Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis
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        <div xml:id="echoid-div105" type="section" level="1" n="57">
          <p>
            <s xml:id="echoid-s3528" xml:space="preserve">
              <pb file="0055" n="55" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
            ter & </s>
            <s xml:id="echoid-s3529" xml:space="preserve">ſinum complementi altitudinis Solis ſupra horizontem, quam ſex rationibus di-
              <lb/>
              <note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">
                <emph style="it">Hoc per la</emph>
                <lb/>
                <emph style="it">teralẽ pro-</emph>
                <lb/>
                <emph style="it">aſſum aſſe</emph>
                <lb/>
                <emph style="it">queris</emph>
              .</note>
            diciſti inuenire, minorem ex ijs duc in totum, & </s>
            <s xml:id="echoid-s3530" xml:space="preserve">productum inde diuide in maiorem pro
              <lb/>
            poſitorũ ſinuum, arcus quotientis à 90. </s>
            <s xml:id="echoid-s3531" xml:space="preserve">ſubtractus, reliquam faciet diſtantiam Solis ho-
              <lb/>
            rizontalẽ ab ortu æquatoris, hoc ſcilicet quod antea Azimuth appellauimus. </s>
            <s xml:id="echoid-s3532" xml:space="preserve">?</s>
            <s xml:id="echoid-s3533" xml:space="preserve">? Eius
              <lb/>
              <note position="right" xlink:label="note-0055-02" xlink:href="note-0055-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſcopi</emph>
              .</note>
            rei gratia exemplũ hoc conſidera. </s>
            <s xml:id="echoid-s3534" xml:space="preserve">Volo ſcire diſtantiam hanc ad horam intronizationis
              <lb/>
            & </s>
            <s xml:id="echoid-s3535" xml:space="preserve">quia diuerſismodis iam ſupra altitudinem Solis ſemper eandem repperi, ſcilicet 44.
              <lb/>
            </s>
            <s xml:id="echoid-s3536" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3537" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3538" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3539" xml:space="preserve">Complementum eius eſt 45. </s>
            <s xml:id="echoid-s3540" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3541" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3542" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3543" xml:space="preserve">ſinus ipſius 70875. </s>
            <s xml:id="echoid-s3544" xml:space="preserve">& </s>
            <s xml:id="echoid-s3545" xml:space="preserve">hic quia maior
              <lb/>
            eſt, diuiſoris fungitur officio. </s>
            <s xml:id="echoid-s3546" xml:space="preserve">Deinde per pronunc. </s>
            <s xml:id="echoid-s3547" xml:space="preserve">39. </s>
            <s xml:id="echoid-s3548" xml:space="preserve">inueni diſtantiam Solis ab ortu
              <lb/>
            æquatoris 48. </s>
            <s xml:id="echoid-s3549" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3550" xml:space="preserve">35. </s>
            <s xml:id="echoid-s3551" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3552" xml:space="preserve">complementum ipſius 41. </s>
            <s xml:id="echoid-s3553" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3554" xml:space="preserve">25. </s>
            <s xml:id="echoid-s3555" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3556" xml:space="preserve">ſinum eius 66145. </s>
            <s xml:id="echoid-s3557" xml:space="preserve">duco
              <lb/>
            in ſinum totum, productum in diuiſorem prius cognitum diuido, & </s>
            <s xml:id="echoid-s3558" xml:space="preserve">prouenient in quo
              <lb/>
            tiente 93326. </s>
            <s xml:id="echoid-s3559" xml:space="preserve">arcum illius 68. </s>
            <s xml:id="echoid-s3560" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3561" xml:space="preserve">56. </s>
            <s xml:id="echoid-s3562" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3563" xml:space="preserve">ſi ſubtraxero à 90. </s>
            <s xml:id="echoid-s3564" xml:space="preserve">remanebunt 21. </s>
            <s xml:id="echoid-s3565" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3566" xml:space="preserve">3, mi. </s>
            <s xml:id="echoid-s3567" xml:space="preserve">
              <lb/>
            Azimuth ſcilicet illud rurſus alia ratione inuentũ, ̈ ſupra in 42. </s>
            <s xml:id="echoid-s3568" xml:space="preserve">& </s>
            <s xml:id="echoid-s3569" xml:space="preserve">43. </s>
            <s xml:id="echoid-s3570" xml:space="preserve">propoſitiõibus.</s>
            <s xml:id="echoid-s3571" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div107" type="section" level="1" n="58">
