Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div703" type="section" level="2" n="131">
            <pb o="268" file="514.01.300" n="300" rhead="LIBER"/>
            <p style="it">
              <s xml:id="echoid-s20047" xml:space="preserve">Quis igitur cum excellentibus illis uiris athletas uel fortiſſimos, & </s>
              <s xml:id="echoid-s20048" xml:space="preserve">gladiatores comparabit ? </s>
              <s xml:id="echoid-s20049" xml:space="preserve">qui eos
                <lb/>
              cum ijs conferet, qui memorabili beneficio præſente uictoria ſibi aliquas gentes deuinxerit? </s>
              <s xml:id="echoid-s20050" xml:space="preserve">Merito igitur
                <lb/>
              cum Vitruuio adiudicabimus diuinos honores his, qui pulchra, & </s>
              <s xml:id="echoid-s20051" xml:space="preserve">honeſta inuenta reliquere, potius quàm
                <lb/>
              Græcis illis, qui robore corpore floruere, & </s>
              <s xml:id="echoid-s20052" xml:space="preserve">præſentes uires in certaminibus Dijs dedicatis oſtendere, cedant
                <lb/>
              Olympij uictorès, nec glorietur Iuppiter. </s>
              <s xml:id="echoid-s20053" xml:space="preserve">cedant Pithij, nec glorietur Thebas. </s>
              <s xml:id="echoid-s20054" xml:space="preserve">cedant Nemei, nec glorietur
                <lb/>
              Archintorus. </s>
              <s xml:id="echoid-s20055" xml:space="preserve">cedant Iſthmij, nec glorietur Palamon, nam Minerua omnes illos deos hæroesq́;</s>
              <s xml:id="echoid-s20056" xml:space="preserve">. in quorum ho-
                <lb/>
              norem ludi eiuſmodi celebrati ſunt, gloria antecellit, cum rerum inuentores cum illis certatoribus compara-
                <lb/>
              tos uiderit. </s>
              <s xml:id="echoid-s20057" xml:space="preserve">Sed nos ad inuenta, & </s>
              <s xml:id="echoid-s20058" xml:space="preserve">rationes præclariſſimorum hominum eorum, qui bene uiuendi inſtituta, & </s>
              <s xml:id="echoid-s20059" xml:space="preserve">
                <lb/>
              doctrinarum præcepta posteris reliquere; </s>
              <s xml:id="echoid-s20060" xml:space="preserve">nam ſi in ſaltu, & </s>
              <s xml:id="echoid-s20061" xml:space="preserve">curſu agilitas requiritur, quid agilius, quid ue-
                <lb/>
                <note position="left" xlink:label="note-514.01.300-01" xlink:href="note-514.01.300-01a" xml:space="preserve">10</note>
              locius animo erudito, & </s>
              <s xml:id="echoid-s20062" xml:space="preserve">in rerum contemplationeuerſato? </s>
              <s xml:id="echoid-s20063" xml:space="preserve">qui terrena, & </s>
              <s xml:id="echoid-s20064" xml:space="preserve">cœlestia quaſi uolando percurrat ?
                <lb/>
              </s>
              <s xml:id="echoid-s20065" xml:space="preserve">Si in diſco, & </s>
              <s xml:id="echoid-s20066" xml:space="preserve">iaculo quis glorietur, quid aget mens eius, qui humana omnia impedimenta proiecerit, & </s>
              <s xml:id="echoid-s20067" xml:space="preserve">ſub-
                <lb/>
              uerterit ? </s>
              <s xml:id="echoid-s20068" xml:space="preserve">Si lucta robur, & </s>
              <s xml:id="echoid-s20069" xml:space="preserve">uires quærit, quid ſapiens faciet, qui cum fortuna continenter luctando, uires
                <lb/>
              eius infringit, & </s>
              <s xml:id="echoid-s20070" xml:space="preserve">uirtute ictus repellit, & </s>
              <s xml:id="echoid-s20071" xml:space="preserve">dexteritate inſultus deijcit, ac proſternit ? </s>
              <s xml:id="echoid-s20072" xml:space="preserve">Non oleaster, non po-
                <lb/>
              ma, non pinus, non apium præmia ſunt bonorum, & </s>
              <s xml:id="echoid-s20073" xml:space="preserve">doctorum hominum, non publicum alimentum, non eorum
                <lb/>
              aduentu murorum proiectio. </s>
              <s xml:id="echoid-s20074" xml:space="preserve">nullum enim par præmium uirtutis habetur in terris: </s>
              <s xml:id="echoid-s20075" xml:space="preserve">Sed cœlum, ſplendor, glo-
                <lb/>
              ria, felicitas eos perpetuo manet.</s>
              <s xml:id="echoid-s20076" xml:space="preserve"/>
            </p>
          </div>
          <div xml:id="echoid-div707" type="section" level="2" n="132">
            <head xml:id="echoid-head140" xml:space="preserve">Platonis inuentumde agro metiendo. Cap. I.</head>
            <note position="left" xml:space="preserve">20</note>
            <p>
              <s xml:id="echoid-s20077" xml:space="preserve">
                <emph style="sc">LOcvs</emph>
              , aut ager patibus lateribus, ſi erit quadratus, eumq́; </s>
              <s xml:id="echoid-s20078" xml:space="preserve">oportuetit iterum ex paribus
                <lb/>
              lateribus duplicare, quia id genere numeri, ac multiplicationibus non inuenitur, ex de-
                <lb/>
              ſcriptionibus linearum emendatis reperitur. </s>
              <s xml:id="echoid-s20079" xml:space="preserve">Eſt autem eius rei hæc demonſtratio.
