Clavius, Christoph, Geometria practica

Table of contents

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[31.] Rurſus
[32.] XI. LATVS.
[33.] XII. LATVS.
[34.] Deinde.
[35.] Hæc autem tangens hoc etiam modo inuenietur, qui priori præferendus videtur.
[36.] Poſt hæc.
[37.] XIII. LATVS.
[38.] XIIII. ANGVLOS DVOS.
[39.] XV. ANGVLOS DVOS.
[40.] XVI. ANGVLOS OMNES TRES. Ex tribus omnibus lateribus perueſtigare.
[41.] Rurſus.
[42.] XVII. PERPENDICVLAREM IN LATVS quodcunque ex angulo oppoſito cadentem. Ex tribus omnibus lateribus efficere notam.
[43.] FINIS LIBRI PRIMI.
[44.] GEOMETRIÆ PRACTICÆ LIBER SECVNDVS.
[45.] PROBLEMA I.
[46.] ALITER
[47.] ALITER
[48.] ALITER
[49.] LEMMA.
[50.] SCHOLIVM.
[51.] COROLLARIVM I.
[52.] COROLLARIVM II.
[53.] PROBLEMA II.
[54.] 2. ITEM ſi fiat.
[55.] ALITER.
[56.] Ergo ſi fiat,
[57.] Si igitur fiat.
[58.] COROLLARIVM I.
[59.] COROLLARIVM II.
[60.] PROBLEMA III.
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          <pb o="49" file="079" n="79" rhead="LIBER PRIMVS."/>
        </div>
        <div xml:id="echoid-div90" type="section" level="1" n="40">
          <head xml:id="echoid-head43" xml:space="preserve">XVI. ANGVLOS OMNES TRES.
            <lb/>
          Ex tribus omnibus lateribus perueſtigare.</head>
          <p style="it">
            <s xml:id="echoid-s2038" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2039" xml:space="preserve">Ducta ad maximum lat{us} perpendiculari ex angulo oppoſito (vt ni@irum
              <note position="right" xlink:label="note-079-01" xlink:href="note-079-01a" xml:space="preserve">11. triang.
                <lb/>
              rectil.</note>
            pendicularis ſemper intratriangulum cadat) inueniantur per problema 9. </s>
            <s xml:id="echoid-s2040" xml:space="preserve">ſegmenta duo
              <lb/>
            @aximi lateris facta à perpendiculari. </s>
            <s xml:id="echoid-s2041" xml:space="preserve">Deinde.</s>
            <s xml:id="echoid-s2042" xml:space="preserve"/>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt minimum \\ lat{us} # ad ſinum \\ totum: # ita min{us} ſegmen- \\ tum maximi late- \\ ris # ad ſinum complementi \\ anguli medi@ lateri \\ oppoſiti.
            <lb/>
          </note>
        </div>
        <div xml:id="echoid-div92" type="section" level="1" n="41">
          <head xml:id="echoid-head44" xml:space="preserve">Rurſus.</head>
          <note position="right" xml:space="preserve">1. triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt me- \\ dium \\ lat{us} # ad ſinum \\ totum: # ita mai{us} ſegmen- \\ tum maximi la- \\ teris # ad ſinum complementi angu- \\ li medio lateri oppoſiti.
            <lb/>
          </note>
          <note position="right" xml:space="preserve">1. triang.
            <lb/>
          rectil.</note>
          <p>
            <s xml:id="echoid-s2043" xml:space="preserve">Inuentis duobus angulis ad maximum latus, qui medio lateri, & </s>
            <s xml:id="echoid-s2044" xml:space="preserve">minimo
              <lb/>
            opponuntur; </s>
            <s xml:id="echoid-s2045" xml:space="preserve">ſi eorum ſumma ex ſemicirculo dematur, reliquus fiet tertius an-
              <lb/>
            gulus lateri maximo oppoſitus.</s>
            <s xml:id="echoid-s2046" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2047" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">In Iſoſcele, ducta perpendiculari ad baſem , quam bifariam ſecabit,</s>
          </p>
          <note position="right" xml:space="preserve">Schol. 26.
