Archimedes, Archimedis De insidentibvs aqvae

Table of handwritten notes

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              <pb o="11" file="0037" n="37" rhead="_LIBER II._"/>
            portionem compoſitam ex proportione quam habet quæ i, l, ad l, a, & </s>
            <s xml:id="echoid-s614" xml:space="preserve">
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            quam habet quæ a, d, ad d, i, habet autem, & </s>
            <s xml:id="echoid-s615" xml:space="preserve">quæ l, i, ad l, a, quàm duo
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            ad quinque. </s>
            <s xml:id="echoid-s616" xml:space="preserve">Quæ enim c, b, ad b, d, habet proportionem, quàm ſex ad
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            quindecim, hoc eſt, quam duo ad quinque, & </s>
            <s xml:id="echoid-s617" xml:space="preserve">est ut quæ c, b, ad b, d, ita
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            quæ e, b, ad b, a, & </s>
            <s xml:id="echoid-s618" xml:space="preserve">quæ d, Z ad d, a, habeat autem d, Z, d, a, duplæ.</s>
            <s xml:id="echoid-s619" xml:space="preserve"/>
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            <s xml:id="echoid-s620" xml:space="preserve">l, i, l, a. </s>
            <s xml:id="echoid-s621" xml:space="preserve">Quæ autem a, d, ad d, i, proportionem habet, quam quinque
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            ad vnum. </s>
            <s xml:id="echoid-s622" xml:space="preserve">Proportio autem compoſita ex proportione, quam habẽt duo
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            ad quinque, & </s>
            <s xml:id="echoid-s623" xml:space="preserve">ex proportione, quam habent quinque ad vnum. </s>
            <s xml:id="echoid-s624" xml:space="preserve">eſt ean
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            dem cum proportione, quam habent duo ad vnum. </s>
            <s xml:id="echoid-s625" xml:space="preserve">Dupla ergo eſt, quæ
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            g, o, ipſius g, x, propter eandem autem, & </s>
            <s xml:id="echoid-s626" xml:space="preserve">quæ p, y, ipſius y, f, quoniam
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            igitur. </s>
            <s xml:id="echoid-s627" xml:space="preserve">quæ d, s, eſt hemiolia ipſius K, r, palam quòd quæ b, s, eſt exceſ
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            ſus, quo axis est maior, quàm hemiolius eius, quæ uſque ad axem, ſiqui-
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            dem igitur portio ad humidum in grauitate banc habet proportionem,
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            quam tetragonum, quod a, b, s, ad id, quod a, b, d, aut maiorem hac pro-
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            portione portio demiſſa in humidum ita, ut baſis ipſius non tangat humi
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            dum recta conſistet, demonſtratum est ei prius, quòd ſi portio habẽs ax ẽ
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            maiorem, quàm hemiolium eius, quæ uſque ad axem minorem propor-
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            tione ſi ad humidum in grauitate n, o, minorem proportionẽ habeat pro-
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            portione, quam habet tetragonum, quod ab exceßu, quo axis eſt maior,
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            quàm hemiolium eius, quæ ad axem ad tetragonum, quod ab axe. </s>
            <s xml:id="echoid-s628" xml:space="preserve">demiſ
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            ſa in humidum, ita ut dictum eſt, recta conſistet. </s>
            <s xml:id="echoid-s629" xml:space="preserve">Si autem portio ad hu-
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            midum in grauitate maiorem quidem proportionem habeat proportione
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            quàm habet tetragonum, quod a, b, s, b, ad tetragonum, quod a, b, d, ma-
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            iorem autem proportionem, quam habet tetragonum quod a, b, x, t, ad
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            id, quod a, b, demiſſain humidum inclinata ita, ut baſis contingat humi-
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            dum conſistet inclinata ita, ut baſis ipſius nibil tangat ſuperficiei humi-
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            di, & </s>
            <s xml:id="echoid-s630" xml:space="preserve">axis ipſius faciat ad ſuperficiem humidi angulum maiorem angu
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            lo m. </s>
            <s xml:id="echoid-s631" xml:space="preserve">Si autem portio ad humidum in grauitate hanc habet proportionẽ.
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            </s>
            <s xml:id="echoid-s632" xml:space="preserve">
              <figure xlink:label="fig-0037-01" xlink:href="fig-0037-01a" number="29">
                <image file="0037-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0037-01"/>
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