Clavius, Christoph, Geometria practica

Table of contents

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[341.] THEOR. 3. PROPOS. 3.
Page: 365 (335)
[342.] COROLLARIVM.
Page: 366 (336)
[343.] PROBL. 1. PROPOS. 4.
Page: 366 (336)
[344.] PROBL. 2. PROPOS. 5.
Page: 367 (339)
[345.] ALITER.
Page: 367 (339)
[346.] PROBL. 3. PROPOS. 6.
Page: 367 (339)
[347.] THEOR. 4. PROPOS. 7.
Page: 368 (340)
[348.] SCHOLIVM.
Page: 368 (340)
[349.] PROBL. 4. PROPOS. 8.
Page: 369 (341)
[350.] PROBL. 5. PROPOS. 9.
Page: 370 (342)
[351.] THEOR. 5. PROPOS. 10.
Page: 371 (343)
[352.] THEOR. 6. PROPOS. 11.
Page: 371 (343)
[353.] COROLLARIVM.
Page: 372 (344)
[354.] THEOR. 7. PROPOS. 12.
Page: 372 (344)
[355.] PROBL. 6. PROPOS. 13.
Page: 372 (344)
[356.] PROBL. 7. PROPOS. 14.
Page: 373 (345)
[357.] THEOR. 8. PROPOS. 15.
Page: 376 (348)
[358.] PROBL. 8. PROPOS. 16.
Page: 377 (349)
[359.] COROLLARIVM.
Page: 378 (350)
[360.] SCHOLIVM.
Page: 379 (351)
[361.] PROBL. 9. PROPOS. 17.
Page: 379 (351)
[362.] PROBL. 10. PROPOS. 18.
Page: 379 (351)
[363.] PROBL. 11. PROPOS. 19.
Page: 380 (352)
[364.] PROBL. 12. PROPOS. 20.
Page: 381 (353)
[365.] THEOR. 9. ROPOS. 21.
Page: 381 (353)
[366.] PROBL. 13. PROPOS. 22.
Page: 382 (354)
[367.] PROBL. 14. PROPOS. 23.
Page: 383 (355)
[368.] PROBL. 15. PROPOS. 24.
Page: 383 (355)
[369.] PROBL. 16. PROPOS. 25.
Page: 384 (356)
[370.] PROBL. 17. PROPOS. 26.
Page: 385 (357)
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        <div xml:id="echoid-div907" type="section" level="1" n="318">
          <pb o="317" file="347" n="347" rhead="LIBER SEPTIMVS."/>
          <p>
            <s xml:id="echoid-s14854" xml:space="preserve">
              <emph style="sc">Sit</emph>
            hexagonum datum A, æquilaterum quidem, ſed non æquiangulum, ita
              <lb/>
            vt B, ad latus quadrati illi æqualis inuentum maius non ſit ſemiſſe,
              <note symbol="a" position="right" xlink:label="note-347-01" xlink:href="note-347-01a" xml:space="preserve">14. ſecundi.</note>
            ambitus hexagoni. </s>
            <s xml:id="echoid-s14855" xml:space="preserve">Sumpta ergo recta C D, æquali ſemiſsi ambitus hexagoni;
              <lb/>
            </s>
            <s xml:id="echoid-s14856" xml:space="preserve">erit B, recta non maior ſemiſſe ipſius C D, ſed vel æqualis, vel minor. </s>
            <s xml:id="echoid-s14857" xml:space="preserve"> Secta
              <note symbol="b" position="right" xlink:label="note-347-02" xlink:href="note-347-02a" xml:space="preserve">ſchol. 13.
                <lb/>
              ſexti.</note>
            tem CD, in E, ita vt B, ſit media proportionalis inter ſegmenta DE, EC, fiatre-
              <lb/>
            ctangulum E G, contentum ſub ſegmentis D E, E C. </s>
            <s xml:id="echoid-s14858" xml:space="preserve">Dico rectangulum E G,
              <lb/>
            æquale eſſe, & </s>
            <s xml:id="echoid-s14859" xml:space="preserve">iſoperimetrum hexagono A. </s>
            <s xml:id="echoid-s14860" xml:space="preserve">Quoniam enim tres D E, B, E C,
              <lb/>
            continuè proportionales ſunt; </s>
            <s xml:id="echoid-s14861" xml:space="preserve"> erit rectangulum E G, quadrato B, id eſt,
              <note symbol="c" position="right" xlink:label="note-347-03" xlink:href="note-347-03a" xml:space="preserve">17. ſexti.</note>
            xagono A, æquale. </s>
            <s xml:id="echoid-s14862" xml:space="preserve">Et quia duo latera DE, EF, æqualia ſunt rectæ CD, hoc eſt,
              <lb/>
            ſemiſsi ambitus hexagoni A, ideo que reliquæ duæ FG, GD, alteri ſemiſsi: </s>
            <s xml:id="echoid-s14863" xml:space="preserve">@erit
              <lb/>
            totum rectangulum E G, hexagono A, iſoperimetrum. </s>
            <s xml:id="echoid-s14864" xml:space="preserve">Dato ergo rectilineo
              <lb/>
            parallelogrammum rectangulum ęquale, & </s>
            <s xml:id="echoid-s14865" xml:space="preserve">iſo perimetrum conſtituimus: </s>
            <s xml:id="echoid-s14866" xml:space="preserve">quod
              <lb/>
            erat faciendum.</s>
            <s xml:id="echoid-s14867" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div909" type="section" level="1" n="319">
          <head xml:id="echoid-head346" xml:space="preserve">SCHOLIVM.</head>
          <figure number="239">
            <image file="347-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/347-01"/>
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          <p>
            <s xml:id="echoid-s14868" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi B, latus quadrati foret maius ſemiſſe di-
              <lb/>
            midij ambitus rectilinei A, hoc eſt, maius recta CD,
