Clavius, Christoph, Geometria practica

Table of contents

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[381.] SCHOLIVM.
Page: 394 (366)
[382.] PROBL. 20. PROPOS. 34.
Page: 394 (366)
[383.] PROBL. 21. PROPOS. 35.
Page: 395 (367)
[384.] PROBL. 22. PROPOS. 36.
Page: 396 (368)
[385.] COROLLARIVM I.
Page: 396 (368)
[386.] COROLLARIVM II.
Page: 397 (369)
[387.] PROBL. 23. PROPOS. 37.
Page: 397 (369)
[388.] PROBL. 24. PROPOS. 38.
Page: 397 (369)
[389.] COROLLARIVM.
Page: 397 (369)
[390.] PROBL. 25. PROPOS. 39.
Page: 398 (370)
[391.] COR OLLARIVM.
Page: 398 (370)
[392.] PROBL. 26. PROPOS. 40.
Page: 398 (370)
[393.] COROLLARIVM I.
Page: 399 (371)
[394.] COROLLARIVM II.
Page: 399 (371)
[395.] PROBL. 27. PROPOS. 41.
Page: 400 (372)
[396.] SCHOLIVM.
Page: 400 (372)
[397.] PROBL. 28. PROPOS. 42.
Page: 400 (372)
[398.] PROBL. 29. PROPOS. 43.
Page: 400 (372)
[399.] SCHOLIVM.
Page: 401 (373)
[400.] PROBL. 30. PROPOS. 44.
Page: 401 (373)
[401.] PROBL. 31. PROPOS. 45.
Page: 401 (373)
[402.] PROBL. 32. PROPOS. 46.
Page: 401 (373)
[403.] SCHOLIVM.
Page: 401 (373)
[404.] PROBL. 33. PROPOS. 47.
Page: 402 (374)
[405.] SCHOLIVM.
Page: 404 (376)
[406.] SEQVITVR TABVLA QVADRATO-rum, & Cuborum, quorum radices maio-res non ſunt, quam 1000.
Page: 405 (377)
[407.] Tabula Quadratorum, & Cuborum.
Page: 406 (378)
[408.] Tabula Quadratorum, & Cuborum.
Page: 407 (379)
[409.] Tabula Quadratorum, & Cuborum.
Page: 408 (380)
[410.] Tabula Quadratorum, & Cuborum.
Page: 409 (381)
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            <s xml:id="echoid-s16455" xml:space="preserve">
              <pb o="353" file="381" n="381" rhead="LIBER OCTAVVS."/>
            reliquæ BH, DN, æquales erunt) erunt quo que BI, AO, æquales; </s>
            <s xml:id="echoid-s16456" xml:space="preserve">necnon
              <lb/>
            BO, AC, &</s>
            <s xml:id="echoid-s16457" xml:space="preserve">c.</s>
            <s xml:id="echoid-s16458" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1015" type="section" level="1" n="364">
          <head xml:id="echoid-head391" xml:space="preserve">PROBL. 12. PROPOS. 20.</head>
          <p>
            <s xml:id="echoid-s16459" xml:space="preserve">DATA chorda alicuius arcus, vna cum perpendiculari, quæ ex medio
              <lb/>
            puncto chordæ ad arcum vſque educitur: </s>
            <s xml:id="echoid-s16460" xml:space="preserve">quot gradus, vel palmos
              <lb/>
            tam arcus, quam ſemidiameter circuli complectitur, inuenire.</s>
            <s xml:id="echoid-s16461" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16462" xml:space="preserve">
              <emph style="sc">Sit</emph>
            data chorda AB, palmorum 74. </s>
            <s xml:id="echoid-s16463" xml:space="preserve">& </s>
            <s xml:id="echoid-s16464" xml:space="preserve">perpendicularis CD, ex medio pun-
              <lb/>
            cto C, educta palmorum 10. </s>
            <s xml:id="echoid-s16465" xml:space="preserve">Iuncta recta AD; </s>
            <s xml:id="echoid-s16466" xml:space="preserve">quoniam in triangulo rectan-
              <lb/>
            gulo ACD, latera AC, CD, nota ſunt, quod CD, ſit 10. </s>
            <s xml:id="echoid-s16467" xml:space="preserve">& </s>
            <s xml:id="echoid-s16468" xml:space="preserve">AC, 37. </s>
            <s xml:id="echoid-s16469" xml:space="preserve">ſemiſsis nimi-
              <lb/>
            rum chordæ AB, 74. </s>
            <s xml:id="echoid-s16470" xml:space="preserve"> Si fiat vt CD, 10. </s>
            <s xml:id="echoid-s16471" xml:space="preserve">ad ſinum
              <figure xlink:label="fig-381-01" xlink:href="fig-381-01a" number="270">
                <image file="381-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/381-01"/>
              </figure>
              <note symbol="a" position="right" xlink:label="note-381-01" xlink:href="note-381-01a" xml:space="preserve">8. triang.