          <head xml:id="echoid-head62" xml:space="preserve">PRONVNCIATVM XLVI.</head>
          <p>
            <s xml:id="echoid-s3572" xml:space="preserve">Angulum quem facit eclyptica cum circulo altitudinis, quem Sol ſiue
              <lb/>
            ſtella attingit, ad horam aliquam propoſitam expedite cognoſcere.</s>
            <s xml:id="echoid-s3573" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3574" xml:space="preserve">Primum omnium diſces hic inuenire angulum quem facit circulus altitudinis
              <lb/>
            cum circulo maioriducto ex polo mundiper corpus ſolare, duc ita ſinum diſtantiæ So
              <lb/>
            lis à meridie in ſinum complementi altitudinis poli, productum diuide in totum ſinum,
              <lb/>
              <note position="right" xlink:label="note-0055-03" xlink:href="note-0055-03a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">ingreſſus</emph>
              .</note>
            & </s>
            <s xml:id="echoid-s3575" xml:space="preserve">quotientem reſerua, ei´ adiunge ſinum complementi altitudinis Solis, minorem duc
              <lb/>
            in ſinum perfectum, & </s>
            <s xml:id="echoid-s3576" xml:space="preserve">rurſus diuide productum in maiorem, arcus quotientis erit ipſe
              <lb/>
              <note position="right" xlink:label="note-0055-04" xlink:href="note-0055-04a" xml:space="preserve">
                <emph style="it">Arealis in-</emph>
                <lb/>
                <emph style="it">greſſus</emph>
              .</note>
            angulus, de quo iam dixi. </s>
            <s xml:id="echoid-s3577" xml:space="preserve">Quod ſi hora obſeruatiõis fuerit ante meridiem, addeangulũ
              <lb/>
            hunc inuentum ad angulum, quem eclyptica facit cum meridiano, ſed ſi pomeridiana ex
              <lb/>
            titerit, ſubtrahe iſtum angulũ ab angulo eclypticæ & </s>
            <s xml:id="echoid-s3578" xml:space="preserve">meridiani, & </s>
            <s xml:id="echoid-s3579" xml:space="preserve">remanebit angulus
              <lb/>
              <note position="right" xlink:label="note-0055-05" xlink:href="note-0055-05a" xml:space="preserve">EXEM.
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi</emph>
              .</note>
            optatus. </s>
            <s xml:id="echoid-s3580" xml:space="preserve">?</s>
            <s xml:id="echoid-s3581" xml:space="preserve">? Exemplo res erit facilior, diſtantia Solis ab aſcendente ſecundum eclypti-
              <lb/>
            cam eſt 45. </s>
            <s xml:id="echoid-s3582" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3583" xml:space="preserve">ſinus eius 70710. </s>
            <s xml:id="echoid-s3584" xml:space="preserve">eum duc in ſinum cõplementi altitudinis poli, ſcilicet
              <lb/>
            66913, productum diuide in ſinum totum, & </s>
            <s xml:id="echoid-s3585" xml:space="preserve">quotientem tanquam minorem rurſus duc
              <lb/>
            in totum ſinum, illud´ productum diuide in ſinum complemẽti altitudinis poli, ſcilicet
              <lb/>
            70875. </s>
            <s xml:id="echoid-s3586" xml:space="preserve">& </s>
            <s xml:id="echoid-s3587" xml:space="preserve">quotiens dabit 66756. </s>
            <s xml:id="echoid-s3588" xml:space="preserve">arcus eius 41. </s>
            <s xml:id="echoid-s3589" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3590" xml:space="preserve">53. </s>
            <s xml:id="echoid-s3591" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3592" xml:space="preserve">erit angulus inter circulum al
              <lb/>
            ritudinis & </s>
            <s xml:id="echoid-s3593" xml:space="preserve">circulum magnum per polos mũdi ductum comprehenſus, hunc ſi addas ad
              <lb/>
            angulum quem facit eclyptica iuxta illum gradum Solis cum meridiano (quando intro
              <lb/>
            nizatïo illa ante meridiem fa cta eſt) prodibũt 120, gra. </s>
            <s xml:id="echoid-s3594" xml:space="preserve">30. </s>
            <s xml:id="echoid-s3595" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3596" xml:space="preserve">qui angulus eſt cõprehen
              <lb/>
            ſus inter circulũ altitudinis & </s>
            <s xml:id="echoid-s3597" xml:space="preserve">eclypticã uerſus ſeptentrionẽ, eum ſubtrahe de ſemicircu-
              <lb/>
            lo, & </s>
            <s xml:id="echoid-s3598" xml:space="preserve">remanebunt 59. </s>
            <s xml:id="echoid-s3599" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3600" xml:space="preserve">30. </s>
            <s xml:id="echoid-s3601" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3602" xml:space="preserve">at is uerus eſt angulus quem quærebamus,</s>
