Vitruvius, M. Vitruvii ... de architectura libri decem, ad Augustum Caesarem accuratiß conscripti: & nunc primum in Germania qua potuit diligentia excusi, atq[ue] hinc inde schematibus non iniucundis exornati

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          <pb o="206" file="0260" n="260" rhead="M. VITRVVII"/>
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        <div xml:id="echoid-div235" type="section" level="1" n="181">
          <head xml:id="echoid-head185" xml:space="preserve">PLATONIS INVENTVM DE AGRO
            <lb/>
          metiendo. CAPTT I.</head>
          <p style="it">
            <s xml:id="echoid-s4222" xml:space="preserve">LOCVS aut ager paribus lateribus, ſi erit quadratus, eumque
              <lb/>
            oportuerit iterum ex paribus lateribus duplicare, quia id genere
              <lb/>
            numeri, ac multiplicationibus non inuenitur, ex deſcriptionibus linearum
              <lb/>
            emendatis reperitur. </s>
            <s xml:id="echoid-s4223" xml:space="preserve">Est autem eius reihæc demonſtratio. </s>
            <s xml:id="echoid-s4224" xml:space="preserve">Quadratus
              <lb/>
            locus, quierit longus & </s>
            <s xml:id="echoid-s4225" xml:space="preserve">latus pedes denos, efficit areæ pedes centum. </s>
            <s xml:id="echoid-s4226" xml:space="preserve">Si
              <lb/>
            ergo opus fuerit eum duplicare, & </s>
            <s xml:id="echoid-s4227" xml:space="preserve">areampedum ducentorum item ex
              <lb/>
            paribus lateribus facere: </s>
            <s xml:id="echoid-s4228" xml:space="preserve">quærendum erit, quàm magnum latus eius qua-
              <lb/>
            drati fiat, ut exeo ducenti pedes duplicationibus areæ reſpondeant. </s>
            <s xml:id="echoid-s4229" xml:space="preserve">Id au
              <lb/>
            tem numero nemo poteſt inuenire: </s>
            <s xml:id="echoid-s4230" xml:space="preserve">nã ſi.</s>
            <s xml:id="echoid-s4231" xml:space="preserve">xiiij. </s>
            <s xml:id="echoid-s4232" xml:space="preserve">conſtituentur, erunt mul
              <lb/>
            tiplicatipedes. </s>
            <s xml:id="echoid-s4233" xml:space="preserve">cxcvi.</s>
            <s xml:id="echoid-s4234" xml:space="preserve">Si.</s>
            <s xml:id="echoid-s4235" xml:space="preserve">xv.</s>
            <s xml:id="echoid-s4236" xml:space="preserve">pedes.</s>
            <s xml:id="echoid-s4237" xml:space="preserve">ccxxv. </s>
            <s xml:id="echoid-s4238" xml:space="preserve">Ergo quoniam id non expli-
              <lb/>
            catur numero ineo quadrato lõgo & </s>
            <s xml:id="echoid-s4239" xml:space="preserve">lato pedes decem, quæ fuerit, linea
              <lb/>
            ab angulo ad angulum diagonios perducatur, uti diuidatur in duo trigo-
              <lb/>
            na æqua magnitudine, ſingula areæ pedum quinquagenum, ad eius lineæ
              <lb/>
            diagonalis longitudinem, locus quadratus paribus lateribus deſcribatur.
              <lb/>
            </s>
            <s xml:id="echoid-s4240" xml:space="preserve">Ita quàm magna duo trigona, in minore quadrato quinquagenũ pedum,
              <lb/>
            linea diagonica fuerint deſignata, eadem magnitudine & </s>
            <s xml:id="echoid-s4241" xml:space="preserve">codem pedum
              <lb/>
            numero quatuor in maiore erunt effecta. </s>
            <s xml:id="echoid-s4242" xml:space="preserve">Hac ratione duplicatio gram-
              <lb/>
            micis rationibus à Platonc, uti eſt ſchema ſubſcriptum, fuit explic ata.</s>
            <s xml:id="echoid-s4243" xml:space="preserve"/>
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          <figure number="76">
            <image file="0260-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0260-01"/>
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