Clavius, Christoph, Geometria practica

Table of figures

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          <p>
            <s xml:id="echoid-s3421" xml:space="preserve">
              <pb o="88" file="118" n="118" rhead="GEOMETR. PRACT."/>
            foramina pinnacidiorum ſtellam videat. </s>
            <s xml:id="echoid-s3422" xml:space="preserve">Idemque fiat cum quadrato ſtabili,
              <lb/>
            collocando nimirum eius latus AD, vel CD, ſupra baſem præparatam, ip ſumq;
              <lb/>
            </s>
            <s xml:id="echoid-s3423" xml:space="preserve">circumducendo, ita vt eius planum per centrum Solis autſtellæ incedat; </s>
            <s xml:id="echoid-s3424" xml:space="preserve">ac de-
              <lb/>
            nique eleuando dioptram, donecradius Solis per foramina pinnacidiorũ tran-
              <lb/>
              <note position="left" xlink:label="note-118-01" xlink:href="note-118-01a" xml:space="preserve">Quando an-
                <lb/>
              gul{us}, quem
                <lb/>
              filism cum
                <lb/>
              pr@ximo qua-
                <lb/>
              drati latere
                <lb/>
              facit, offerat
                <lb/>
              altitudinem
                <lb/>
              ſolis; & quan-
                <lb/>
              do complemẽ-
                <lb/>
              tum altitudi-
                <lb/>
              nis.</note>
            ſeat, vel radius viſualis per eadem foramina ſtellam conſpiciat. </s>
            <s xml:id="echoid-s3425" xml:space="preserve">Quo peracto,
              <lb/>
            conſideretur ſumma diligentia angulus, quem filum perpendiculi, vel linea fi-
              <lb/>
            duciæ in dioptra cum proximo latere quadrati conſtituit, inueſtigando magna
              <lb/>
            cum cura, & </s>
            <s xml:id="echoid-s3426" xml:space="preserve">diligentia perea, quæ lib. </s>
            <s xml:id="echoid-s3427" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3428" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s3429" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3430" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s3431" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3432" xml:space="preserve">tradidimus, quot par-
              <lb/>
            tes milleſimæ ex vmbra ſiue recta, ſine verſa abſciſſæ ſint à filo perpendiculi, vel
              <lb/>
            linea fiduciæ. </s>
            <s xml:id="echoid-s3433" xml:space="preserve">Ille enim angulus, ſi quidem vmbra recta interſecetur, (quæin
              <lb/>
            quadrato ſtabili vel ſupremum locum, vel infimum occupat: </s>
            <s xml:id="echoid-s3434" xml:space="preserve">Inpendulo vero
              <lb/>
            cumlatere pinnacidiorum coniungitur, vt ſupra diximus) dabit, vt Num. </s>
            <s xml:id="echoid-s3435" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3436" xml:space="preserve">de-
              <lb/>
            monſtrabimus, complementum altitudinis Solis autſtellæ: </s>
            <s xml:id="echoid-s3437" xml:space="preserve">Si vero vmbram
              <lb/>
              <figure xlink:label="fig-118-01" xlink:href="fig-118-01a" number="52">
                <image file="118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/118-01"/>
              </figure>
            verſam filum, aut dioptra interſecet, ipſemet angulus altitu-
              <lb/>
            dinem exhibebit. </s>
            <s xml:id="echoid-s3438" xml:space="preserve">Quantitatem porro huius anguli ita cogno-
              <lb/>
              <handwritten xlink:label="hd-118-2" xlink:href="hd-118-2a" number="48"/>
              <handwritten xlink:label="hd-118-2" xlink:href="hd-118-2a" number="49"/>
              <handwritten xlink:label="hd-118-2" xlink:href="hd-118-2a" number="50"/>
            ſcemus. </s>
            <s xml:id="echoid-s3439" xml:space="preserve">Sit quadratum ſiue pendulum ſiue ſtabile (eadem e-
              <lb/>
            nim eſt in vtroque ratio) A B C D, abſciſſaque ſit vmbra recta
              <lb/>
            B E, quæ in partibus milleſimis lateris B C, reperietur, vt cap. </s>
