, AF, cylindrus,
              <lb/>
            AF. </s>
            <s xml:id="echoid-s8710" xml:space="preserve">extriangulo, VEF, conus, VEF,
              <lb/>
            & </s>
            <s xml:id="echoid-s8711" xml:space="preserve">ex parabola, VEF, conoides para-
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            bolicum, VEF, vnde patebit cylindrũ,
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            AF, eſſe duplum conoidis, VEF, & </s>
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            hoc eſſe ſexquialterum coni, VEF; </s>
            <s xml:id="echoid-s8713" xml:space="preserve">& </s>
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            vniuerſaliſsimè, vt dictum eſt, ſoli-
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            dum ſimilare genitum ex, AF, ad ſibi
              <lb/>
            ſimilare genitum ex parabola, VEF, habere duplam rationem, hoc
              <lb/>
            verò ad ſibi ſimilare gentium ex triangulo, VEF, rationem ſexqui-
              <lb/>
            alteram, quod tamen, ne figuræ multiplicentur, ſeu nimis confun-
              <lb/>
            dantur (quod etiã impofteru obſeruabimus) vno tãtũ adhibito exẽ-
              <lb/>
            plo, reuolutionis figurarũ
              <unsure/>
            genitriciũ circa ſuos axes, explicare volui.</s>
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          </p>
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        <div xml:id="echoid-div832" type="section" level="1" n="492">
          <head xml:id="echoid-head512" xml:space="preserve">COROLLARIVM II.</head>
          <p>
            <s xml:id="echoid-s8716" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s8717" xml:space="preserve">22. </s>
            <s xml:id="echoid-s8718" xml:space="preserve">aſſumpta eius figura, fiat exemplum per reuolutio-
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              <figure xlink:label="fig-0366-02" xlink:href="fig-0366-02a" number="248">
                <image file="0366-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0366-02"/>
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            nem parabolæ, FCH, circa axẽ,
              <lb/>
            CG, dimiſsis parallelogrammis, AH,
              <lb/>
            RM, fient igitur in hac reuolutione
              <lb/>
            conoidea parabolica ex, FCH, OCM,
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            parabolis, quæ fint, FCH, OCM; </s>
            <s xml:id="echoid-s8719" xml:space="preserve">vn-
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            de patebit conoides parabolicum,
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            FCH, ad conoides parabolicũ, OCM,
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            eſſe, vt quadratũ, GG, ad </s>
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