Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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        <div xml:id="echoid-div55" type="section" level="1" n="32">
          <p>
            <s xml:id="echoid-s2027" xml:space="preserve">
              <pb file="0042" n="42" rhead="GENVINVS VSVS"/>
            uocare conſueuerunt, ab eo puncto ſi protrahas cir culum ab ipſo occaſu æquinoctialis
              <lb/>
            uſ ad ortum æ quinoctialem, circulus ille dicetur uerticalis, ad quem Sol peruenire non
              <lb/>
              <note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">
                <emph style="it">per arcalẽ</emph>
                <lb/>
                <emph style="it">introitum</emph>
                <lb/>
                <emph style="it">ſimile inue</emph>
                <lb/>
                <emph style="it">nies.</emph>
              </note>
            poteſt, niſi fuerit in aliquo ſignorũ ſeptentrionalium, ubi ſi extiterit, & </s>
            <s xml:id="echoid-s2028" xml:space="preserve">tu iam ſcire cupi-
              <lb/>
            as altitudinem ipſius in circulo uerticali, propone tibi ſinum rectum altitudinis poli, & </s>
            <s xml:id="echoid-s2029" xml:space="preserve">
              <lb/>
            ſinum rectum declinationis Solis, minorem duc in ſinum perfectum, productũ diuide in
              <lb/>
            maiorem, & </s>
            <s xml:id="echoid-s2030" xml:space="preserve">tũc arcus quotientis cõmonſtrabit tibi altitudinem Solis quæſitã. </s>
            <s xml:id="echoid-s2031" xml:space="preserve">?</s>
            <s xml:id="echoid-s2032" xml:space="preserve">? Ex-
              <lb/>
            emplo rem planius intelliges, eo loco ubi intronizatio ornatiſsimi præſulis facta eſt, po
              <lb/>
              <note position="left" xlink:label="note-0042-02" xlink:href="note-0042-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            lus eleuatus eſt ad 48. </s>
            <s xml:id="echoid-s2033" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2034" xml:space="preserve">Sol aũt in ipſo die intronizationis fuit in 2. </s>
            <s xml:id="echoid-s2035" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2036" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2037" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2038" xml:space="preserve">II, de-
              <lb/>
            clinatio ergo Solis eſt 20. </s>
            <s xml:id="echoid-s2039" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2040" xml:space="preserve">42. </s>
            <s xml:id="echoid-s2041" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2042" xml:space="preserve">ſinus declinationis 35347. </s>
            <s xml:id="echoid-s2043" xml:space="preserve">ſinus uero altitudinis po
              <lb/>
            li 74314. </s>
            <s xml:id="echoid-s2044" xml:space="preserve">ſi ita 35347. </s>
            <s xml:id="echoid-s2045" xml:space="preserve">ducas in ſinum totum ſiue perfectũ, & </s>
            <s xml:id="echoid-s2046" xml:space="preserve">diuidas in 74314. </s>
            <s xml:id="echoid-s2047" xml:space="preserve">proue-
              <lb/>
            nient 47564. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">arcus illius ſinus 28. </s>
            <s xml:id="echoid-s2049" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2050" xml:space="preserve">24. </s>
            <s xml:id="echoid-s2051" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2052" xml:space="preserve">altitudo ſcilicet Solis in circulo uerticali.</s>
            <s xml:id="echoid-s2053" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div57" type="section" level="1" n="33">
          <head xml:id="echoid-head37" xml:space="preserve">PRONVNCIATVM XXI.</head>
          <p>
            <s xml:id="echoid-s2054" xml:space="preserve">Altitudinem ſeu eleuationem poli ex altitudine Solis in circulo uerticali
              <lb/>
            inquirere.</s>
            <s xml:id="echoid-s2055" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2056" xml:space="preserve">Pronunciatũ hoc planê inuerſo modo ꝓpoſitũ eſt cũ ſuperiori, ſi ergo altitudinem po
              <lb/>
              <note position="left" xlink:label="note-0042-03" xlink:href="note-0042-03a" xml:space="preserve">
                <emph style="it">Areatim.</emph>
              </note>
            li ſic q̊ ſcire deſideras rurſus utrũ tibi ſinũ ꝓpone, puta ſinũ altitudinis Solis in circu
              <lb/>
            lo uerticali & </s>
            <s xml:id="echoid-s2057" xml:space="preserve">declinationis, minorem duc in ſinũ totũ, ꝓductũ deinde in maiorem diui-
