Clavius, Christoph, Geometria practica

Table of handwritten notes

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          <pb o="266" file="296" n="296" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s12250" xml:space="preserve">
              <emph style="sc">Sit</emph>
            primò parallelo grammum A B C D, per rectam ex puncto E, exteriori
              <lb/>
            ductam ſecundum bifariam. </s>
            <s xml:id="echoid-s12251" xml:space="preserve">Ducta diametro B D, eaque ſecta bifariam in F,
              <lb/>
            ducatur ex E, per F, recta EH, quam dico parallelogrammum
              <lb/>
              <figure xlink:label="fig-296-01" xlink:href="fig-296-01a" number="201">
                <image file="296-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/296-01"/>
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            partiri bifariam. </s>
            <s xml:id="echoid-s12252" xml:space="preserve">Nam vt in ſcholio Propoſ. </s>
            <s xml:id="echoid-s12253" xml:space="preserve">34. </s>
            <s xml:id="echoid-s12254" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12255" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12256" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s12257" xml:space="preserve">de-
              <lb/>
            monſtrauimus, recta G H, diuidens diametrum B D, in F, bifa-
              <lb/>
            riam, ſecat parallelo grammum bifariam. </s>
            <s xml:id="echoid-s12258" xml:space="preserve">Idem fiet, ſi recta IK,
              <lb/>
            latera AD, BC, ſecans bifariam, diuidatur bifariam in F, & </s>
            <s xml:id="echoid-s12259" xml:space="preserve">per
              <lb/>
            F, extendatur recta E F, propterea quod I K, diametrum ſecat
              <lb/>
            bifariam, ac proinde per F, punctum medium diametritranſit.
              <lb/>
            </s>
            <s xml:id="echoid-s12260" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-296-01" xlink:href="note-296-01a" xml:space="preserve">29. primi.</note>
            Cum enim anguli IDF, F I D, angulis alternis KBF, FKB, æquales ſint, & </s>
            <s xml:id="echoid-s12261" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-296-02" xlink:href="note-296-02a" xml:space="preserve">26. primi.</note>
            I D, KB, quibus adiacent, æqualia; </s>
            <s xml:id="echoid-s12262" xml:space="preserve"> erunt tam latera D F, quam I
              <unsure/>
            F, K F, inter æqualia.</s>
            <s xml:id="echoid-s12263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12264" xml:space="preserve">
              <emph style="sc">Eodem</emph>
            modo ex puncto interioriL; </s>
            <s xml:id="echoid-s12265" xml:space="preserve">Item ex puncto G, in latere BC, recta
              <lb/>
            ducta LF, vel GF, parallelogrammum bifariam diuidet.</s>
            <s xml:id="echoid-s12266" xml:space="preserve"/>
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        <div xml:id="echoid-div768" type="section" level="1" n="264">
          <head xml:id="echoid-head289" xml:space="preserve">PROBL. 10. PROPOS. 15.</head>
          <p>
            <s xml:id="echoid-s12267" xml:space="preserve">INTER datas duas rectas, duas medias proportionales prope verum
              <lb/>
            inuenire.</s>
            <s xml:id="echoid-s12268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12269" xml:space="preserve">
              <emph style="sc">Exposita</emph>
            Geodæſia noſtra prioribus quinq; </s>
            <s xml:id="echoid-s12270" xml:space="preserve">propoſitionibus huius lib.