            <s xml:id="echoid-s3440" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s3441" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s3442" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3443" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3444" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3445" xml:space="preserve">docuimus, etiamſi latusipſum ſit ſolumin 10. </s>
            <s xml:id="echoid-s3446" xml:space="preserve">
              <lb/>
            vel 100. </s>
            <s xml:id="echoid-s3447" xml:space="preserve">partes diuiſum: </s>
            <s xml:id="echoid-s3448" xml:space="preserve">quæ quidem vmbra B E, ſtatuatur
              <lb/>
            verbi gratia, eſſe partium 850. </s>
            <s xml:id="echoid-s3449" xml:space="preserve">Quia ergo duo latera AB, BE, triangulirectanguli
              <lb/>
              <note symbol="a" position="left" xlink:label="note-118-02" xlink:href="note-118-02a" xml:space="preserve">8. trìang. re-
                <lb/>
              ctil.</note>
            ABE, nota ſunt, cum AB, ſit 1000. </s>
            <s xml:id="echoid-s3450" xml:space="preserve">& </s>
            <s xml:id="echoid-s3451" xml:space="preserve">BE, 850. </s>
            <s xml:id="echoid-s3452" xml:space="preserve"> ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt lat{us} quadra- \\ ti A B, 1000. # ad ſinum to- \\ tum 100000. # Ita lat{us}, vel vmbra \\ BE, 850. # ad Tangentem \\ anguli BAE, \\ 85000
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3453" xml:space="preserve">(quod quidem factum erit, ſi ad latus B E, hoc eſt, ad 850. </s>
            <s xml:id="echoid-s3454" xml:space="preserve">duæ cifræ apponan-
              <lb/>
            tur) reperietur Tangens anguli B A E, 85000. </s>
            <s xml:id="echoid-s3455" xml:space="preserve">quæ in tabula Tangentium non
              <lb/>
            reperitur; </s>
            <s xml:id="echoid-s3456" xml:space="preserve">ſed proxime minor eſt 84956. </s>
            <s xml:id="echoid-s3457" xml:space="preserve">cuireſpondent gradus 40. </s>
            <s xml:id="echoid-s3458" xml:space="preserve">min. </s>
            <s xml:id="echoid-s3459" xml:space="preserve">21. </s>
            <s xml:id="echoid-s3460" xml:space="preserve">Et
              <lb/>
            quia differentia inter Tangentem inuentam 85000. </s>
            <s xml:id="echoid-s3461" xml:space="preserve">& </s>
            <s xml:id="echoid-s3462" xml:space="preserve">84956. </s>
            <s xml:id="echoid-s3463" xml:space="preserve">in tabula ſum-
              <lb/>
              <handwritten xlink:label="hd-118-2" xlink:href="hd-118-2a" number="48"/>
              <handwritten xlink:label="hd-118-2" xlink:href="hd-118-2a" number="49"/>
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            ptam, eſt 44. </s>
            <s xml:id="echoid-s3464" xml:space="preserve">Differentia autẽ inter duas Tangentes proximas 84956. </s>
            <s xml:id="echoid-s3465" xml:space="preserve">& </s>
            <s xml:id="echoid-s3466" xml:space="preserve">85006.
              <lb/>
            </s>
            <s xml:id="echoid-s3467" xml:space="preserve">eſt 50. </s>
            <s xml:id="echoid-s3468" xml:space="preserve">cui debetur 1. </s>
            <s xml:id="echoid-s3469" xml:space="preserve">minutum, ſiue Sec. </s>
            <s xml:id="echoid-s3470" xml:space="preserve">60. </s>
            <s xml:id="echoid-s3471" xml:space="preserve">propterea quòd poſteriori Tãgen-
              <lb/>
            ti 85006. </s>
            <s xml:id="echoid-s3472" xml:space="preserve">reſpondet vnum minutum amplius, quàm Tangenti priori 84956. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">re-
              <lb/>
            periemus perregulam trium, quot ſecunda differentiæ 44. </s>
            <s xml:id="echoid-s3474" xml:space="preserve">congruant; </s>
            <s xml:id="echoid-s3475" xml:space="preserve">ſi dica-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s3476" xml:space="preserve">Si differentia 50. </s>
            <s xml:id="echoid-s3477" xml:space="preserve">poſcit, ſec. </s>
            <s xml:id="echoid-s3478" xml:space="preserve">60. </s>
            <s xml:id="echoid-s3479" xml:space="preserve">quot ſecunda poſcit differentia 44? </s>
            <s xml:id="echoid-s3480" xml:space="preserve">inue-
              <lb/>
            niemuſque ſec. </s>
            <s xml:id="echoid-s3481" xml:space="preserve">52 {4/5}. </s>
