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

Table of contents

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[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)
[291.] THEOREMA XXXIX. PROPOS. XXXIX:
Page: 211 (191)
[292.] THEOREMA XL. PROPOS. XL.
Page: 212 (192)
[293.] COROLLARIVM.
Page: 212 (192)
[294.] THEOREMA XLI. PROPOS. XLI.
Page: 212 (192)
[295.] THEOREMA XLII. PROPOS. XLII.
Page: 213 (193)
[296.] COROLLARIVM.
Page: 214 (194)
[297.] SCHOLIVM.
Page: 215 (195)
[298.] Finis Secundi Libri.
Page: 215 (195)
[299.] CAVALERII LIBER TERTIVS. In quo de circulo, & Ellipſi, ac ſolidis ab eiſdem genitis, traditur doctrina.
Page: 217 (197)
[300.] THEOREMA I. PROPOS. I.
Page: 217 (197)
[301.] COROLLARIVM.
Page: 219 (199)
[302.] THEOREMA II. PROPOS. II.
Page: 220 (200)
[303.] THEOREMA III. PROPOS. III.
Page: 221 (201)
[304.] THEOREMA IV. PROPOS. IV.
Page: 223 (203)
[305.] THEOREMA V. PROPOS. V.
Page: 224 (204)
[306.] COROLLARIV M.
Page: 225 (205)
[307.] THEOREMA VI. PROPOS. VI.
Page: 226 (206)
[308.] COROLLARIVM.
Page: 228 (208)
[309.] THEOREMA VII. PROPOS. VII.
Page: 228 (208)
[310.] PROBLEMA I PROPOS. VIII.
Page: 229 (209)
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          <pb o="265" file="0285" n="285" rhead="LIBER III."/>
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        <div xml:id="echoid-div633" type="section" level="1" n="367">
          <head xml:id="echoid-head384" xml:space="preserve">COROLLARIVM VIII.</head>
          <p>
            <s xml:id="echoid-s6594" xml:space="preserve">IN Propof. </s>
            <s xml:id="echoid-s6595" xml:space="preserve">octaua diſcimus à data ſphæra, vel ſphæroide, vel ſo-
              <lb/>
            lido quocunque genito ex circulo, vel ellipſi, iuxta regulam, quę
              <lb/>
            ſit vna ex ordinatim applicatis, abſcindere portionem, quæ ad ſoli-
              <lb/>
            dum ſimilare ſibi genitum ex triangulo in eadem baſi, & </s>
            <s xml:id="echoid-s6596" xml:space="preserve">circa eun-
              <lb/>
            dem axim, vel diametrum cum portione conſtituto, habeat datam
              <lb/>
            rationem, quam oportet eſſe maiorem ſexquialtera; </s>
            <s xml:id="echoid-s6597" xml:space="preserve">quæ omniaibi
              <lb/>
            clarè patent, & </s>
            <s xml:id="echoid-s6598" xml:space="preserve">ideo figuram non appono.</s>
            <s xml:id="echoid-s6599" xml:space="preserve"/>
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        <div xml:id="echoid-div634" type="section" level="1" n="368">
          <head xml:id="echoid-head385" xml:space="preserve">COROLL. IX. SECTIO PRIOR.</head>
          <p>
            <s xml:id="echoid-s6600" xml:space="preserve">IN Propof. </s>
            <s xml:id="echoid-s6601" xml:space="preserve">nona patet ratio, quam
              <lb/>
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                <image file="0285-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0285-01"/>
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            habet ſolidum ſimilare genitum ex
              <lb/>
            circulo, vel ellipſi, iuxta regulam pri-
              <lb/>
            mum axim, vel diametrum, ad ſolidum
              <lb/>
            ſimilare genitum ex eodem, iuxta ſe-
              <lb/>
            cundum axim, vel diametrum tamquam
              <lb/>
            regulam, ſiue hæc ſolida ſint ſphæra, vel
              <lb/>
            ſphæroides, vel tantum ſolida ſimilaria,
              <lb/>
            quæ in his appoſitis figuris clarè patent,
              <lb/>
            in quarum vna conſpici poteſt ſphęroi-
              <lb/>
            des prolatum, in altera oblongum, præ-
              <lb/>
            dicta autem ratio eſt ea, quam habet
              <lb/>
            prima axis, vel diameter ad ſecundam
              <lb/>
            axim, vel diametrum: </s>
            <s xml:id="echoid-s6602" xml:space="preserve">quę etiam pro re-
              <lb/>
            liquis ſolidis ad inuicem ſimilaribus ma-
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            nifeſta ſunt.</s>
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          <head xml:id="echoid-head386" xml:space="preserve">SECTIO POSTERIOR.</head>
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            <s xml:id="echoid-s6604" xml:space="preserve">IN Corollario autem eiuſdem Theorematis colligimus eſſe notam
              <lb/>
            rationem omnium quadratorum duarum portionum circuli, vel
              <lb/>
            ellipſis abſeiſlarum per lineas, quarum vna ſit parallela primo, alte-
              <lb/>
            ra ſecundo axi, vel diametro, quales ſint in appoſitis figuris portio-
              <lb/>
            nes, BMS, VPX, vnde etiam nota eritratio ſolidorum ſimilarium,
              <lb/>
            BMS, VPX, exipſis genitorum, vnumiuxta regulam, BS, alte-
              <lb/>
            rum iuxta regulam, VX, ſiue ſint hæc portiones ſphæræ, velſphæ-
              <lb/>
            roidis, ſiue ſolida ſimilaria genita ex portionibus, BMS, VFX.</s>
            <s xml:id="echoid-s6605" xml:space="preserve"/>
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