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

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            ſimiles ſunt circuli, ſemidiametros in figura genitrice, OV, haben-
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            tes, à trilineo autem, DCV, deſcribetur quoddam ſolidum, quod
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              <figure xlink:label="fig-0288-01" xlink:href="fig-0288-01a" number="180">
                <image file="0288-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0288-01"/>
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            vocetur, Apex ſphæralis, ſi, OCD, ſit
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            quarta circuli; </s>
            <s xml:id="echoid-s6655" xml:space="preserve">vel ſphæroidalis, ſi, OC
              <lb/>
            D, ſit quarta ellipſis, ideſt ſolidum ſimila-
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            re, quod poteſt dici genitum ex trilineo,
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            DCV, habens omnes ſuas ſimiles figuras
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            circulos ſemidiametros in figura genitri-
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            ce, DCV, ſitos habentes, eſt igitur inter
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            hæc duo ſimilaria ſolida, quęin particulari
              <lb/>
            hoc exemplo ſunt cylindrus, & </s>
            <s xml:id="echoid-s6656" xml:space="preserve">apex ſphę-
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            ralis, vel ſphæroidalis, ratio eadem ſupradictę, quam breuitatis caufa
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            aliter exemplificare dimiſi. </s>
            <s xml:id="echoid-s6657" xml:space="preserve">Conſimili autem vnico exemplo.</s>
            <s xml:id="echoid-s6658" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6659" xml:space="preserve">affu-
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            mendo pro ſiguris ſimilibus ipſos circulos, ſemidiametros in figuris
              <lb/>
            genitricibus habentibus, breuitatis cauſa, & </s>
            <s xml:id="echoid-s6660" xml:space="preserve">ob ſeruandam in figuris
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            claritatem impoſterum contenti erimus.</s>
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        <div xml:id="echoid-div644" type="section" level="1" n="376">
          <head xml:id="echoid-head393" xml:space="preserve">COROLLARIVM XII.</head>
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            <s xml:id="echoid-s6662" xml:space="preserve">IN Propof. </s>
            <s xml:id="echoid-s6663" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6664" xml:space="preserve">patet ratio ſolidi ſimilaris geniti ex, FD, ad ſoli-
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            dum ſimilare genitum ex figura, FQBDZ. </s>
            <s xml:id="echoid-s6665" xml:space="preserve">Appoſita. </s>
            <s xml:id="echoid-s6666" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6667" xml:space="preserve">hic
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            illius figura, dimiffa, HC, &</s>
            <s xml:id="echoid-s6668" xml:space="preserve">, AP, & </s>
            <s xml:id="echoid-s6669" xml:space="preserve">retenta, BD, tantum in, V,
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            diuifa, reuoluatur, FD, circa manentem axim, ZD, modò ſupra-
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              <figure xlink:label="fig-0288-02" xlink:href="fig-0288-02a" number="181">
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            dicto, ex, FD, igitur fiet cylin-
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            drus, FA, & </s>
            <s xml:id="echoid-s6670" xml:space="preserve">ex figura, FQBD
              <lb/>
            Z, fiet quoddam ſolidum rotun-
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            dum, quod vocetur, Tympanum
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            fphærale, ſi, FQB, ſit ſemicircu-
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            lus, vel ſphæroidale, ſi, FQB, ſit
              <lb/>
            ellipſis, erunt autem hæc duo ſo-
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            lida ſimilaria genita ex figuris, F
              <lb/>
            D, FQBDZ, figuras ſimiles cir-
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            culos habentia, quorum ſemidia-
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            metri iacent in ſuis genitricibus fi-
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            guris, & </s>
            <s xml:id="echoid-s6671" xml:space="preserve">patet, quod ratio cylin-
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            dri, FA, ad tympanum ſphærale, vel ſphæroidale, FQRA, eſt ea-
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            dem ei, quam habet, BD, ad, DV, eandem autem habet quodli-
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            bet ſolidum ſimilare genitum ex, FD, ad ſimilare ſibi genitum ex fi-
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            gura, FQBDZ, qualecunque ſit.</s>
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