Vitruvius, M. Vitrvvivs Per Iocvndvm Solito Castigatior Factvs Cvm Figvris Et Tabvla Vt Iam Legi Et Intelligi Possit, 1511

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            <s xml:id="echoid-s3062" xml:space="preserve">
              <pb file="0176" n="176" rhead="LIBER"/>
            infinitas vtilitates æuo ꝑpetuo oibus gentibus p̃ſtant, Id enim magis erat
              <lb/>
            inſtitui dignũ, q athletæ ſua corpora exercitatiõibus efficiunt fortiora, ſcri
              <lb/>
            ptores non ſolũ ſuos ſenſus ꝑficiunt, Sed etiã oĩum, libris ad diſcendum, & </s>
            <s xml:id="echoid-s3063" xml:space="preserve">
              <lb/>
            aĩos exacuendos p̃parantes præcepta, Quid enim milo crotoniates, q fuit
              <lb/>
            inuictus prodeſt hominibus? </s>
            <s xml:id="echoid-s3064" xml:space="preserve">aut cæteri ꝗ eo genere fuerũt uictores, niſi q
              <lb/>
            dũ uixerũt ipſi inter ſuos ciues habuerũt nobilitatẽ, Pythagoræ uero præce
              <lb/>
            pta, Democriti, Platonis, Ariſtotelis, cæterorũ ſapiẽtum quotidiana ꝑpe-
              <lb/>
            tuis induſtriis culta, nõ ſolũ ſuis ciuibus, ſed etiã omnibus gẽtibus recentes
              <lb/>
            & </s>
            <s xml:id="echoid-s3065" xml:space="preserve">floridos edunt fructus, e quibus qui a teneris ætatibus doctrina℞ abũdã
              <lb/>
            tia ſatiant̃, optimos habent ſapiẽtiæ ſenſus, inſtituunt ciuitatibus huma-
              <lb/>
            nitatis mores, æqua iura, leges, quibus abſentibus, nulla põt eſſe ciuitas ĩ co
              <lb/>
            lumis, Cũ ergo tanta munera ab ſcripto ℞ prudẽtia priuatim publicæ fue
              <lb/>
            rint hominib{us} p̃parata, non ſolũ arbitror palmas & </s>
            <s xml:id="echoid-s3066" xml:space="preserve">coronas his tribui opor
              <lb/>
            tere, ſed etiã decerni triumphos, & </s>
            <s xml:id="echoid-s3067" xml:space="preserve">inter deo℞ ſedes eos dedicandos, iudica
              <lb/>
            ri, Eo℞ aũt cogitata vtiliter hominibus ad vitã explicandã, e pluribus ſin-
              <lb/>
            gula pauco℞ vti exẽpla ponã, quæ recognoſcẽtes neceſſario his tribui ho-
              <lb/>
            nores oportere hoĩes confitebuntur, & </s>
            <s xml:id="echoid-s3068" xml:space="preserve">primũ platonis e multis rõcinatio-
              <lb/>
            nibus utiliſſimis unã quẽadmodũ ab eo explicata ſit, ponam.</s>
            <s xml:id="echoid-s3069" xml:space="preserve"/>
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        <div xml:id="echoid-div100" type="section" level="1" n="76">
          <head xml:id="echoid-head75" xml:space="preserve">Platonis inuentum de agro metiendo. # Caput. I.</head>
          <p>
            <s xml:id="echoid-s3070" xml:space="preserve">Locus aut ager paribus lateribus ſi erit quadratus, eũ oportuerit iterum ex
              <lb/>
            paribus lateribus duplicare, quia id genere numeri ac multiplicationibus
              <lb/>
            non inuenitur, eo deſcriptionibus linea℞ emendatis reperitur, Eſt aũt eius
              <lb/>
            rei hæc demõſtratio. </s>
            <s xml:id="echoid-s3071" xml:space="preserve">Quadratus locus qui erit longus & </s>
            <s xml:id="echoid-s3072" xml:space="preserve">latus pedes denos
              <lb/>
            efficit areæ pedes centũ, Si ergo opus fuerit eum duplicare, & </s>
            <s xml:id="echoid-s3073" xml:space="preserve">areã pedũ du
              <lb/>
            centorum item ex paribus lateribus facere, quærendum erit ꝗ̃ magnum la-
              <lb/>
            tus eius quadrati fiat, ut ex eo ducenti pedes duplicationibus areæ reſpon-
              <lb/>
            deant, Id autem numero nemo poteſt inuenire, nan ſi.</s>
            <s xml:id="echoid-s3074" xml:space="preserve">xiiii. </s>
            <s xml:id="echoid-s3075" xml:space="preserve">conſtituentur
              <lb/>
            erunt multiplicati pedes, cxcvi. </s>
            <s xml:id="echoid-s3076" xml:space="preserve">Si. </s>
            <s xml:id="echoid-s3077" xml:space="preserve">
              <emph style="sc">XV</emph>
            . </s>
            <s xml:id="echoid-s3078" xml:space="preserve">pedes. </s>
            <s xml:id="echoid-s3079" xml:space="preserve">
              <emph style="sc">CCXXV</emph>
            . </s>
            <s xml:id="echoid-s3080" xml:space="preserve">Ergo quoniã id nõ ex
              <lb/>
            plicatur numero in eo quadrato longo & </s>
            <s xml:id="echoid-s3081" xml:space="preserve">lato pedes decẽ, quæ fuerit linea
              <lb/>
            ab angulo ad angulum diagonios perducatur, vti diuidatur in duo trigo-
              <lb/>
            na æqua magnitudine, ſingula areæ pedum quinquagenum, ad eius lineæ
              <lb/>
            diagonalis longitudinem locus quadratus paribus lateribus deſcribatur,
              <lb/>
            Ita ꝗ̃ magna duo trigona in minore quadrato quinquagenum pedum li-
              <lb/>
            nea diagonia fuerint deſignata, eadem magnitudine, & </s>
            <s xml:id="echoid-s3082" xml:space="preserve">eodem pedum nu-
              <lb/>
            mero quatuor in maiore erũt effecta, Hac ratiõe duplicatio grammicis ra-
              <lb/>
            tionibus a Platone uti eſt ſchema ſubſcriptum, fuit explicata.</s>
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