Clavius, Christoph, Geometria practica

Table of figures

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        <div xml:id="echoid-div105" type="section" level="1" n="47">
          <p>
            <s xml:id="echoid-s2211" xml:space="preserve">
              <pb o="55" file="085" n="85" rhead="LIBER SECVNDVS."/>
            includantur. </s>
            <s xml:id="echoid-s2212" xml:space="preserve">Atque tot palmos, aut pedes quælibet illarum rectarum comple-
              <lb/>
            ctetur, quot particulæ in earum interuallis deprehenſæ fuerint.</s>
            <s xml:id="echoid-s2213" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div111" type="section" level="1" n="48">
          <head xml:id="echoid-head51" xml:space="preserve">ALITER</head>
          <p>
            <s xml:id="echoid-s2214" xml:space="preserve">7. </s>
            <s xml:id="echoid-s2215" xml:space="preserve">
              <emph style="sc">Idem</emph>
            aſſequentur via quadam generali, quæ in omnes dimenſiones
              <lb/>
            quadrat, videlicet. </s>
            <s xml:id="echoid-s2216" xml:space="preserve">Fiat angulus quicunque B A C. </s>
            <s xml:id="echoid-s2217" xml:space="preserve">Deinde ſumpta verbigra-
              <lb/>
            tia, in exemplum regula trium Num. </s>
            <s xml:id="echoid-s2218" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2219" xml:space="preserve">huius propoſitionis, accipiatur primæ
              <lb/>
            quantitati O P, (hoc eſt, differentiæ Tangentium angulorum obſeruatorum)
              <lb/>
              <figure xlink:label="fig-085-01" xlink:href="fig-085-01a" number="21">
                <image file="085-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/085-01"/>
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            æqualis; </s>
            <s xml:id="echoid-s2220" xml:space="preserve">vel ſi nimis paru
              <unsure/>
            a eſt, multiplex A D.
              <lb/>
            </s>
            <s xml:id="echoid-s2221" xml:space="preserve">
              <note position="right" xlink:label="note-085-01" xlink:href="note-085-01a" xml:space="preserve">Problema hoc
                <lb/>
              1. qua ratione
                <lb/>
              aliter ſine nu-
                <lb/>
              meris abſolua
                <lb/>
              tur</note>
            (Nos duplam accepimus) Item ſecũ dæ P N, (hoc
              <lb/>
            eſt, Tangenti minoris anguli) æqualis, vel ęque
              <lb/>
            multiplex cum A D, nimirum D B. </s>
            <s xml:id="echoid-s2222" xml:space="preserve">Poſt hæc ex
              <lb/>
            inſtrumento partium capiantur tot particulę A E,
              <lb/>
            quot palmi, aut pedes in ED, differentia ſtationum
              <lb/>
            continentur. </s>
            <s xml:id="echoid-s2223" xml:space="preserve">Ducta autemrecta D E, agatur ei pa-
              <lb/>
            rallela BC. </s>
            <s xml:id="echoid-s2224" xml:space="preserve">Nam quot partes inſtrumenti partium includetinteruallum EC, tot
              <lb/>
            palmos, aut pedes diſtantia DF, complectetur; </s>
            <s xml:id="echoid-s2225" xml:space="preserve"> cum quatuor quantitates
              <note symbol="a" position="right" xlink:label="note-085-02" xlink:href="note-085-02a" xml:space="preserve">4. Sexti.</note>
            DB, AE, EC, proportionales ſint.</s>
            <s xml:id="echoid-s2226" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2227" xml:space="preserve">
              <emph style="sc">Eodem</emph>
            modo procedes in alijs exemplis, hoc obſeruato, vt quando ſinus
              <lb/>
            alicuius anguli in regula trium reperitur, accipias ex tabula ſinuum ſinum, abie-
              <lb/>
            ctis quinque figuris, vtſinus totus ſit 100. </s>
            <s xml:id="echoid-s2228" xml:space="preserve">Verbi gratia. </s>
            <s xml:id="echoid-s2229" xml:space="preserve">In vltimo exemplo
              <lb/>
            Num. </s>
            <s xml:id="echoid-s2230" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2231" xml:space="preserve">recta AD, ſumenda eſſet æqualis 100. </s>
            <s xml:id="echoid-s2232" xml:space="preserve">particulis inſtrumenti partium, ni-
              <lb/>
            mirum ſinui tori. </s>
            <s xml:id="echoid-s2233" xml:space="preserve">At D B, æqualis hypotenuſę E G, vel D G, in figura Num. </s>
            <s xml:id="echoid-s2234" xml:space="preserve">6.