                <lb/>
              </s>
              <s xml:id="echoid-s20080" xml:space="preserve">Quadratus locus, qui erit longus, & </s>
              <s xml:id="echoid-s20081" xml:space="preserve">latus pedes denos, efficit areæ pedes centum. </s>
              <s xml:id="echoid-s20082" xml:space="preserve">Si
                <lb/>
              ergo opus fuerit eum duplicare, & </s>
              <s xml:id="echoid-s20083" xml:space="preserve">aream pedum ducentorum item ex paribus lateribus facere, quæ-
                <lb/>
              rendum erit quàm magnum latus eius quadratifiat, ut ex eo ducenti pedes duplicationibus areæ re-
                <lb/>
              ſpondeant. </s>
              <s xml:id="echoid-s20084" xml:space="preserve">Idautem numero nemo poteſt inuenire; </s>
              <s xml:id="echoid-s20085" xml:space="preserve">nanque ſi 14. </s>
              <s xml:id="echoid-s20086" xml:space="preserve">conſtituentur, erunt multipli-
                <lb/>
              catipedes 196. </s>
              <s xml:id="echoid-s20087" xml:space="preserve">ſi quindecim, pedes 125. </s>
              <s xml:id="echoid-s20088" xml:space="preserve">Ergo quoniam id non explicatur numero in eo quadra-
                <lb/>
              to longo, & </s>
              <s xml:id="echoid-s20089" xml:space="preserve">lato pedes decem, quæ fuerit, linea ab angulo ad angulum diagonios perducatur, uti
                <lb/>
              diuidatur in duo trigona æqua magnitudine, ſingula areæ pedum quinquagenum, ad eius lineæ dia-
                <lb/>
                <note position="left" xlink:label="note-514.01.300-03" xlink:href="note-514.01.300-03a" xml:space="preserve">30</note>
              gonalis longitudinem, locus quadratus paribus lateribus deſcribatur. </s>
              <s xml:id="echoid-s20090" xml:space="preserve">Ita quam magna duo trigona,
                <lb/>
              in minore quadrato quinquagenum pedum linea diagonica fuerint deſignata, eadem magnitudine, & </s>
              <s xml:id="echoid-s20091" xml:space="preserve">
                <lb/>
              codem pedum numero, quaturo in maiore erunt effecta, Hac ratione duplicatio grammicis ratio-
                <lb/>
              nibus a Platone, uti eſt ſchema ſubſcriptum, fuit explicata.</s>
              <s xml:id="echoid-s20092" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s20093" xml:space="preserve">Quadratum menſuratur duorum laterum inter ſe multiplicatione facta. </s>
              <s xml:id="echoid-s20094" xml:space="preserve">Duplicatur quadratum ſumpta
                <lb/>
              eius diagonia linea pro latere quadrati, quod duplex faciendum erit. </s>
              <s xml:id="echoid-s20095" xml:space="preserve">Diagonia hoc modo inuenitur, duo
                <lb/>
              latera quadrati per ſe ſingula in ſe ipſa uertendo multiplica, ſummam collige ipſius multiplicationis, & </s>
              <s xml:id="echoid-s20096" xml:space="preserve">eius
                <lb/>
              ſummæ quadratam radicem quærito, tanta erit diagonia. </s>
              <s xml:id="echoid-s20097" xml:space="preserve">Sit quadratum a, b, c, d, in ſingulis lateri-
                <lb/>
              bus pedes quinque, duc unius lateris puinque in ſe reddentur 25. </s>
              <s xml:id="echoid-s20098" xml:space="preserve">& </s>
              <s xml:id="echoid-s20099" xml:space="preserve">iterum alterius lateris quinque in ſe du-
                <lb/>
              cito reddentur 25. </s>
              <s xml:id="echoid-s20100" xml:space="preserve">hæc collecta cum prioribus 25. </s>
              <s xml:id="echoid-s20101" xml:space="preserve">ſummam efficient quinquaginta, quorum quadratara-
                <lb/>
                <note position="left" xlink:label="note-514.01.300-04" xlink:href="note-514.01.300-04a" xml:space="preserve">40</note>
              dix est ped. </s>
              <s xml:id="echoid-s20102" xml:space="preserve">7. </s>
