Clavius, Christoph, Geometria practica

Table of contents

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[11.] QVINTI LIBRI CAPITA.
[12.] SEXTI LIBRI PROPOSITIONES.
[13.] SEP TIMI LIBRI Propoſitiones.
[14.] FINIS.
[15.] PRÆFATIO.
[16.] GEOMETRIÆ PRACTICÆ. LIBER PRIMVS. Tria capita ad dimenſionem linearum ſum-me neceſſaria complectens.
[17.] INSTRVMENTI PARTIVM Conſtructio, atque vſus. CAPVT I.
[18.] CAPVT II.
[19.] SEQVITVR TABELLA.
[20.] PROBLEMATA VARIA TRIANGV-lorum rectilineorum. Capvt III.
[21.] TRIANGVLORVM RECTILINEORVM RECTAN-gulorum problemata. I. PROPORTIONES LATERVM
[22.] II. LATVS.
[23.] III. LATVS.
[24.] IIII. LATVS.
[25.] V. BASEM.
[26.] VI. BASEM.
[27.] VII. ANGVLVM.
[28.] VIII. ANGVLVM.
[29.] TRIANGVLORVM RECTILINEO-rum obliquangulorum Problemata. IX. SEGMENTA LATERIS A Perpendiculari facta.
[30.] X. LATERA DVO.
[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.
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          <p>
            <s xml:id="echoid-s2829" xml:space="preserve">
              <pb o="72" file="102" n="102" rhead="GEOMETR. PRACT."/>
            intueri poſsit, longitu dinem A B, venabimur. </s>
            <s xml:id="echoid-s2830" xml:space="preserve">Sinamque ex C, ad ſiniſtram,
              <lb/>
            vel dextram procedemus, donec in D, vtrumq; </s>
            <s xml:id="echoid-s2831" xml:space="preserve">extremũ videamus, inuenietur
              <lb/>
            tranſuerſa longitu do AB, per problema 10. </s>
            <s xml:id="echoid-s2832" xml:space="preserve">vt prius. </s>
            <s xml:id="echoid-s2833" xml:space="preserve">Neque vero refert, ſiue per
              <lb/>
            angulum rectum BCD, recedatur in latus, ſiue per angulum acutum BAD, & </s>
            <s xml:id="echoid-s2834" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2835" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2836" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2837" xml:space="preserve">
              <emph style="sc">Operatio</emph>
            ſine numeris inſtituenda eſt, vt in ſuperioribus.</s>
            <s xml:id="echoid-s2838" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2839" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2840" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            menſor in A, exiſtens videre poteſt extremum B, inueſtigabi-
              <lb/>
            tur longitudo AB, per problema 8.</s>
            <s xml:id="echoid-s2841" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2842" xml:space="preserve">
              <emph style="sc">Si</emph>
            autem è directo longitudinis exiſtat in C, & </s>
            <s xml:id="echoid-s2843" xml:space="preserve">vtrumque etremum cernat,
              <lb/>
            explorabitur per problema 9. </s>
            <s xml:id="echoid-s2844" xml:space="preserve">eadem longitudo A B.</s>
            <s xml:id="echoid-s2845" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2846" xml:space="preserve">DISTANTIAM alicuius ſigni in Horizonte poſiti, à ſummitate tur-
              <lb/>
            ris, vel muri alicuius, licet ad ipſum ſignum acceſſus non pateat, per
              <lb/>
            quadrantem colligere.</s>
            <s xml:id="echoid-s2847" xml:space="preserve"/>
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        <div xml:id="echoid-div183" type="section" level="1" n="78">
          <head xml:id="echoid-head81" xml:space="preserve">PROBLEMA XIII.</head>
          <p>
            <s xml:id="echoid-s2848" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2849" xml:space="preserve">
              <emph style="sc">In</emph>
            Horizontis plano punctum A, diſtet à ſummi-
              <lb/>
              <figure xlink:label="fig-102-01" xlink:href="fig-102-01a" number="37">
                <image file="102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/102-01"/>
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            tate D, alicuius altitudinis CD, per rectam AD, quam me-
              <lb/>
            tiri iubemur, Vbicunq; </s>
            <s xml:id="echoid-s2850" xml:space="preserve">oculus menſoris exiſtat, nimirum