                <lb/>
              rectil.</note>
            100000. </s>
            <s xml:id="echoid-s16472" xml:space="preserve">ita AC, 37. </s>
            <s xml:id="echoid-s16473" xml:space="preserve">ad aliud; </s>
            <s xml:id="echoid-s16474" xml:space="preserve">inuenietur AC, 370000, tangẽs
              <lb/>
            anguli ADC; </s>
            <s xml:id="echoid-s16475" xml:space="preserve">ac proinde ipſe angulus erit gr. </s>
            <s xml:id="echoid-s16476" xml:space="preserve">74. </s>
            <s xml:id="echoid-s16477" xml:space="preserve">min. </s>
            <s xml:id="echoid-s16478" xml:space="preserve">53. </s>
            <s xml:id="echoid-s16479" xml:space="preserve">fe-
              <lb/>
            re. </s>
            <s xml:id="echoid-s16480" xml:space="preserve">Et ſi concipiatur duci AE, ad centrum E, erit quo que an-
              <lb/>
            gulus DAE, gr. </s>
            <s xml:id="echoid-s16481" xml:space="preserve">74. </s>
            <s xml:id="echoid-s16482" xml:space="preserve">min. </s>
            <s xml:id="echoid-s16483" xml:space="preserve">53. </s>
            <s xml:id="echoid-s16484" xml:space="preserve">fere; </s>
            <s xml:id="echoid-s16485" xml:space="preserve"> quippe cum anguli
              <note symbol="b" position="right" xlink:label="note-381-02" xlink:href="note-381-02a" xml:space="preserve">5. primi.</note>
            DAE, æquales ſint. </s>
            <s xml:id="echoid-s16486" xml:space="preserve">Quod ſi vtriuſque ſumma gr. </s>
            <s xml:id="echoid-s16487" xml:space="preserve">149. </s>
            <s xml:id="echoid-s16488" xml:space="preserve">min.
              <lb/>
            </s>
            <s xml:id="echoid-s16489" xml:space="preserve">46. </s>
            <s xml:id="echoid-s16490" xml:space="preserve">fere, detrahatur ex duobusrectis, hoc eſt, ex gr. </s>
            <s xml:id="echoid-s16491" xml:space="preserve">180. </s>
            <s xml:id="echoid-s16492" xml:space="preserve">re-
              <lb/>
            liquus fiet tertius angulus E, in centro gr. </s>
            <s xml:id="echoid-s16493" xml:space="preserve">30. </s>
            <s xml:id="echoid-s16494" xml:space="preserve">min. </s>
            <s xml:id="echoid-s16495" xml:space="preserve">14. </s>
            <s xml:id="echoid-s16496" xml:space="preserve">fere, ac
              <lb/>
            totidem grad. </s>
            <s xml:id="echoid-s16497" xml:space="preserve">erit arcus AD; </s>
            <s xml:id="echoid-s16498" xml:space="preserve">ideoque eius duplus ADB, grad. </s>
            <s xml:id="echoid-s16499" xml:space="preserve">60. </s>
            <s xml:id="echoid-s16500" xml:space="preserve">min. </s>
            <s xml:id="echoid-s16501" xml:space="preserve">28. </s>
            <s xml:id="echoid-s16502" xml:space="preserve">
              <lb/>
            fermè.</s>
            <s xml:id="echoid-s16503" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16504" xml:space="preserve">Quia verò quadratum ex AC, æquale eſt rectangulo ſub CD, & </s>
            <s xml:id="echoid-s16505" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-381-03" xlink:href="note-381-03a" xml:space="preserve">35. tertii.</note>
            parte diametri: </s>
            <s xml:id="echoid-s16506" xml:space="preserve">ſi AC, 37, palm. </s>
            <s xml:id="echoid-s16507" xml:space="preserve">ducatur in ſe, & </s>
            <s xml:id="echoid-s16508" xml:space="preserve">productus numerus 1369. </s>
            <s xml:id="echoid-s16509" xml:space="preserve">diui-
              <lb/>
            datur per CD, palm. </s>
            <s xml:id="echoid-s16510" xml:space="preserve">10. </s>
            <s xml:id="echoid-s16511" xml:space="preserve">prodibit reliqua pars diametri palm. </s>
            <s xml:id="echoid-s16512" xml:space="preserve">136 {9/10}. </s>
            <s xml:id="echoid-s16513" xml:space="preserve">ac proinde
              <lb/>
            addita CD, palm. </s>
            <s xml:id="echoid-s16514" xml:space="preserve">10. </s>
            <s xml:id="echoid-s16515" xml:space="preserve">tota diameter erit palm. </s>
            <s xml:id="echoid-s16516" xml:space="preserve">146 {9/10}. </s>
            <s xml:id="echoid-s16517" xml:space="preserve">& </s>
            <s xml:id="echoid-s16518" xml:space="preserve">ſemidiameter palm.
