Vitruvius; Philandrier, Guillaume, Gvlielmi Philandri Castilionii ... In decem libros M. Vitruuii Pollionis de architectura annotationes, 1544

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        <div xml:id="echoid-div121" type="section" level="1" n="92">
          <p style="it">
            <s xml:id="echoid-s9748" xml:space="preserve">
              <pb o="303" file="0321" n="321" rhead="IN LIB. IX."/>
            &</s>
            <s xml:id="echoid-s9749" xml:space="preserve">. pn. </s>
            <s xml:id="echoid-s9750" xml:space="preserve">triangula. </s>
            <s xml:id="echoid-s9751" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9752" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9753" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9754" xml:space="preserve">&</s>
            <s xml:id="echoid-s9755" xml:space="preserve">. p. </s>
            <s xml:id="echoid-s9756" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9757" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9758" xml:space="preserve">erunt per. </s>
            <s xml:id="echoid-s9759" xml:space="preserve">6. </s>
            <s xml:id="echoid-s9760" xml:space="preserve">&</s>
            <s xml:id="echoid-s9761" xml:space="preserve">. 4.
              <lb/>
            </s>
            <s xml:id="echoid-s9762" xml:space="preserve">ſexti ſimilia & </s>
            <s xml:id="echoid-s9763" xml:space="preserve">proportionalia, quum ſint anguli ad. </s>
            <s xml:id="echoid-s9764" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9765" xml:space="preserve">re-
              <lb/>
            cti & </s>
            <s xml:id="echoid-s9766" xml:space="preserve">circum eos later a proportionalia. </s>
            <s xml:id="echoid-s9767" xml:space="preserve">Sed quoniam an-
              <lb/>
            gulis. </s>
            <s xml:id="echoid-s9768" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9769" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9770" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9771" xml:space="preserve">&</s>
            <s xml:id="echoid-s9772" xml:space="preserve">. c. </s>
            <s xml:id="echoid-s9773" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9774" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9775" xml:space="preserve">ſubtenduntur proportionalia la-
              <lb/>
            tera. </s>
            <s xml:id="echoid-s9776" xml:space="preserve">erunt per. </s>
            <s xml:id="echoid-s9777" xml:space="preserve">6. </s>
            <s xml:id="echoid-s9778" xml:space="preserve">ſexti anguli æquales. </s>
            <s xml:id="echoid-s9779" xml:space="preserve">& </s>
            <s xml:id="echoid-s9780" xml:space="preserve">per eandem,
              <lb/>
            angulus, m. </s>
            <s xml:id="echoid-s9781" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9782" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9783" xml:space="preserve">angulo. </s>
            <s xml:id="echoid-s9784" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9785" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9786" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9787" xml:space="preserve">etiam æqualis, erit per
              <lb/>
            32. </s>
            <s xml:id="echoid-s9788" xml:space="preserve">primi & </s>
            <s xml:id="echoid-s9789" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9790" xml:space="preserve">communem ſententiam, angulus. </s>
            <s xml:id="echoid-s9791" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9792" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9793" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9794" xml:space="preserve">
              <lb/>
            rectus, & </s>
            <s xml:id="echoid-s9795" xml:space="preserve">triangula. </s>
            <s xml:id="echoid-s9796" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9797" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9798" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9799" xml:space="preserve">&</s>
            <s xml:id="echoid-s9800" xml:space="preserve">. n. </s>
            <s xml:id="echoid-s9801" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9802" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9803" xml:space="preserve">&</s>
            <s xml:id="echoid-s9804" xml:space="preserve">. m. </s>
            <s xml:id="echoid-s9805" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9806" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9807" xml:space="preserve">ad inui-
              <lb/>
            cem ſimilia. </s>
            <s xml:id="echoid-s9808" xml:space="preserve">Et rurſus quoniá angulus. </s>
            <s xml:id="echoid-s9809" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9810" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9811" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9812" xml:space="preserve">rectus est
              <lb/>
            per hypotheſim, at it a angulo. </s>
            <s xml:id="echoid-s9813" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9814" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9815" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9816" xml:space="preserve">æqualis, et angulus
              <lb/>
            n. </s>
            <s xml:id="echoid-s9817" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9818" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9819" xml:space="preserve">communis eſt. </s>
            <s xml:id="echoid-s9820" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9821" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9822" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9823" xml:space="preserve">&</s>
            <s xml:id="echoid-s9824" xml:space="preserve">. m. </s>
            <s xml:id="echoid-s9825" xml:space="preserve">p. </s>
            <s xml:id="echoid-s9826" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9827" xml:space="preserve">triangulis, erunt
              <lb/>
            etiam ea triangula per eaſdem æquiangula, ac omnino ſi-
              <lb/>
            milia, necnon & </s>
            <s xml:id="echoid-s9828" xml:space="preserve">triangulum. </s>
            <s xml:id="echoid-s9829" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9830" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9831" xml:space="preserve">b. </s>
            <s xml:id="echoid-s9832" xml:space="preserve">eiſidem ſimile, quun@
              <lb/>
            ſit angulus. </s>
            <s xml:id="echoid-s9833" xml:space="preserve">b. </s>
