Clavius, Christoph, Geometria practica

Table of figures

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            <s xml:id="echoid-s3529" xml:space="preserve">
              <pb o="89" file="119" n="119" rhead="LIBER TERTIVS."/>
            49. </s>
            <s xml:id="echoid-s3530" xml:space="preserve">Min 38. </s>
            <s xml:id="echoid-s3531" xml:space="preserve">veluti prius. </s>
            <s xml:id="echoid-s3532" xml:space="preserve">ſolum deſunt ſec. </s>
            <s xml:id="echoid-s3533" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3534" xml:space="preserve">quæ nullius ſunt momenti. </s>
            <s xml:id="echoid-s3535" xml:space="preserve">Vt au-
              <lb/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="51"/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="52"/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="53"/>
            tem ſtudioſos moleſtia hac ſupputandi liberem, conſtruxi ſequentem tabulam
              <lb/>
            pro ſingulis partibus milleſimis vtriuſque vmbræ: </s>
            <s xml:id="echoid-s3536" xml:space="preserve">In qua ſi centenæ in vertice,
              <lb/>
            & </s>
            <s xml:id="echoid-s3537" xml:space="preserve">reliquæ vnitates in latere ſumantur, illico in angulo communi reperientur
              <lb/>
            gradus, ac Min. </s>
            <s xml:id="echoid-s3538" xml:space="preserve">pro angulo quæſito: </s>
            <s xml:id="echoid-s3539" xml:space="preserve">qui videlicet altitudinem Solis aut ſtellæ
              <lb/>
              <note position="right" xlink:label="note-119-01" xlink:href="note-119-01a" xml:space="preserve">Vſus tabule
                <lb/>
              gnomonicæ
                <lb/>
              ſequentis.
                <lb/>
                <lb/>
              </note>
            indicabit, ſi partes milleſimæ ad vmbram verſam ſpectent: </s>
            <s xml:id="echoid-s3540" xml:space="preserve">ſi autem partes ad
              <lb/>
            vmbram rectam pertinent Complementum eius anguli altitu dinem Solis ſtel-
              <lb/>
            læue oſtendet, vt paulo infra demonſtrabimus. </s>
            <s xml:id="echoid-s3541" xml:space="preserve">Componetur autẽ tabula hęc,
              <lb/>
            ſi ſingulis partibus milleſimis vmbræ apponantur ad dextram quinque cifræ, & </s>
            <s xml:id="echoid-s3542" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-119-02" xlink:href="note-119-02a" xml:space="preserve">Compoſiti@
                <lb/>
              tabulæ gno-
                <lb/>
              monicæfacil-
                <lb/>
              lima.</note>
            ex toto illo numero abijciantur tres cifræ: </s>
            <s xml:id="echoid-s3543" xml:space="preserve">quod idem eſt, ac ſi apponantur tã-
              <lb/>
            tum duæ cifræ, vt Tangentes angulorum habeantur, Ita factum eſſe vides ſupra:
              <lb/>
            </s>
            <s xml:id="echoid-s3544" xml:space="preserve">Nam ad partes vmbræ 850. </s>
            <s xml:id="echoid-s3545" xml:space="preserve">adiectæ ſunt duæ cifræ, vt Tangens fieret 85000. </s>
            <s xml:id="echoid-s3546" xml:space="preserve">
              <lb/>
            Hac enim ratione fit multip licatio vmbræ abſciſſæ per ſinum totum 100000. </s>
            <s xml:id="echoid-s3547" xml:space="preserve">& </s>
            <s xml:id="echoid-s3548" xml:space="preserve">
              <lb/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="51"/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="52"/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="53"/>
            diuiſio per 1000. </s>
            <s xml:id="echoid-s3549" xml:space="preserve">vtin Arithmetica noſtra practica ſcripſimus. </s>
            <s xml:id="echoid-s3550" xml:space="preserve">Quod ſi quatuor
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            cifræ partibus milleſimis apponantur, habentur eadem ratione Tangẽtes, poſi-
              <lb/>
            to ſinu toto 10000000.</s>
            <s xml:id="echoid-s3551" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3552" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3553" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            demonſtremus prius, angulum, quem filum perpendiculi, vel
              <lb/>