            <s xml:id="echoid-s3482" xml:space="preserve">hoc eſt, ſec. </s>
            <s xml:id="echoid-s3483" xml:space="preserve">53. </s>
            <s xml:id="echoid-s3484" xml:space="preserve">fere. </s>
            <s xml:id="echoid-s3485" xml:space="preserve">Angulus ergo BAE, continent grad. </s>
            <s xml:id="echoid-s3486" xml:space="preserve">
              <lb/>
            40. </s>
            <s xml:id="echoid-s3487" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s3488" xml:space="preserve">21. </s>
            <s xml:id="echoid-s3489" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s3490" xml:space="preserve">53. </s>
            <s xml:id="echoid-s3491" xml:space="preserve">paulo minus. </s>
            <s xml:id="echoid-s3492" xml:space="preserve">Complementum igitur, nimirum grad. </s>
            <s xml:id="echoid-s3493" xml:space="preserve">49. </s>
            <s xml:id="echoid-s3494" xml:space="preserve">
              <lb/>
            Min. </s>
            <s xml:id="echoid-s3495" xml:space="preserve">38. </s>
            <s xml:id="echoid-s3496" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s3497" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3498" xml:space="preserve">fere, oſtendet altitudinem Solis, vel ſtellæ. </s>
            <s xml:id="echoid-s3499" xml:space="preserve">Et ſi vmbra D F, eſt
              <lb/>
            verſa partium quo que 850. </s>
            <s xml:id="echoid-s3500" xml:space="preserve">eritip ſemet angulus DAF, inuentus grad. </s>
            <s xml:id="echoid-s3501" xml:space="preserve">40. </s>
            <s xml:id="echoid-s3502" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s3503" xml:space="preserve">
              <lb/>
            21. </s>
            <s xml:id="echoid-s3504" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s3505" xml:space="preserve">53. </s>
            <s xml:id="echoid-s3506" xml:space="preserve">altitudo Solis, vel ſtellæ. </s>
            <s xml:id="echoid-s3507" xml:space="preserve">Atque hoc modo ſi diligenter partes vm-
              <lb/>
            brę explorabimus reſpectu lateris BC, vel CD, 1000. </s>
            <s xml:id="echoid-s3508" xml:space="preserve">quemadmodum lib. </s>
            <s xml:id="echoid-s3509" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3510" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s3511" xml:space="preserve">
              <lb/>
            2. </s>
            <s xml:id="echoid-s3512" xml:space="preserve">Numer. </s>
            <s xml:id="echoid-s3513" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3514" xml:space="preserve">traditum eſt, inuenietur ſemper altitudo Solis, autſtellæ in grad. </s>
            <s xml:id="echoid-s3515" xml:space="preserve">
              <lb/>
            Min. </s>
            <s xml:id="echoid-s3516" xml:space="preserve">& </s>
            <s xml:id="echoid-s3517" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s3518" xml:space="preserve">Sed quia moleſtũ eſt, ac laborioſum, per differentias Tangentium
              <lb/>
            Secunda inquirere, ſatis erit Tangentem anguli inuentam in tabula quærere, & </s>
            <s xml:id="echoid-s3519" xml:space="preserve">
              <lb/>
            ſi quidem reperta fuerit, accipere gradus, & </s>
            <s xml:id="echoid-s3520" xml:space="preserve">minuta reſpondentia; </s>
            <s xml:id="echoid-s3521" xml:space="preserve">ſi vero non
              <lb/>
            fuerit inuenta, ſumere Tangentem, vel minorem, vel maiorem quæ nimirum mi-
              <lb/>
            nus ab inuenta differat, &</s>
            <s xml:id="echoid-s3522" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3523" xml:space="preserve">Hac ratione ſumenda erit in noſtro exemplo Tan-
              <lb/>
            gens 86006. </s>
            <s xml:id="echoid-s3524" xml:space="preserve">cui reſp ondent grad. </s>
            <s xml:id="echoid-s3525" xml:space="preserve">40. </s>
            <s xml:id="echoid-s3526" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s3527" xml:space="preserve">22. </s>
            <s xml:id="echoid-s3528" xml:space="preserve">complementum autem erit grad. </s>
            <s xml:id="echoid-s3529" xml:space="preserve">
              <lb/>
              <handwritten xlink:label="hd-118-2" xlink:href="hd-118-2a" number="48"/>
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