Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
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          <pb o="18" file="0047" n="47" rhead="DE IIS QVAE VEH. IN AQVA."/>
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            <s xml:space="preserve">Itaque quoniam no ad f ω maiorem habetproportio-
              <lb/>
              <anchor type="note" xlink:label="note-0047-01a" xlink:href="note-0047-01"/>
            nem, quam ad eam, quæ uſque ad axem.</s>
            <s xml:space="preserve">] _Habet enim diame-_
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            _ter portioms n o ad f ω proportionem eandem, quam quindeeim ad_
              <lb/>
            _quatuor; </s>
            <s xml:space="preserve">ad eam uero, quæ uſque ad axem minorem proportionem_
              <lb/>
            _habere ponitur, quàm quindecim ad quatuor. </s>
            <s xml:space="preserve">quare n o ad f ω ma_
              <lb/>
            _iorem habebit proportionem, quàm ad eam, quæ uſque ad axem: </s>
            <s xml:space="preserve">&_</s>
            <s xml:space="preserve">
              <lb/>
            _propterea quæ uſque ad axem ipſa f ω maior erit_.
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            </s>
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          </p>
          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">B</note>
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          <note position="right" xml:space="preserve">10. quinti</note>
          <p>
            <s xml:space="preserve">Quoniam ergo in portione a p o l, quæ continetur re-
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            cta linea, & </s>
            <s xml:space="preserve">rectanguli coni ſectione, _k_ ω quidem æ quidi-
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            ſtans eſt ipſi a l; </s>
            <s xml:space="preserve">p i uero diametro æquidiſtat; </s>
            <s xml:space="preserve">ſecaturq;
              <lb/>
            </s>
            <s xml:space="preserve">ab ipſa k ω in h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a c æquidiſtat contingenti in p neceſ-
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            ſarium eſt ipſam p i ad p h uel eandem proportionem ha
              <lb/>
            bere, quam habet n ω ad ω o, uel maiorem. </s>
            <s xml:space="preserve">hoc enim iam
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            demonſtratum eſt] _Vbi hoc demonſtratum ſit uel ab ipſo Ar-_
              <lb/>
            _chimede, uel ab alio, numdum apparet, quocircanos demonstra-_
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            _tionem afferemus, poſteaquam non nulla, quæ ad eam pertinent ex-_
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            _plicauerimus_.</s>
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        <div type="section" level="1" n="31">
          <head xml:space="preserve">LEMMAI.</head>
          <p style="it">
            <s xml:space="preserve">Sint lineæ a b, a c angulum b a c continentes: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à
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            puncto d, quod in linea a c ſumptum ſit, ducantur d e,
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            d f utcunque ad ipſam a b. </s>
            <s xml:space="preserve">Sumptis uero in eadem li.
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            </s>
            <s xml:space="preserve">nea quotlibet punctis g l, ducantur g h, l m ipſi d e
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            æquidistantes; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">g k, l n æquidiſtantes f d. </s>
            <s xml:space="preserve">deinde à
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            punctis d, g uſque ad lineam m l ducantur, d o p qui
              <lb/>
            dem ſecans g h in o; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">g q, quæ æquidistent ipſi b a. </s>
            <s xml:space="preserve">
              <lb/>
            Dico lineas, quæ inter æquidiſtantes ipſi f d ad eas, quæ
              <lb/>
            inter æquidiſtantes d e interiiciuntur, uidelicet k n ad g q,
              <lb/>
            uel ad o p; </s>
            <s xml:space="preserve">f k ad d o; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">f n ad d p eandem inter ſe ſe
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            proportionem habere: </s>
            <s xml:space="preserve">nempe eam, quã habet a f ad a e.</s>
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