            <lb/>
          lib. 1. Eucl.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt alterum \\ laterum æ- \\ qualium # ad ſinum \\ totum: # ita ſemiſſis \\ baſis # ad ſinum complementi vni{us} \\ angulorum æqualium ad ba- \\ ſem.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2049" xml:space="preserve">Summa duorum angulorum æqualium inuentorum ex ſemicirculo detra-
              <lb/>
            cta, reliquum faciet tertium angulum.</s>
            <s xml:id="echoid-s2050" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2051" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2052" xml:space="preserve">
              <emph style="sc">In</emph>
            æquilatero triangulo dabuntur anguli, etiamſi latera non dentur, e
              <unsure/>
            um
              <lb/>
            quilibet gradus 60. </s>
            <s xml:id="echoid-s2053" xml:space="preserve">tertiam videlicet partem duorum rectorum, vel duas tertias
              <lb/>
            partes vnius recti, complectatur.</s>
            <s xml:id="echoid-s2054" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div93" type="section" level="1" n="42">
          <head xml:id="echoid-head45" xml:space="preserve">XVII. PERPENDICVLAREM IN LATVS
            <lb/>
          quodcunque ex angulo oppoſito cadentem.
            <lb/>
          Ex tribus omnibus lateribus efficere notam.</head>
          <p style="it">
            <s xml:id="echoid-s2055" xml:space="preserve">Per problema 9. </s>
            <s xml:id="echoid-s2056" xml:space="preserve">inquirantur ſegmenta lateris facta à perpendiculari. </s>
            <s xml:id="echoid-s2057" xml:space="preserve">Deinde diffe-
              <lb/>
            rentia inter vtrumuis ſegmentum, & </s>
            <s xml:id="echoid-s2058" xml:space="preserve">lat{us} adiacens ducatur in ſummam eiuſdem ſeg-
              <lb/>
            menti, & </s>
            <s xml:id="echoid-s2059" xml:space="preserve">lateris adiacentis. </s>
            <s xml:id="echoid-s2060" xml:space="preserve">Radix namque quadrata numeriproducti perpendicula-
              <lb/>
            rem quæſitam indicabit.</s>
            <s xml:id="echoid-s2061" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2062" xml:space="preserve">In triangulo enim A B C, ſit A B, 10. </s>
            <s xml:id="echoid-s2063" xml:space="preserve">A C, 17. </s>
            <s xml:id="echoid-s2064" xml:space="preserve">& </s>
            <s xml:id="echoid-s2065" xml:space="preserve">B C, 21. </s>
            <s xml:id="echoid-s2066" xml:space="preserve">inueſtiganda{q́ue} ſit perpen-
              <lb/>
            dicularis A D. </s>
            <s xml:id="echoid-s2067" xml:space="preserve">Per problema 9. </s>
            <s xml:id="echoid-s2068" xml:space="preserve">reperi{et}ur ſegmen-
              <lb/>
              <figure xlink:label="fig-079-01" xlink:href="fig-079-01a" number="14">
                <image file="079-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/079-01"/>
              </figure>
            tum B D, 6. </s>
            <s xml:id="echoid-s2069" xml:space="preserve">& </s>
            <s xml:id="echoid-s2070" xml:space="preserve">C D, 15. </s>
            <s xml:id="echoid-s2071" xml:space="preserve">Differentia inter B D, & </s>
            <s xml:id="echoid-s2072" xml:space="preserve">
              <lb/>
            A B, eſt 4. </s>
            <s xml:id="echoid-s2073" xml:space="preserve">quæducta in 16. </s>
            <s xml:id="echoid-s2074" xml:space="preserve">ſummam rectarum B D
              <lb/>
            & </s>
            <s xml:id="echoid-s2075" xml:space="preserve">A B, faci{et} 64. </s>
            <s xml:id="echoid-s2076" xml:space="preserve">cui{us} radix quadrata 8. </s>
            <s xml:id="echoid-s2077" xml:space="preserve">d{at}
              <lb/>
            perpendicularem A D. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">Quod quia in noſtro tra-
              <lb/>
            ctatis triangulorum rectilineorum demonſtratum
              <lb/>
            non est, demonſtro hoc propoſito Theoremate.</s>
            <s xml:id="echoid-s2079" xml:space="preserve"/>
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