Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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          <p style="it">
            <s xml:id="echoid-s5694" xml:space="preserve">
              <pb o="131" file="143" n="143" rhead=""/>
            sinus reſpectu sinus totius 100000. </s>
            <s xml:id="echoid-s5695" xml:space="preserve">& </s>
            <s xml:id="echoid-s5696" xml:space="preserve">quidem multò exquisitiores, quàm si sinus
              <lb/>
            ſupputentur reſpectu sinus totius 10000000. </s>
            <s xml:id="echoid-s5697" xml:space="preserve">& </s>
            <s xml:id="echoid-s5698" xml:space="preserve">ex singulis duæ figuræ abijciantur.
              <lb/>
            </s>
            <s xml:id="echoid-s5699" xml:space="preserve">Quòd si sinubus reſpectu sinus totius 100000. </s>
            <s xml:id="echoid-s5700" xml:space="preserve">inuentis adijciantur tres cifræ, fient
              <lb/>
            sinus reſpectu sinus totius 100000000. </s>
            <s xml:id="echoid-s5701" xml:space="preserve">at que ita de cæteris.</s>
            <s xml:id="echoid-s5702" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Cognitis
            <lb/>
          duabus li-
            <lb/>
          neis rectis
            <lb/>
          reſpectu ali
            <lb/>
          cuius men-
            <lb/>
          ſuræ, dein-
            <lb/>
          de vero v-
            <lb/>
          na earum
            <lb/>
          reſpectu al
            <lb/>
          terius men
            <lb/>
          ſuræ cogni
            <lb/>
          ta, quo pa-
            <lb/>
          cto alterare
            <lb/>
          ſpectu hu-
            <lb/>
          ius alteri
            <lb/>
          mẽſurę co.
            <lb/>
          gnoſcatur.
            <lb/>
          Id qd Aſtro
            <lb/>
          nomis eſt
            <lb/>
          familiatiſ-
            <lb/>
          ſimum.</note>
          <p style="it">
            <s xml:id="echoid-s5703" xml:space="preserve">_E X_ his patet ratio illius operationis, qua frequenter & </s>
            <s xml:id="echoid-s5704" xml:space="preserve">in mea Gnomonica, & </s>
            <s xml:id="echoid-s5705" xml:space="preserve">
              <lb/>
            alijs in locis vſus ſum; </s>
            <s xml:id="echoid-s5706" xml:space="preserve">cum duabus lineis cognitis reſpectu alicuius lineæ rectæ, tan-
              <lb/>
            quam sinus totius, deinde vero vna earum iterum cognita reſpectu alterius lineæ
              <lb/>
            rectæ maioris vel minoris veluti sinus totius, vel reſpectu alterius cuiuſpiam menſu-
              <lb/>
            ræ, alteram reſpectu huius alterius sinus totius, vel reſpectu alterius huius menſuræ
              <lb/>
            inueſtigo. </s>
            <s xml:id="echoid-s5707" xml:space="preserve">Id quod & </s>
            <s xml:id="echoid-s5708" xml:space="preserve">Ptolemæus, & </s>
            <s xml:id="echoid-s5709" xml:space="preserve">alij Aſtronomi non raro etiam faciunt. </s>
            <s xml:id="echoid-s5710" xml:space="preserve">Exempli
              <lb/>
            gratia; </s>
            <s xml:id="echoid-s5711" xml:space="preserve">cum duabus lineis rectis A, B, co-
              <lb/>
              <figure xlink:label="fig-143-01" xlink:href="fig-143-01a" number="134">
                <image file="143-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/143-01"/>
              </figure>
            gnitis reſpectu lineæ rectæ C, tanquã sinus
              <lb/>
            totius cõ tinentis particulas 100000. </s>
            <s xml:id="echoid-s5712" xml:space="preserve">linea
              <lb/>
            quidem A, partium 91354. </s>
            <s xml:id="echoid-s5713" xml:space="preserve">linea vero
              <lb/>
            B, partium 40673. </s>
            <s xml:id="echoid-s5714" xml:space="preserve">Deinde vero recta A,
              <lb/>
            reſpectu alterius lineæ maioris D, veluti
              <lb/>
            sinus totius cõplectentis quoque particulas
              <lb/>
            100000. </s>
            <s xml:id="echoid-s5715" xml:space="preserve">deprehenſa iterum sit partium
              <lb/>
            80901. </s>
            <s xml:id="echoid-s5716" xml:space="preserve">vel palmorum. </s>
            <s xml:id="echoid-s5717" xml:space="preserve">4 reſpectu menſuræ
              <lb/>
            E. </s>
            <s xml:id="echoid-s5718" xml:space="preserve">quæ palmo ſit æqualis, vel reſpectu men
              <lb/>
            ſuræ F, quæ plures palmos, nempe quinque, cõtineat, inquiro, quot partes, aut palmos
              <lb/>
            linea B, contineat reſpectu poſterioris sinus totius, aut reſpectu dictæ illius menſuræ
              <lb/>
            E, vel F. </s>
            <s xml:id="echoid-s5719" xml:space="preserve">Quod quidem expedio per regulam proportionum hoc modo. </s>
            <s xml:id="echoid-s5720" xml:space="preserve">Si linea A, partiũ
              <lb/>
            91354. </s>
            <s xml:id="echoid-s5721" xml:space="preserve">dat lineam B, partium 40673. </s>
            <s xml:id="echoid-s5722" xml:space="preserve">Eadem linea A, partium 80901. </s>
            <s xml:id="echoid-s5723" xml:space="preserve">vel palmo-
              <lb/>
            r@m 4. </s>
            <s xml:id="echoid-s5724" xml:space="preserve">quot partium, aut palmorũ dabit eandem lineã B ? </s>
            <s xml:id="echoid-s5725" xml:space="preserve">Inuenietur namque lineæ
              <lb/>
            B, partium 36019. </s>
            <s xml:id="echoid-s5726" xml:space="preserve">& </s>
            <s xml:id="echoid-s5727" xml:space="preserve">paulo amplius, vel palmorũ 1 {35669/45677}. </s>
            <s xml:id="echoid-s5728" xml:space="preserve">Cuius operationis
              <lb/>
            ratio à ſuperiori non differt, cum recta A, ad rectam B, habeat ſemper vnam & </s>
            <s xml:id="echoid-s5729" xml:space="preserve">ean
              <lb/>
            dem, determinatamq́; </s>
            <s xml:id="echoid-s5730" xml:space="preserve">proportionem.</s>
            <s xml:id="echoid-s5731" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div404" type="section" level="1" n="168">
          <head xml:id="echoid-head194" xml:space="preserve">SEQVITVR TABVLA SINVVM RECTORVM
            <lb/>
          per ſingula Quadrantis Minuta extenſa, & à Ioan. Regio-
            <lb/>
          montano quondam ſupputata, nunc autem per me
            <lb/>
          examinata, & pleriſque in locis caſtigata,
            <lb/>
          atque correcta.</head>
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