              <lb/>
            </s>
            <s xml:id="echoid-s2235" xml:space="preserve">Et A E, ſi angulus E, eſt grad. </s>
            <s xml:id="echoid-s2236" xml:space="preserve">30. </s>
            <s xml:id="echoid-s2237" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s2238" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2239" xml:space="preserve">æqualis 50 {4/10}. </s>
            <s xml:id="echoid-s2240" xml:space="preserve">ferme particulis: </s>
            <s xml:id="echoid-s2241" xml:space="preserve">quia
              <lb/>
            tantus eſt ſinus grad. </s>
            <s xml:id="echoid-s2242" xml:space="preserve">30. </s>
            <s xml:id="echoid-s2243" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s2244" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2245" xml:space="preserve">Vel ſi angulus G D F, eſt grad. </s>
            <s xml:id="echoid-s2246" xml:space="preserve">53. </s>
            <s xml:id="echoid-s2247" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s2248" xml:space="preserve">20. </s>
            <s xml:id="echoid-s2249" xml:space="preserve">ac-
              <lb/>
            cipienda eſſet AE, æqualis particulis 80 {3/10}. </s>
            <s xml:id="echoid-s2250" xml:space="preserve">fere. </s>
            <s xml:id="echoid-s2251" xml:space="preserve">Ita enim interuallum E C,
              <lb/>
            dabit tot palmos, aut pedes rectę F G, quot particulę in eo comprehenduntur,
              <lb/>
            Et ſic de cęteris.</s>
            <s xml:id="echoid-s2252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2253" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            autem tota regula 100. </s>
            <s xml:id="echoid-s2254" xml:space="preserve">partium eſt nimis longa, ſumi poteſt pro
              <lb/>
            ſinu toto quoduis interuallum inter 100, & </s>
            <s xml:id="echoid-s2255" xml:space="preserve">100. </s>
            <s xml:id="echoid-s2256" xml:space="preserve">dummodo reſpectu huius ſi-
              <lb/>
            nus totius accipiantur poſtea ſinus, vt cap. </s>
            <s xml:id="echoid-s2257" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2258" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2259" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2260" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s2261" xml:space="preserve">12. </s>
            <s xml:id="echoid-s2262" xml:space="preserve">declarauimus.</s>
            <s xml:id="echoid-s2263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2264" xml:space="preserve">
              <emph style="sc">Poteris</emph>
            autem nonnunquam ordinemimmutare, ponendo nimirum ſe-
              <lb/>
            cundamquantitatem DB, in recta AC; </s>
            <s xml:id="echoid-s2265" xml:space="preserve">& </s>
            <s xml:id="echoid-s2266" xml:space="preserve">tertiam AE, in recta DB, prout videli-
              <lb/>
            cetid expedire cognoueris ad parallelas DE, BC, ducendas.</s>
            <s xml:id="echoid-s2267" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div113" type="section" level="1" n="49">
          <head xml:id="echoid-head52" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s2268" xml:space="preserve">DATIS duabus rectis ad inuicem inclinatis, punctum, in quo con-
              <lb/>
            ueniant, inuenire.</s>
            <s xml:id="echoid-s2269" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2270" xml:space="preserve">QVOD hic proponitur, demonſtratum à
              <lb/>
              <figure xlink:label="fig-085-02" xlink:href="fig-085-02a" number="22">
                <image file="085-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/085-02"/>
              </figure>
            nobis fuit lẽmate 13. </s>
            <s xml:id="echoid-s2271" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2272" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2273" xml:space="preserve">noſtri Aſtrolabij plu-
              <lb/>
            rib{us} viis. </s>
            <s xml:id="echoid-s2274" xml:space="preserve">Sed quia ei{us} inſignis eſt vtilit{as} in
              <lb/>
            puncto concurſ{us} duarum rectarum exquiren-
              <lb/>
            do demonſtrabim{us} illud ipſum hoc loco paulo
              <lb/>
            aliter. </s>
            <s xml:id="echoid-s2275" xml:space="preserve">Sint ergo duærectæ A B, C D, oblique
              <lb/>
            ſe in concurſu B, ſecant{es}. </s>
            <s xml:id="echoid-s2276" xml:space="preserve">Ex quotli-
              <lb/>
            lib{et} punctis E, F, G, vtcunque in </s>
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