              <lb/>
            </s>
            <s xml:id="echoid-s12271" xml:space="preserve">& </s>
            <s xml:id="echoid-s12272" xml:space="preserve">nouem alijs propoſitionibus, ijs demonſtratis, quæ addenda eſſe cenſuimus
              <lb/>
            adidem argumentum ſpectantia: </s>
            <s xml:id="echoid-s12273" xml:space="preserve">agendumiam eſſet de augendis minuendiſq; </s>
            <s xml:id="echoid-s12274" xml:space="preserve">
              <lb/>
            figuris in data proportione, vt in titulo huius lib. </s>
            <s xml:id="echoid-s12275" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12276" xml:space="preserve">propoſuimus. </s>
            <s xml:id="echoid-s12277" xml:space="preserve">Verum quia
              <lb/>
            ſicutid in planis figuris effi ci non poteſt ſine inuentione medię proportionalis
              <lb/>
            inter duasrectas propoſitas, quam inuentionem Euclid. </s>
            <s xml:id="echoid-s12278" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12279" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12280" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12281" xml:space="preserve">13. </s>
            <s xml:id="echoid-s12282" xml:space="preserve">nobis
              <lb/>
            tradidit: </s>
            <s xml:id="echoid-s12283" xml:space="preserve">ita idem abſolui in figuris ſolidis nulla ratione poteſt, niſi inter duas
              <lb/>
            rectas datas duæ mediæ reperiantur proportionales. </s>
            <s xml:id="echoid-s12284" xml:space="preserve">Quo circa prius in hac pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s12285" xml:space="preserve">in medium afferemus, quæ antiqui Geometræ nobis hac de reſcripta relin-
              <lb/>
            querunt. </s>
            <s xml:id="echoid-s12286" xml:space="preserve">Multorum enim ingenia res hęc exercuit, at qu
              <unsure/>
            e torſit, quamuis ne-
              <lb/>
            mo ad hanc vſque diem, verè, ac Geometricè duas medias proportionales inter
              <lb/>
            duas rectas datas inuenerit. </s>
            <s xml:id="echoid-s12287" xml:space="preserve">Prætermi@sis autem modis Eratoſthenis; </s>
            <s xml:id="echoid-s12288" xml:space="preserve">Plato-
              <lb/>
            nis; </s>
            <s xml:id="echoid-s12289" xml:space="preserve">Pappi Alexandrini; </s>
            <s xml:id="echoid-s12290" xml:space="preserve">Spori; </s>
            <s xml:id="echoid-s12291" xml:space="preserve">menechmi tum beneficio Hyperbolę, ac para-
              <lb/>
            bolę, tum ope duarum parabolarum; </s>
            <s xml:id="echoid-s12292" xml:space="preserve">& </s>
            <s xml:id="echoid-s12293" xml:space="preserve">Architæ Tarentini, quamuis acutiſsi-
              <lb/>
            mis ſubtiliſsimiſque: </s>
            <s xml:id="echoid-s12294" xml:space="preserve">ſolum quatu or ab Herone, Apollonio Pergæo, Philone
              <lb/>
            Byſantio, Philoppono, Diocle, & </s>
            <s xml:id="echoid-s12295" xml:space="preserve">Nicomede traditos explicabimus, quos cõ-
              <lb/>
            modiores, facilioreſque, & </s>
            <s xml:id="echoid-s12296" xml:space="preserve">errori minus obnoxiosiudicauimus. </s>
            <s xml:id="echoid-s12297" xml:space="preserve">Qui aliorum
              <lb/>
            rationes deſiderat, legere eas poterit in Commentarijs Euto cij Aſcalonitæ in li-
              <lb/>
            brum 2. </s>
            <s xml:id="echoid-s12298" xml:space="preserve">Archimedis de Sphęra, & </s>
            <s xml:id="echoid-s12299" xml:space="preserve">Cylindro: </s>
            <s xml:id="echoid-s12300" xml:space="preserve">Item in libello Ioannis Verneri
              <lb/>
            Norimbergenſis de ſectionibus Conicis. </s>
            <s xml:id="echoid-s12301" xml:space="preserve">Hinc ita que exor diamur.</s>
            <s xml:id="echoid-s12302" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div769" type="section" level="1" n="265">
          <head xml:id="echoid-head290" xml:space="preserve">MODVS HERONIS IN MECHANICIS
            <lb/>
          introductionibus, & telis fabricandis: qui etiam Apollo-
            <lb/>
          nio Pergæo aſcribitur.</head>
          <p>
            <s xml:id="echoid-s12303" xml:space="preserve">
              <emph style="sc">Sint</emph>
            duæ lineęrectę AB, BC, inter quas oporteat duas medias proportio-
              <lb/>
            nales in quirere. </s>
            <s xml:id="echoid-s12304" xml:space="preserve">Conſtituautur ad angulumrectum B, & </s>
            <s xml:id="echoid-s12305" xml:space="preserve">perficiatur </s>
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