              <lb/>
            </s>
            <s xml:id="echoid-s16519" xml:space="preserve">73. </s>
            <s xml:id="echoid-s16520" xml:space="preserve">{9/20}. </s>
            <s xml:id="echoid-s16521" xml:space="preserve">Si igitur fiat vt 7. </s>
            <s xml:id="echoid-s16522" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s16523" xml:space="preserve">ita 146 {9/10}. </s>
            <s xml:id="echoid-s16524" xml:space="preserve">palmi ad aliud; </s>
            <s xml:id="echoid-s16525" xml:space="preserve">reperietur per 1. </s>
            <s xml:id="echoid-s16526" xml:space="preserve">re-
              <lb/>
            gulam Num. </s>
            <s xml:id="echoid-s16527" xml:space="preserve">2. </s>
            <s xml:id="echoid-s16528" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s16529" xml:space="preserve">7. </s>
            <s xml:id="echoid-s16530" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16531" xml:space="preserve">4. </s>
            <s xml:id="echoid-s16532" xml:space="preserve">huius, circumferentia circuli palm. </s>
            <s xml:id="echoid-s16533" xml:space="preserve">430 {9/35}. </s>
            <s xml:id="echoid-s16534" xml:space="preserve">Ergo
              <lb/>
            ſi rurſus fiat, vt tota circumferentia grad. </s>
            <s xml:id="echoid-s16535" xml:space="preserve">360. </s>
            <s xml:id="echoid-s16536" xml:space="preserve">ad palmos 430 {9/35}. </s>
            <s xml:id="echoid-s16537" xml:space="preserve">ita arcus ADB,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s16538" xml:space="preserve">60. </s>
            <s xml:id="echoid-s16539" xml:space="preserve">min. </s>
            <s xml:id="echoid-s16540" xml:space="preserve">28. </s>
            <s xml:id="echoid-s16541" xml:space="preserve">ad aliud, inuenietur hic arcus palm. </s>
            <s xml:id="echoid-s16542" xml:space="preserve">72 {54513/189000}. </s>
            <s xml:id="echoid-s16543" xml:space="preserve">hoc eſt, 72 {10/39}. </s>
            <s xml:id="echoid-s16544" xml:space="preserve">
              <lb/>
            paulò amplius.</s>
            <s xml:id="echoid-s16545" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1018" type="section" level="1" n="365">
          <head xml:id="echoid-head392" xml:space="preserve">THEOR. 9. ROPOS. 21.</head>
          <p>
            <s xml:id="echoid-s16546" xml:space="preserve">IN omni triangulo quadratum maximi lateris minus eſt, quam duplum
              <lb/>
            ſummæ quadratorum ex reliquis duobus lateribus deſcriptorum.</s>
            <s xml:id="echoid-s16547" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16548" xml:space="preserve">
              <emph style="sc">In</emph>
            triangulo ABC, maximum latus ſit AC,
              <lb/>
              <figure xlink:label="fig-381-02" xlink:href="fig-381-02a" number="271">
                <image file="381-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/381-02"/>
              </figure>
            & </s>
            <s xml:id="echoid-s16549" xml:space="preserve">angulus oppoſitus B, obtuſus. </s>
            <s xml:id="echoid-s16550" xml:space="preserve">Si namque re-
              <lb/>
            ctus eſſet, vel acutus; </s>
            <s xml:id="echoid-s16551" xml:space="preserve"> eſſet quadratum
              <note symbol="d" position="right" xlink:label="note-381-04" xlink:href="note-381-04a" xml:space="preserve">47. primi.</note>
            AC, vel æquale duobus quadratis rectarum
              <lb/>
            AB, BC; </s>
            <s xml:id="echoid-s16552" xml:space="preserve"> vel minus: </s>
            <s xml:id="echoid-s16553" xml:space="preserve">ac proinde
              <note symbol="e" position="right" xlink:label="note-381-05" xlink:href="note-381-05a" xml:space="preserve">13. ſecund.</note>
            minus duplo ſummæ quadratorum AB, BC.
              <lb/>
            </s>
            <s xml:id="echoid-s16554" xml:space="preserve">Ex maiore latere AC, dematur AD, recta æ-
              <lb/>
            qualis lateri AB. </s>
            <s xml:id="echoid-s16555" xml:space="preserve"> Et quia duo@ latera AB,
              <note symbol="f" position="right" xlink:label="note-381-06" xlink:href="note-381-06a" xml:space="preserve">20. primi.</note>
            </s>
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