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

Table of contents

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[71.] THEOREMA IX. PROPOS. XII.
Page: 47 (27)
[72.] COROLLARIV M.
Page: 48 (28)
[73.] THEOREMA X. PROPOS. XIII.
Page: 48 (28)
[74.] THEOREMA XI. PROPOS. XIV.
Page: 50 (30)
[75.] THEOREMA XII. PROPOS. XV.
Page: 51 (31)
[76.] SCHOLIVM.
Page: 52 (32)
[77.] THEOREMA XIII. PROPOS. XVI.
Page: 52 (32)
[78.] COROLLARIVM.
Page: 52 (32)
[79.] THEOREMA XIV. PROPOS. XVII.
Page: 53 (33)
[80.] COROLLARIVM.
Page: 53 (33)
[81.] THEOREMA XV. PROPOS. XVIII.
Page: 54 (34)
[82.] COROLLARIVM.
Page: 55 (35)
[83.] THEOREMA XVI. PROPOS. XIX.
Page: 55 (35)
[84.] COROLLARIVMI.
Page: 57 (37)
[85.] COROLLARIVM II.
Page: 57 (37)
[86.] THEOREMA XVII. PROPOS. XX.
Page: 58 (38)
[87.] THE OREMA XVIII. PROPOS. XXI.
Page: 58 (38)
[88.] COROLLARIVM.
Page: 59 (39)
[89.] THEOREMA XIX. PROPOS. XXII.
Page: 60 (40)
[90.] COROLLARIVM I.
Page: 62 (42)
[91.] COROLLARIVM II.
Page: 62 (42)
[92.] LEMMA PRO ANTECED. PROP.
Page: 62 (42)
[93.] THEOREMA XX. PROPOS. XXIII.
Page: 63 (43)
[94.] COROLLARIVM.
Page: 63 (43)
[95.] THEOREMA XXI. PROPOS. XXIV.
Page: 63 (43)
[96.] COROLLARIVM.
Page: 65 (45)
[97.] THEOREMA XXII. PROPOS. XXV.
Page: 65 (45)
[98.] COROLLARIVM.
Page: 66 (46)
[99.] THEOREMA XXIII. PROPOS. XXVI.
Page: 67 (47)
[100.] THEOREMA XXIV. PROPOS XXVII.
Page: 69 (49)
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          <head xml:id="echoid-head136" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s1973" xml:space="preserve">_H_Inc patet ipſam, BE, communem ſectionem trianguli por axem
              <lb/>
            ducti, & </s>
            <s xml:id="echoid-s1974" xml:space="preserve">circuli, BRE, eſſe eiuſdem diametrum, cum per eius
              <lb/>
            centrum tranſedt.</s>
            <s xml:id="echoid-s1975" xml:space="preserve"/>
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          <head xml:id="echoid-head137" xml:space="preserve">THEOREMA XXXIII. PROPOS. XXXVI.</head>
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            <s xml:id="echoid-s1976" xml:space="preserve">SI ſolidum rotundum, vel conus ſcalenus ſecentur plano
              <lb/>
            per axem, deinde ſecetur ſolidum rotundum (niſi baſim
              <lb/>
            habeat, quę circulus erit) plano ad axem recto circulum pro-
              <lb/>
            ducente, in cuius plano, & </s>
            <s xml:id="echoid-s1977" xml:space="preserve">illius, qui eſt coni baſis perpen-
              <lb/>
            dicularis ducta ſit baſi figurę per axim ductę; </s>
            <s xml:id="echoid-s1978" xml:space="preserve">deinde ſumpto
              <lb/>
            puncto in ambitu figuræ per axem, per illum æquidiſtans di-
              <lb/>
            ctæ perpendiculari ducta fueritrecta linea, hæc tanget dicta
              <lb/>
            ſolida, at ſi ſumptus punctus ſit extra talem ambitum, ſed in
              <lb/>
            ſuperficie ambiente dicta ſolida, quæ per ipſum ducitur ei-
              <lb/>
            dem æquidiſtans intra dicta ſolida cadet, & </s>
            <s xml:id="echoid-s1979" xml:space="preserve">producta vſque
              <lb/>
            ad ſuperficiem ambientem à figura ducta per axem bifariam
              <lb/>
            diuidetur.</s>
            <s xml:id="echoid-s1980" xml:space="preserve"/>
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            <s xml:id="echoid-s1981" xml:space="preserve">Sit ſolidum rotundum, ABTF, vel conus ſcalenus, APR, in
              <lb/>
            baſi circulo, PXRZ, quorum axis, AT, & </s>
            <s xml:id="echoid-s1982" xml:space="preserve">ſi ſolidum rotundum
              <lb/>
            non habeat baſim, ſe-
              <lb/>
              <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a" number="54">
                <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0098-01"/>
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            cetur plano recto ad
              <lb/>
            axem, quod in eo pro-
              <lb/>
            ducat circulum, PXR
              <lb/>
            Z, ſecentur autem am-
              <lb/>
            bo planis per axem-
              <lb/>
            quæ producant in ſo-
              <lb/>
            lido rotundo figuram,
              <lb/>
            APTF, & </s>
            <s xml:id="echoid-s1983" xml:space="preserve">in cono
              <lb/>
            triangulum, APR,
              <lb/>
            deinde in plano circu-
              <lb/>
            li, PZRX, ducatur
              <lb/>
            ipſi, PR, communi
              <lb/>
            ſectioni dicti circuli, & </s>
            <s xml:id="echoid-s1984" xml:space="preserve">
              <lb/>
            figuræ per axem, perpendicularis, ZX, & </s>
            <s xml:id="echoid-s1985" xml:space="preserve">ſumpto puncto in ambitu
              <lb/>
            figurę per axem, vt, 2, per ipſum ducatur recta linea parallela </s>
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