              <s xml:id="echoid-s20103" xml:space="preserve">& </s>
              <s xml:id="echoid-s20104" xml:space="preserve">unius quartæ, eadem ratio in alijs rectangulis quadratis inuenitur, ut in oblongo quadrato
                <lb/>
              e, f, g, h, latus, e, g, pedum octo, ducti in ſe efficiunt 64. </s>
              <s xml:id="echoid-s20105" xml:space="preserve">latus e, f, pedes ſex. </s>
              <s xml:id="echoid-s20106" xml:space="preserve">hi @ducti in ſe red-
                <lb/>
              dunt 36. </s>
              <s xml:id="echoid-s20107" xml:space="preserve">qui cum 64. </s>
              <s xml:id="echoid-s20108" xml:space="preserve">collecti efficiunt centum, quorum radix quadrata ſunt decem, tanta igitur eſt dia-
                <lb/>
              gonios, & </s>
              <s xml:id="echoid-s20109" xml:space="preserve">duplicis quadrati latus. </s>
              <s xml:id="echoid-s20110" xml:space="preserve">Exemplum ſchematis Vitr. </s>
              <s xml:id="echoid-s20111" xml:space="preserve">facile eſt. </s>
              <s xml:id="echoid-s20112" xml:space="preserve">nam quadratum, a, c, h, d, du-
                <lb/>
              plum eſt quadrato a, d, quoniam eius latus fit ex diagonali a, d, minoris quadrati, & </s>
              <s xml:id="echoid-s20113" xml:space="preserve">quod numeri ge-
                <lb/>
              nerenullo efficitur, id grammicis rationibus abſoluitur. </s>
              <s xml:id="echoid-s20114" xml:space="preserve">Vtiliſſima uero, & </s>
              <s xml:id="echoid-s20115" xml:space="preserve">huius reiratio in plurimis obſer-
                <lb/>
              uationibus quotidiani uſus, ut experientibus erit manifeſtum.</s>
              <s xml:id="echoid-s20116" xml:space="preserve"/>
            </p>
          </div>
          <div xml:id="echoid-div710" type="section" level="2" n="133">
            <note position="left" xml:space="preserve">50</note>
            <head xml:id="echoid-head141" style="it" xml:space="preserve">De norma Pythagoricum inuentum ex orthogonij trigoni
              <lb/>
            deformatione. Cap. II.</head>
            <p>
              <s xml:id="echoid-s20117" xml:space="preserve">
                <emph style="sc">ITem</emph>
              Pythagoras normam ſine artificis fabricationibusinuentam oſtendit, & </s>
              <s xml:id="echoid-s20118" xml:space="preserve">quàm ma-
                <lb/>
              gno labore fabri normam facientes uix ad uerum perducere poſſunt. </s>
              <s xml:id="echoid-s20119" xml:space="preserve">id rationibus, & </s>
              <s xml:id="echoid-s20120" xml:space="preserve">
                <lb/>
              methodis emendatum, ex eius præceptis explicatur. </s>
              <s xml:id="echoid-s20121" xml:space="preserve">Nanque ſi ſumantur regulæ tres, e
                <lb/>
              quibus una ſit pedes tres, altera pedes quatuor, tertia pedes quinque, eæq́; </s>
              <s xml:id="echoid-s20122" xml:space="preserve">regulæ inter
                <lb/>
              ſe compoſitæ tangat alia aliam ſuis cacuminibus extremis, ſchema habentes trigoni, deformabunt nor
                <lb/>
              mam emendatam. </s>
              <s xml:id="echoid-s20123" xml:space="preserve">Ad eas autem regularum ſingularum longitudines, ſi ſingula quadrata paribus
                <lb/>
              lateribus deſeribantur, quod erit pedum trium latus areæ, habebit pedes nouem, quod erit quatuor,
                <lb/>
              ſexdecim, quod quinque erit, uigintiquinque. </s>
              <s xml:id="echoid-s20124" xml:space="preserve">Ita quantum areæ pedum numerum duo quadrata, ex
                <lb/>
                <note position="left" xlink:label="note-514.01.300-06" xlink:href="note-514.01.300-06a" xml:space="preserve">60</note>
              </s>
            </p>
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