Ceva, Giovanni, Geometria motus, 1692

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              <s id="s.000245">
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              Tab.
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              2.
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              Fig.
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              9.</s>
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              PROP. XI. THEOR. XI.
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              <s id="s.000247">IIſdem adhuc manentibus, idem de Angelis monſtrat eo­
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              dem illo tractatu pr. 3. ſi quæcunque ex dictis parabo­
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              lis ſecta ſit qualibet recta parallela baſi BC, eſſe parabolam
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              ad reſectam portionem verſus verticem, vt poteſtas baſis,
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              cuius exponens eſt numerus parabolæ vnitate auctus ad
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              ſimilem poteſtatem ex baſi reſectæ portionis; itaque iņ
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              prima parabola eſt vt quadratum ad quadratum, in ſecun­
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              da vt cubus ad cubum, & ſic de cæteris. </s>
              <s id="s.000248">Similiter ſi ſece­
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              tur quodlibet ex infinitis trilineis linea GF baſi CD paral­
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              lela, erit trilineum ad ſuperius ſui ſegmentum vt poteſtas
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              ex DA, cuius exponens eſt numerus trilinei vnitate auctus
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              ad ſimilem poteſtatem ex AF. quare trilineum primum̨
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              CAD ad GAF erit vt quadratum ex DA ad quadratum
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              ex FA, ſecundum CHAD ad ſegmentum HAF vt cubus
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              ad cubum, & ita in cæteris eodem ordine. </s>
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              PROP. XII. THEOR. XII.
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                <emph type="italics"/>
              Tab.
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              3.
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              fig.
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              1.</s>
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            <p type="main">
              <s id="s.000251">SIt modò ACD angulus rectus, & linea FE talis naturæ,
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              vt deductis ad libitum rectis AF, BE parallelis ipſi
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              CD, poteſtas ex CA ad ſimilem poteſtatem ex CB ſit reci­
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              procè vt alia quædam poteſtas ex BE ad ſimilem huic po­
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              teſtatem ex AF; patet rectas CA, CD nondum iungi cum
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              EF, quamuis in immenſum vnà producerentur. </s>
              <s id="s.000252">Ab hoc
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              proprietate VValliſius & Fermatius ſubtiliſſimi authores
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              vocauerunt curuam FE nouam hyperbolam, & eius aſ­
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              ſymptotos AC, CD. </s>
              <s id="s.000253">Omnes huiuſmodi hyperbolæ, quæ
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              infinitæ numero ſunt, terminantur ad vnam partem ma­
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              gnitudine, cum hyperbola
                <expan abbr="cõmunis">communis</expan>
              , ſeu Apolloniaca ſit in
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              vtranque partem magnitudine infinita. </s>
              <s id="s.000254">Quod ergo exi­
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              mium eſt, oſtenderunt ipſi authores rectangulum FA iņ </s>
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