            <s xml:id="echoid-s9834" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9835" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9836" xml:space="preserve">per. </s>
            <s xml:id="echoid-s9837" xml:space="preserve">31. </s>
            <s xml:id="echoid-s9838" xml:space="preserve">tertii, etiam rectus. </s>
            <s xml:id="echoid-s9839" xml:space="preserve">Erit igi-
              <lb/>
            tur ſicut. </s>
            <s xml:id="echoid-s9840" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9841" xml:space="preserve">b. </s>
            <s xml:id="echoid-s9842" xml:space="preserve">ad. </s>
            <s xml:id="echoid-s9843" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9844" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9845" xml:space="preserve">later a trianguli. </s>
            <s xml:id="echoid-s9846" xml:space="preserve">b. </s>
            <s xml:id="echoid-s9847" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9848" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9849" xml:space="preserve">circũ angu-
              <lb/>
            lum. </s>
            <s xml:id="echoid-s9850" xml:space="preserve">b. </s>
            <s xml:id="echoid-s9851" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9852" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9853" xml:space="preserve">ſic per. </s>
            <s xml:id="echoid-s9854" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9855" xml:space="preserve">ſexti. </s>
            <s xml:id="echoid-s9856" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9857" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9858" xml:space="preserve">ad. </s>
            <s xml:id="echoid-s9859" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9860" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9861" xml:space="preserve">quæ circa ſimi-
              <lb/>
            lem immo eundem. </s>
            <s xml:id="echoid-s9862" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9863" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9864" xml:space="preserve">. K. </s>
            <s xml:id="echoid-s9865" xml:space="preserve">angulum trianguli. </s>
            <s xml:id="echoid-s9866" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9867" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9868" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9869" xml:space="preserve">po-
              <lb/>
            ſita ſunt & </s>
            <s xml:id="echoid-s9870" xml:space="preserve">æquis angulis in ſimili triágulo ſimiliter ſub-
              <lb/>
            tenduntur, & </s>
            <s xml:id="echoid-s9871" xml:space="preserve">per eandem eodem modo ſicut. </s>
            <s xml:id="echoid-s9872" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9873" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9874" xml:space="preserve">ad. </s>
            <s xml:id="echoid-s9875" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9876" xml:space="preserve">
              <lb/>
            n. </s>
            <s xml:id="echoid-s9877" xml:space="preserve">ſic. </s>
            <s xml:id="echoid-s9878" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9879" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9880" xml:space="preserve">ad. </s>
            <s xml:id="echoid-s9881" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9882" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9883" xml:space="preserve">later a trianguli. </s>
            <s xml:id="echoid-s9884" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9885" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9886" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9887" xml:space="preserve">circum angu-
              <lb/>
            lum. </s>
            <s xml:id="echoid-s9888" xml:space="preserve">n. </s>
            <s xml:id="echoid-s9889" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9890" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9891" xml:space="preserve">Sed manifeſtum eſt. </s>
            <s xml:id="echoid-s9892" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9893" xml:space="preserve">m. </s>
            <s xml:id="echoid-s9894" xml:space="preserve">eſſe æqualem. </s>
            <s xml:id="echoid-s9895" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9896" xml:space="preserve">
              <lb/>
            d. </s>
            <s xml:id="echoid-s9897" xml:space="preserve">quum neceſſe ſit. </s>
            <s xml:id="echoid-s9898" xml:space="preserve">d. </s>
            <s xml:id="echoid-s9899" xml:space="preserve">&</s>
            <s xml:id="echoid-s9900" xml:space="preserve">. m. </s>
            <s xml:id="echoid-s9901" xml:space="preserve">ſigna a. </s>
            <s xml:id="echoid-s9902" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9903" xml:space="preserve">coni fastigio æqua-
              <lb/>
            liter diſtare eo quod in circulo ab vno & </s>
            <s xml:id="echoid-s9904" xml:space="preserve">eodem ſigno in
              <lb/>
            coni ſu perficie circũſcripto poſita ſunt, inter. </s>
            <s xml:id="echoid-s9905" xml:space="preserve">b. </s>
            <s xml:id="echoid-s9906" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9907" xml:space="preserve">igitur
              <lb/>
            &</s>
            <s xml:id="echoid-s9908" xml:space="preserve">. c. </s>
            <s xml:id="echoid-s9909" xml:space="preserve">d. </s>
            <s xml:id="echoid-s9910" xml:space="preserve">inuenta erũt duo media proportionalia. </s>
            <s xml:id="echoid-s9911" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9912" xml:space="preserve">K. </s>
            <s xml:id="echoid-s9913" xml:space="preserve">&</s>
            <s xml:id="echoid-s9914" xml:space="preserve">. c. </s>
            <s xml:id="echoid-s9915" xml:space="preserve">
              <lb/>
            n. </s>
            <s xml:id="echoid-s9916" xml:space="preserve">quod fuer at ostendendũ. </s>
            <s xml:id="echoid-s9917" xml:space="preserve">Cæterum quoniam problema
              <lb/>
            non theorema istud eſt, non alienũ erit explicare quo pa-
              <lb/>
            cto istiuſmodi media per hanc ipſam ratiocinationem non
              <lb/>
            tam intelligi quam re ipſa inueniri queant, at inuentis
              <lb/>
            quomodo vti poſſimus, & </s>
            <s xml:id="echoid-s9918" xml:space="preserve">ſi hoc Eratoſthenes neget, </s>
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