              <lb/>
              <note position="left" xlink:label="note-0042-04" xlink:href="note-0042-04a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            de, & </s>
            <s xml:id="echoid-s2058" xml:space="preserve">arcus ſinus q̊tientis exhibebit tibi altitudinem poli tuæ regiõis. </s>
            <s xml:id="echoid-s2059" xml:space="preserve">?</s>
            <s xml:id="echoid-s2060" xml:space="preserve">? Accipe & </s>
            <s xml:id="echoid-s2061" xml:space="preserve">hu
              <lb/>
            iusrei exemplũ, Eſto ut ſit mihi eleuatio poli incognita, eo autem die quo intronizatus
              <lb/>
            eſt ampliſs. </s>
            <s xml:id="echoid-s2062" xml:space="preserve">ille pater Epiſcopus Auguſtanus, altitudinem Solis inuentã iã & </s>
            <s xml:id="echoid-s2063" xml:space="preserve">obſerua tã
              <lb/>
            habeo in circulo uerticali ad 28. </s>
            <s xml:id="echoid-s2064" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2065" xml:space="preserve">24. </s>
            <s xml:id="echoid-s2066" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2067" xml:space="preserve">ſinũ igitur declinationis, puta minorẽ 35347
              <lb/>
            duco in ſinum totũ, productũ diuido in ſinum altitudinis, ſcilicet 47564. </s>
            <s xml:id="echoid-s2068" xml:space="preserve">& </s>
            <s xml:id="echoid-s2069" xml:space="preserve">proueniunt in
              <lb/>
            quotiente 74312. </s>
            <s xml:id="echoid-s2070" xml:space="preserve">arcus illius eſt 48. </s>
            <s xml:id="echoid-s2071" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2072" xml:space="preserve">eleuatio poli inquiſita ad locũ intronizatiõis.</s>
            <s xml:id="echoid-s2073" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div59" type="section" level="1" n="34">
          <head xml:id="echoid-head38" xml:space="preserve">PRONVNCIATVM XXII.</head>
          <p>
            <s xml:id="echoid-s2074" xml:space="preserve">Gradum Solis & </s>
            <s xml:id="echoid-s2075" xml:space="preserve">quotidie & </s>
            <s xml:id="echoid-s2076" xml:space="preserve">expedite inuenire ex altitudine eiuſdem in
              <lb/>
            circulo uerticali, ſi modo Sol ſuerit in ſignis ſeptentrionalibus.</s>
            <s xml:id="echoid-s2077" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2078" xml:space="preserve">Iam antea ꝓnũciato 20. </s>
            <s xml:id="echoid-s2079" xml:space="preserve">admonitus es, Solem nũ̈ attingere cir culũ uerticalem, niſi
              <lb/>
            in aliq̊ ſigno℞ ſeptentrionaliũ fuerit. </s>
            <s xml:id="echoid-s2080" xml:space="preserve">actũ ita egeris, ſi à fefto Michaelis ꝑ totã hyemẽ
              <lb/>
            uſ ad ferias D. </s>
            <s xml:id="echoid-s2081" xml:space="preserve">Gregorij in quadrageſima gradum Solis ex altitudine ipſius in circulo
              <lb/>
            uerticali inuenire labores, ꝗa tunc ipſum attingere nõ poteſt. </s>
            <s xml:id="echoid-s2082" xml:space="preserve">Verum in æſtate quando
              <lb/>
              <note position="left" xlink:label="note-0042-05" xlink:href="note-0042-05a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
              </note>
            eũ tangit, & </s>
            <s xml:id="echoid-s2083" xml:space="preserve">inde gradũ Solis ſcire cupis, duc ſinũ altitudinis Solis in cir culo uerticali, in
              <lb/>
            ſinũ altitudinis poli, & </s>
            <s xml:id="echoid-s2084" xml:space="preserve">diuide ꝓductũ in ſinũ totũ, mox quære arcũ q̊tientis, is tibi mon-
              <lb/>
            ſtrabit declinationẽ Solis abæ ꝗnoctiali, deinde adhuc quære ꝑ pronunciatũ 6. </s>
            <s xml:id="echoid-s2085" xml:space="preserve">gradum
              <lb/>
            eclypticæ huic de clinatiõi reſpõi reſpõdentem, & </s>
            <s xml:id="echoid-s2086" xml:space="preserve">is ſanè eſt gradus Solis quæſitus. </s>
            <s xml:id="echoid-s2087" xml:space="preserve">?</s>
            <s xml:id="echoid-s2088" xml:space="preserve">? Exem
              <lb/>
              <note position="left" xlink:label="note-0042-06" xlink:href="note-0042-06a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            plo res erit apertior: </s>
            <s xml:id="echoid-s2089" xml:space="preserve">Eſto, in die intronizatiõis fuerit Sol in circulo uerticali 28. </s>
            <s xml:id="echoid-s2090" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2091" xml:space="preserve">24.
