Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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            C F, hoc eſt, quam cubi S ad cubum C F. </s>
            <s xml:id="echoid-s1606" xml:space="preserve">Sicut autem
              <lb/>
            R B ad B F, ita eſt cubus R B ad id quod fit ex quadra-
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            to R B in B F. </s>
            <s xml:id="echoid-s1607" xml:space="preserve">Ergo major quoque ratio cubi R B ad qua-
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            dratum R B in B F, quam cubi S ad cubum C F. </s>
            <s xml:id="echoid-s1608" xml:space="preserve">Qua-
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            drato autem R B in B F minus eſt rectangulum ſub R B,
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            B G, in F C; </s>
            <s xml:id="echoid-s1609" xml:space="preserve">quod ſic oſtenditur. </s>
            <s xml:id="echoid-s1610" xml:space="preserve">Quia enim proportiona-
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            les ſunt R C, C F, C G, Erit id quo major mediam exce-
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            dit, hoc eſt F G, major quam quo media minimam, hoc
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            eſt, quam F R. </s>
            <s xml:id="echoid-s1611" xml:space="preserve">Major autem eſt F C quam F B. </s>
            <s xml:id="echoid-s1612" xml:space="preserve">Ergo o-
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            mnino major erit ratio C F ad F R, quam B F ad F G. </s>
            <s xml:id="echoid-s1613" xml:space="preserve">Et
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            per converſionem rationis, minor ratio F C ad C R, quam
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            F B ad B G. </s>
            <s xml:id="echoid-s1614" xml:space="preserve">Et permutando minor F C ad F B, quam
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            C R ſeu R B ad B G: </s>
            <s xml:id="echoid-s1615" xml:space="preserve">hoc eſt, (ſumptâ communi altitu-
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            dine B R) quam quadrati R B ad rectangulum R B G. </s>
            <s xml:id="echoid-s1616" xml:space="preserve">Un-
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            de quod fit ex rectangulo R B G in F C minus erit quam
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            quod ex quadrato R B in F B, uti dictum fuit. </s>
            <s xml:id="echoid-s1617" xml:space="preserve">Quum ita-
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            que major oſtenſa fuerit ratio cubi R B ad quadratum R B
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            in B F, quam cubi S ad cubum C F; </s>
            <s xml:id="echoid-s1618" xml:space="preserve">omnino quoque major
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            erit ratio cubi R B ad ſolidum ſub rectangulo R B G in
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            F C, quam cubi S ad cubum C F. </s>
            <s xml:id="echoid-s1619" xml:space="preserve">Et permutando major
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            ratio cubi R B ad cubum S, quam rectanguli R B G in
              <lb/>
            F C ad cubum C F; </s>
            <s xml:id="echoid-s1620" xml:space="preserve">hoc eſt, quam rectanguli R B G ad
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            quadratum C F. </s>
            <s xml:id="echoid-s1621" xml:space="preserve">Eſt autem quadrato C F æquale rectan-
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            gulum G C R, hoc eſt rectangulum ſub G C, R B, quia
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            proportionales ſunt C R, C F, C G. </s>
            <s xml:id="echoid-s1622" xml:space="preserve">Itaque major erit ra-
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            tio cubi R B ad cubum S, quam rectanguli R B G ad re-
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            ctangulum ſub G C, R B, hoc eſt, quam B G ad G C.
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            </s>
            <s xml:id="echoid-s1623" xml:space="preserve">Sicut autem B G ad G C, ita R C ad E K. </s>
            <s xml:id="echoid-s1624" xml:space="preserve">Quia enim
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            eſt C R ad C G, ut quadratum C R ad quadratum C F ſeu
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            quadratum C E: </s>
            <s xml:id="echoid-s1625" xml:space="preserve">ut autem quadratum C R ad quadratum
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            C E, ita eſt P R ad P E diametrum: </s>
            <s xml:id="echoid-s1626" xml:space="preserve">Erit idcirco C R ad
              <lb/>
            C G, ut P R ad P E. </s>
            <s xml:id="echoid-s1627" xml:space="preserve">Unde dupla C R, hoc eſt, C B ad
              <lb/>
            C G, ut dupla P R ad P E, hoc eſt, ut P R ad P A. </s>
            <s xml:id="echoid-s1628" xml:space="preserve">Et
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            dividendo, B G ad G C, ut R A ad A P, ſeu A E, hoc
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            eſt, ut R C ad E K, quod dicebamus. </s>
            <s xml:id="echoid-s1629" xml:space="preserve">Itaque major quo-
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            que ratio cubi R B ad cubum S, hoc eſt, ratio </s>
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