              <lb/>
            in B, vt ſit ſtatura menſoris BG, inueſtigentur per proble-
              <lb/>
            ma 6. </s>
            <s xml:id="echoid-s2851" xml:space="preserve">diſtantiæ punctorum A, D, ab oculo menſoris B.</s>
            <s xml:id="echoid-s2852" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2853" xml:space="preserve">Deinde angulus exploretur A B D, quem nobis præ-
              <lb/>
            bebit Quadrãs cum dioptra, ſi ad oculum ita applicetur,
              <lb/>
            vt eius planum per tria puncta B, A, D, tranſeat, poſito centro in B; </s>
            <s xml:id="echoid-s2854" xml:space="preserve">atque vnum
              <lb/>
            eius latus rectæ B A, incumbat, dioptra vero ad punctum D, dirigatur, & </s>
            <s xml:id="echoid-s2855" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2856" xml:space="preserve">Itaq;
              <lb/>
            </s>
            <s xml:id="echoid-s2857" xml:space="preserve">cum in triangulo B A D, duo latera nota B A, B D, angulum notum contineant
              <lb/>
            B; </s>
            <s xml:id="echoid-s2858" xml:space="preserve"> cognoſcetur quo que latus AD.</s>
            <s xml:id="echoid-s2859" xml:space="preserve"/>
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          <note symbol="a" position="left" xml:space="preserve">10. triang.
            <lb/>
          rectil.</note>
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            <s xml:id="echoid-s2860" xml:space="preserve">2. </s>
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              <emph style="sc">Qva</emph>
            ratione eadem diſtantia AD, exquirenda ſit abſque numeris, do-
              <lb/>
            cuimus Num. </s>
            <s xml:id="echoid-s2862" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2863" xml:space="preserve">problematis 7.</s>
            <s xml:id="echoid-s2864" xml:space="preserve"/>
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            <s xml:id="echoid-s2865" xml:space="preserve">ALTITVDINEM inacceſſibilem, cuius baſis non videatur, & </s>
            <s xml:id="echoid-s2866" xml:space="preserve">ad
              <lb/>
            quam per nullum ſpatium ſecundum lineam rectam accedere poſſi-
              <lb/>
            mus, aut recedere, vt duæ ſtationes fieri poſſint, ſed ſolũ ad dextram,
              <lb/>
            ſiniſtramue ad locum, è quo eius baſis appareat, per Quadrantem ex-
              <lb/>
            plorare.</s>
            <s xml:id="echoid-s2867" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div185" type="section" level="1" n="79">
          <head xml:id="echoid-head82" xml:space="preserve">PROBLEMA XIV.</head>
          <figure number="38">
            <image file="102-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/102-02"/>
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            <s xml:id="echoid-s2868" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2869" xml:space="preserve">Sit altitudo A B, ad quam ex C, loco menſoris
              <lb/>
            non liceat accedere, aut ab earecedere ſecundum li-
              <lb/>
            neam rectam, ſed ſolum in latus, verbigratia vſque ad
              <lb/>
            D, vnde baſem videre poſsimus. </s>
            <s xml:id="echoid-s2870" xml:space="preserve">Inquiratur per pro-
              <lb/>
            blema 10. </s>
            <s xml:id="echoid-s2871" xml:space="preserve">longitudo tranſuerſa A C, ex loco D: </s>
            <s xml:id="echoid-s2872" xml:space="preserve">inſpi-
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            ciatur que vertex B, ex C, per angulum ACB. </s>
            <s xml:id="echoid-s2873" xml:space="preserve">Et quia,
              <lb/>
            poſito ſinu toto A C, altitudo A B, Tangens eſt an-
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            guli obſeruationis ACB, ſi fiat.</s>
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          <note symbol="b" position="left" xml:space="preserve">4. Triang.
            <lb/>
          rectil.</note>
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