Vitruvius, Marci Vitruvii Pollionis De architectura libri decem : ope codicis Guelferbytani, editionis principis, ceterorumque subsidiorum recensuit, et glossario in quo vocabula artis propria Germ. Ital. Gall. et Angl. explicantur, 1800

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        <div xml:id="echoid-div178" type="section" level="1" n="96">
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            <s xml:id="echoid-s3605" xml:space="preserve">
              <pb o="203" file="0227" n="227" rhead="LIBER IX. (CAPUT I.)"/>
            erit longus et latus pedes denos, efficit areae pedes centum. </s>
            <s xml:id="echoid-s3606" xml:space="preserve">Si ergo
              <lb/>
            opus fuerit eum duplicare, et aream pedum ducentorum item ex paribus
              <lb/>
            lateribus facere, quaerendum erit, quam magnum latus ejus quadrati fiat,
              <lb/>
            ut ex eo ducenti pedes duplicationibus areae reſpondeant. </s>
            <s xml:id="echoid-s3607" xml:space="preserve">Id autem nu-
              <lb/>
            mero nemo poteſt invenire: </s>
            <s xml:id="echoid-s3608" xml:space="preserve">namque ſi XIIII. </s>
            <s xml:id="echoid-s3609" xml:space="preserve">conſtituentur, erunt multi-
              <lb/>
            plicati pedes CXCVI. </s>
            <s xml:id="echoid-s3610" xml:space="preserve">Si XV pedes CCXXV. </s>
            <s xml:id="echoid-s3611" xml:space="preserve">Ergo quoniam id non ex-
              <lb/>
            plicatur numero in eo quadrato longo et lato pedes decem (a b c d), quae
              <lb/>
            fuerit linea ab angulo (b) ad angulum (d) diagonios (b d) perducatur, uti
              <lb/>
            dividatur in duo trigona aequa magnitudine (b a d et b c d), ſingula areae pedum quinquagenum: </s>
            <s xml:id="echoid-s3612" xml:space="preserve">ad ejus lineae diagonalis longitudinem locus
              <lb/>
            quadratus (b e f d) paribus lateribus deſcribatur. </s>
            <s xml:id="echoid-s3613" xml:space="preserve">Ita quam magna duo
              <lb/>
            trigona in minore quadrato quinquagenum pedum linea diagonia fuerint
              <lb/>
            deſignata, eadem magnitudine, et eodem pedum numero quaturo in ma-
              <lb/>
            jore erunt effecta. </s>
            <s xml:id="echoid-s3614" xml:space="preserve">Hac ratione duplicatio grammicis rationibus a Plato-
              <lb/>
            ne, uti eſt ſchema ſubſcriptum, fuit explicata.</s>
            <s xml:id="echoid-s3615" xml:space="preserve"/>
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        <div xml:id="echoid-div180" type="section" level="1" n="97">
          <head xml:id="echoid-head102" xml:space="preserve">(CAPUT II.)</head>
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            <s xml:id="echoid-s3616" xml:space="preserve">Item Pythagoras normam ſine artiſicis fabricationibus inventam oſtendit,
              <lb/>
            et quam magno labore fabri normam facientes vix ad verum perducere
              <lb/>
            poſſunt, id rationibus et methodis emendatum ex ejus praeceptis expli-
              <lb/>
            catur. </s>
            <s xml:id="echoid-s3617" xml:space="preserve">Namque ſi ſumantur regulae tres, e quibus una ſit pedes tres,
              <lb/>
            (A B) altera pedes quatuor, (A C) tertia pedes quinque (C B): </s>
            <s xml:id="echoid-s3618" xml:space="preserve">haeque regulae inter ſe compoſitae tangant alia aliam ſuis cacuminibus extremis,
              <lb/>
            ſchema habentes trigoni (A B C), deformabunt normam emendatam. </s>
            <s xml:id="echoid-s3619" xml:space="preserve">Ad
              <lb/>
            eas autem regularum ſingularum longitudines, ſi ſingula quadrata paribus
              <lb/>
            lateribus deſcribantur, quod erit pedum trium latus, (A B D E) areae ha-
              <lb/>
            bebit pedes novem: </s>
            <s xml:id="echoid-s3620" xml:space="preserve">quod erit quatuor (A C F G), ſexdecim: </s>
            <s xml:id="echoid-s3621" xml:space="preserve">quod quin-
              <lb/>
              <note symbol="*)" position="foot" xlink:label="note-0227-01" xlink:href="note-0227-01a" xml:space="preserve">Forma I.</note>
              <note symbol="**)" position="foot" xlink:label="note-0227-02" xlink:href="note-0227-02a" xml:space="preserve">Forma II.</note>
            </s>
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