              <lb/>
            </s>
            <s xml:id="echoid-s2092" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2093" xml:space="preserve">& </s>
            <s xml:id="echoid-s2094" xml:space="preserve">ibidẽ ubi illa facta eſt, ſit altitudo poli 48. </s>
            <s xml:id="echoid-s2095" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2096" xml:space="preserve">Iam nũc ſinũ altitudinis poli 74314. </s>
            <s xml:id="echoid-s2097" xml:space="preserve">
              <lb/>
            duco in ſinũ altitudinis Solis in circulo uerticali 47564. </s>
            <s xml:id="echoid-s2098" xml:space="preserve">ꝓductũ diuido in ſinũ totum, & </s>
            <s xml:id="echoid-s2099" xml:space="preserve">
              <lb/>
            in quotiente prodibunt 35347. </s>
            <s xml:id="echoid-s2100" xml:space="preserve">arcus illius eſt declinatio Solis quæſita 20. </s>
            <s xml:id="echoid-s2101" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2102" xml:space="preserve">42. </s>
            <s xml:id="echoid-s2103" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2104" xml:space="preserve">
              <lb/>
            Nũc inuenies tandem ex ꝓnunciato 6. </s>
            <s xml:id="echoid-s2105" xml:space="preserve">Solem eſſe in 2. </s>
            <s xml:id="echoid-s2106" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2107" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2108" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2109" xml:space="preserve">II q̊d erat in ꝗrendũ.</s>
            <s xml:id="echoid-s2110" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div61" type="section" level="1" n="35">
          <head xml:id="echoid-head39" xml:space="preserve">PRONVNCIATVM XXIII.</head>
          <p>
            <s xml:id="echoid-s2111" xml:space="preserve">Cognita iam & </s>
            <s xml:id="echoid-s2112" xml:space="preserve">altitudine Solis in circulo uerticali, & </s>
            <s xml:id="echoid-s2113" xml:space="preserve">eleuatione poli, per
              <lb/>
            utran illam amplitudinem Solis ad eum diem, quo altitudinem Solis in
              <lb/>
            circulo uerticali obſeruaſti, inuenire.</s>
            <s xml:id="echoid-s2114" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2115" xml:space="preserve">Iam ſupra ꝓnunciato 12. </s>
            <s xml:id="echoid-s2116" xml:space="preserve">docuimus inuentionẽ amplitudinis Solis ortiuæ ex eleuatio
              <lb/>
            ne poli & </s>
            <s xml:id="echoid-s2117" xml:space="preserve">declinatione Solis, nunc aũt eandem illã docebimus te colligere ex altitudine
              <lb/>
              <note position="left" xlink:label="note-0042-07" xlink:href="note-0042-07a" xml:space="preserve">
                <emph style="it">Illud habe-</emph>
                <lb/>
                <emph style="it">bis per in-</emph>
                <lb/>
                <emph style="it">troitum</emph>
                <lb/>
                <emph style="it">arealem.</emph>
              </note>
            Solis in circulo uerticali & </s>
            <s xml:id="echoid-s2118" xml:space="preserve">eleuatiõe poli, Principio duc ſinũ altitudinis uerticalis in ſinũ
              <lb/>
            totũ, productũ diuide in ſinum complementi altitudinis poli, quotientem in ſe multipli-
              <lb/>
            ca quadrate, ſimiliter quo quadrate in ſe ducito ſinũ altitudinis Solis uerticalẽ, ꝗ̃dratũ
              <lb/>
            illud ſubtrahe à priori numero quadrato, ex reſiduo quære radicem quadratã, radicis </s>
          </p>
        </div>
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