Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[91. THEOREMA XXI. PROPOSITIO XXVI.]
[92. THEOREMA XXII. PROPOSITIO XXVII.]
[93. PROBLEMA VI. PROPOSITIO XX VIII.]
[94. THE OREMA XXIII. PROPOSITIO XXIX.]
[95. THEOREMA XXIIII. PROPOSITIO XXX.]
[96. THEOREMA XXV. PROPOSITIO XXXI.]
[97. FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.]
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DE CENTRO GRAVIT. SOLID.
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        <div type="section" level="1" n="94">
          <p>
            <s xml:space="preserve">
              <pb o="45" file="0201" n="201" rhead="DE CENTRO GRAVIT. SOLID."/>
            ad punctum ω. </s>
            <s xml:space="preserve">Sed quoniam π circum ſcripta itidem alia
              <lb/>
            figura æquali interuallo ad portionis centrum accedit, ubi
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            primum φ applieuerit ſe ad ω, & </s>
            <s xml:space="preserve">π ad punctũ ψ, hoc eſt ad
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            portionis centrum ſe applicabit. </s>
            <s xml:space="preserve">quod fieri nullo modo
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            poſſe perſpicuum eſt. </s>
            <s xml:space="preserve">non aliter idem abſurdum ſequetur,
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            ſi ponamus centrum portionis recedere à medio ad par-
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            tes ω; </s>
            <s xml:space="preserve">eſſet enim aliquando centrum figuræ inſcriptæ idem
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            quod portionis centrũ. </s>
            <s xml:space="preserve">ergo punctum e centrum erit gra
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            uitatis portionis a b c. </s>
            <s xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0195-01" xlink:href="fig-0195-01a">
              <image file="0195-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0195-01"/>
            </figure>
            <note position="right" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">7. huius</note>
            <figure xlink:label="fig-0196-01" xlink:href="fig-0196-01a">
              <image file="0196-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0196-01"/>
            </figure>
            <note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">8. primi
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            libri Ar-
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            chimedis</note>
            <note position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">11. duo-
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            decimi.</note>
            <note position="left" xlink:label="note-0196-03" xlink:href="note-0196-03a" xml:space="preserve">15. quinti</note>
            <note position="left" xlink:label="note-0196-04" xlink:href="note-0196-04a" xml:space="preserve">2. duode-
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            cimi.</note>
            <note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">20. primi
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            conicorũ</note>
            <figure xlink:label="fig-0198-01" xlink:href="fig-0198-01a">
              <image file="0198-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0198-01"/>
            </figure>
            <note position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">19. quinti</note>
            <figure xlink:label="fig-0200-01" xlink:href="fig-0200-01a">
              <image file="0200-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0200-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Quod autem ſupra demõſtratum eſt in portione conoi-
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            dis recta per figuras, quæ ex cylindris æqualem altitudi-
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            dinem habentibus conſtant, idem ſimiliter demonſtrabi-
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            mus per figuras ex cylindri portionibus conſtantes in ea
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            portione, quæ plano non ad axem recto abſcinditur. </s>
            <s xml:space="preserve">ut
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            enim tradidimus in commentariis in undecimam propoſi
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            tionem libri Archimedis de conoidibus & </s>
            <s xml:space="preserve">ſphæroidibus.
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            </s>
            <s xml:space="preserve">portiones cylindri, quæ æquali ſunt altitudine eam inter ſe
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            ſe proportionem habent, quam ipſarum baſes; </s>
            <s xml:space="preserve">baſes autẽ
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            quæ ſunt ellipſes ſimiles eandem proportionem habere,
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              <anchor type="note" xlink:label="note-0201-01a" xlink:href="note-0201-01"/>
            quam quadrata diametrorum eiuſdem rationis, ex corol-
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            lario ſeptimæ propoſitionis libri de conoidibus, & </s>
            <s xml:space="preserve">ſphæ-
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            roidibus, manifeſte apparet.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">corol. 15
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            deconoi-
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            dibus &
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            ſphæroi-
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            dibus.</note>
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        <div type="section" level="1" n="95">
          <head xml:space="preserve">THEOREMA XXIIII. PROPOSITIO XXX.</head>
          <p>
            <s xml:space="preserve">SI à portione conoidis rectanguli alia portio
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            abſcindatur, plano baſi æquidiſtante; </s>
            <s xml:space="preserve">habebit
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            portio tota ad eam, quæ abſciſſa eſt, duplam pro
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            portio nem eius, quæ eſt baſis maioris portionis
              <lb/>
            ad baſi m minoris, uel quæ axis maioris ad axem
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            minoris.</s>
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          </p>
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