            linea fiduciæ ſecans vmbramrectam cum pro ximo latere facit, in vtro que Qua-
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            drato eſſe complementum altitudinis Solis, ſeu ſtellæ; </s>
            <s xml:id="echoid-s3554" xml:space="preserve">illum vero, quem filum
              <lb/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="51"/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="52"/>
              <handwritten xlink:label="hd-119-1" xlink:href="hd-119-1a" number="53"/>
            aut fiduciæ linea vmbram verſam ſecans efficit, exhibere ipſam altitudinem. </s>
            <s xml:id="echoid-s3555" xml:space="preserve">Sit
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            ergo primum quadratum pendulum ABCD, & </s>
            <s xml:id="echoid-s3556" xml:space="preserve">Quadrans circuli Verticalis per
              <lb/>
            ſtellam ducti AEF, ita vt AE, Horizonti æquidiſter: </s>
            <s xml:id="echoid-s3557" xml:space="preserve">ſintq; </s>
            <s xml:id="echoid-s3558" xml:space="preserve">tres altitudines ſtel-
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            læ, EG, grad. </s>
            <s xml:id="echoid-s3559" xml:space="preserve">45. </s>
            <s xml:id="echoid-s3560" xml:space="preserve">EH, maior, & </s>
            <s xml:id="echoid-s3561" xml:space="preserve">EK, minor. </s>
            <s xml:id="echoid-s3562" xml:space="preserve">Quando ergo latus pinnacidiorum
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            AB, cum radio GA, coincidit, erit angulus altitudinis ſemirectus GAE,
              <note symbol="a" position="right" xlink:label="note-119-03" xlink:href="note-119-03a" xml:space="preserve">27. tertij.</note>
            qualis eſt ſuo complemento FAG, propter æquales arcus EG, FG, hoc eſt,
              <note symbol="b" position="right" xlink:label="note-119-04" xlink:href="note-119-04a" xml:space="preserve">15. primi.</note>
              <figure xlink:label="fig-119-01" xlink:href="fig-119-01a" number="53">
                <image file="119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/119-01"/>
              </figure>
              <note position="right" xlink:label="note-119-05" xlink:href="note-119-05a" xml:space="preserve">Filum per-
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              pendiculi ſe-
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              cansvmbra@
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              rectam facit
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              angulum cõ-
                <lb/>
              plementi alti-
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              tudinis; ſecans
                <lb/>
              vero vmbram
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              verſam angu-
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              lum conſtituit
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              ipſi{us} altitu-
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              dinis.</note>
              <note symbol="c" position="right" xlink:label="note-119-06" xlink:href="note-119-06a" xml:space="preserve">ſchol 34.
                <lb/>
              primi.</note>
            gulo quem filum cumlatere AB, facit. </s>
            <s xml:id="echoid-s3563" xml:space="preserve">Cum ergo diameter quadrati ſecet an- gulos eius rectos bifariam, in ſemirectos nimirum, tranſibit filum per angulum
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            C: </s>
            <s xml:id="echoid-s3564" xml:space="preserve">Ac proinde tam CAB, quam CAD, æqualis tunc erit angulo altitudinis E-
              <lb/>
            AG. </s>
            <s xml:id="echoid-s3565" xml:space="preserve">Quando autem pinnacidiorum latus cum radio HA, coincidit, erit angu-
              <lb/>
            lus altitudinis EAH, ſemirecto maior, & </s>
            <s xml:id="echoid-s3566" xml:space="preserve">angulus complementi FAH, ſemirecto
              <lb/>
            minor, cui æqualis eſt angulus IAB: </s>
            <s xml:id="echoid-s3567" xml:space="preserve">Acpropterea filum vmbram rectam
              <note symbol="d" position="right" xlink:label="note-119-07" xlink:href="note-119-07a" xml:space="preserve">15. primi.</note>
            </s>
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