              <lb/>
            non poſſet C D, ita ſecari, vt B, eſſet medio loco pro-
              <lb/>
            portionalis inter ſegmenta, vt liquidò conſtat.</s>
            <s xml:id="echoid-s14869" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14870" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò ſi ſumatur punctum H, inter C, & </s>
            <s xml:id="echoid-s14871" xml:space="preserve">E,
              <lb/>
            vtcunque; </s>
            <s xml:id="echoid-s14872" xml:space="preserve">erit rectangulum ſub D H, H C, adhuc
              <lb/>
            iſoperimetrum figuræ A, ſed tamen minus. </s>
            <s xml:id="echoid-s14873" xml:space="preserve">Si verò ac-
              <lb/>
            cipiatur punctum I, vtcunque inter E, & </s>
            <s xml:id="echoid-s14874" xml:space="preserve">L, punctum
              <lb/>
            medium rectæ C D; </s>
            <s xml:id="echoid-s14875" xml:space="preserve">erit adhuc rectangulum ſub D I,
              <lb/>
            I C, figuræ A, iſoperimetrum, maius tamen. </s>
            <s xml:id="echoid-s14876" xml:space="preserve">Sic et-
              <lb/>
            iam quadratum ſemiſsis D L, erit iſo perimetrum ei-
              <lb/>
            dem figuræ & </s>
            <s xml:id="echoid-s14877" xml:space="preserve">maius; </s>
            <s xml:id="echoid-s14878" xml:space="preserve">quæ omnia demonſtrabun-
              <lb/>
            tur, vt in ſcholio præcedentis problematis dictum
              <lb/>
            eſt.</s>
            <s xml:id="echoid-s14879" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div910" type="section" level="1" n="320">
          <head xml:id="echoid-head347" xml:space="preserve">APPENDIX.</head>
          <p>
            <s xml:id="echoid-s14880" xml:space="preserve">De circulo per lineas quadrando.</s>
            <s xml:id="echoid-s14881" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14882" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14883" xml:space="preserve">
              <emph style="sc">Locvs</emph>
            hic me admonet, vt quoniam hoc libro demonſtratum eſt, cir-
              <lb/>
            culum figurarum omnium ſibi iſoperimetrarum eſſe maximum, breuiter do-
              <lb/>
            ceam, quaratione dato circulo quadratum conſtrui poſsit æquale, & </s>
            <s xml:id="echoid-s14884" xml:space="preserve">viciſsim
              <lb/>
            dato quadrato circulus æqualis; </s>
            <s xml:id="echoid-s14885" xml:space="preserve">atqueid per lineas: </s>
            <s xml:id="echoid-s14886" xml:space="preserve">cum lib. </s>
            <s xml:id="echoid-s14887" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14888" xml:space="preserve">cap 7. </s>
            <s xml:id="echoid-s14889" xml:space="preserve">copiosè
              <lb/>
              <note position="right" xlink:label="note-347-04" xlink:href="note-347-04a" xml:space="preserve">Quo pacto re-
                <lb/>
              periatur per
                <lb/>
              numeros qua-
                <lb/>
              dratum cir-
                <lb/>
              culo æquale,
                <lb/>
              & contra ex
                <lb/>
              doctrina Ar-
                <lb/>
              chimedis.</note>
            traditum ſit, quo pacto ex inuentis ab Archimede, per numeros circulus qua-
              <lb/>
            drandus ſit, hoc eſt, qua ratione area circuli, ſiue capacitas tum ex diametro, tum
              <lb/>
            ex circumferentia cognita ſit inuenienda: </s>
            <s xml:id="echoid-s14890" xml:space="preserve">Huius enim areæ radix quadrata, la-
              <lb/>
            tus eſt quadrati, quod circulo æquale eſt. </s>
            <s xml:id="echoid-s14891" xml:space="preserve">Sic è contrario cap. </s>
            <s xml:id="echoid-s14892" xml:space="preserve">8. </s>
            <s xml:id="echoid-s14893" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s14894" xml:space="preserve">re-
              <lb/>
            gula 1. </s>
            <s xml:id="echoid-s14895" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s14896" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14897" xml:space="preserve">docuimus qua via ex data circuli area indaganda ſit tam circum-
              <lb/>
            ferentia, quam diameter illius circuli: </s>
            <s xml:id="echoid-s14898" xml:space="preserve">hoc eſt, propoſito quadrato, inſtar areæ
              <lb/>
            circuli alicuius, quomodo circulus deſcribendus ſit illi quadrato æqualis. </s>
            <s xml:id="echoid-s14899" xml:space="preserve"/>
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