          </p>
        </div>
        <div xml:id="echoid-div109" type="section" level="1" n="59">
          <head xml:id="echoid-head63" xml:space="preserve">PRONVNCIATVM XLVII.</head>
          <p>
            <s xml:id="echoid-s3603" xml:space="preserve">Eundẽ hũc angulũ eclypticę & </s>
            <s xml:id="echoid-s3604" xml:space="preserve">altitudĩs circuli alio adhuc modo inueſtigare.</s>
            <s xml:id="echoid-s3605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3606" xml:space="preserve">Propone & </s>
            <s xml:id="echoid-s3607" xml:space="preserve">hic tibi ſinum complementi diſtantiæ Solis ab aſcendente, ſimul´ ſinum
              <lb/>
              <note position="right" xlink:label="note-0055-06" xlink:href="note-0055-06a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
              </note>
            complementi altitudinis Solis, minorem duc in totum, productum diuide in maiorẽ nu-
              <lb/>
              <note position="right" xlink:label="note-0055-07" xlink:href="note-0055-07a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
              </note>
            merum ſinuum, quotientem rurſus duc in ſinum anguli eclypticæ & </s>
            <s xml:id="echoid-s3608" xml:space="preserve">horizontis quem
              <lb/>
            faciunt tempore conſiderationis, productum diuide in ſinũ totum, quotiente ſubtracto à
              <lb/>
              <note position="right" xlink:label="note-0055-08" xlink:href="note-0055-08a" xml:space="preserve">EXEM.
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſcopi</emph>
              .</note>
            quadrante, remanebit angulus optatus, ſicut in exemplo ſubiecto conſpicis. </s>
            <s xml:id="echoid-s3609" xml:space="preserve">?</s>
            <s xml:id="echoid-s3610" xml:space="preserve">? Fuerit
              <lb/>
            ergo in die intronizationis diſtantia Solis ab aſcẽdente 62. </s>
            <s xml:id="echoid-s3611" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3612" xml:space="preserve">59. </s>
            <s xml:id="echoid-s3613" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3614" xml:space="preserve">Complementũ
              <lb/>
            eius eſt 27, gra. </s>
            <s xml:id="echoid-s3615" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3616" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3617" xml:space="preserve">ſinum illius 45424. </s>
            <s xml:id="echoid-s3618" xml:space="preserve">tan̈ minorẽ numerũ duc in ſinũ totũ, productũ
              <lb/>
            diuide in ſinum cõplementi altitudinis Solis. </s>
            <s xml:id="echoid-s3619" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3620" xml:space="preserve">45. </s>
            <s xml:id="echoid-s3621" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3622" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3623" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3624" xml:space="preserve">is eſt 70875. </s>
            <s xml:id="echoid-s3625" xml:space="preserve">& </s>
            <s xml:id="echoid-s3626" xml:space="preserve">proueniũt
              <lb/>
            in quotiente 60490. </s>
            <s xml:id="echoid-s3627" xml:space="preserve">hunc iterum duc in ſinum anguli eclypticæ & </s>
            <s xml:id="echoid-s3628" xml:space="preserve">horizontis iuxta gra-
              <lb/>
            dum aſcendentis, ſcilicet 5. </s>
            <s xml:id="echoid-s3629" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3630" xml:space="preserve">25. </s>
            <s xml:id="echoid-s3631" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3632" xml:space="preserve">♌ cauſſatum, quia antea ſæpius repræſentabat
              <lb/>
            52. </s>
            <s xml:id="echoid-s3633" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3634" xml:space="preserve">21. </s>
            <s xml:id="echoid-s3635" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3636" xml:space="preserve">ſinus autem eius eſt 79175, mox diuide productum in ſinum totum, & </s>
            <s xml:id="echoid-s3637" xml:space="preserve">quo
              <lb/>
            tiens dabit 50743. </s>
            <s xml:id="echoid-s3638" xml:space="preserve">arcus illius erit 30. </s>
            <s xml:id="echoid-s3639" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3640" xml:space="preserve">30. </s>
            <s xml:id="echoid-s3641" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3642" xml:space="preserve">eo ſubtracto â quadra circuli, rema-
              <lb/>
            nent 59. </s>
            <s xml:id="echoid-s3643" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3644" xml:space="preserve">30. </s>
            <s xml:id="echoid-s3645" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3646" xml:space="preserve">non aliter at in exemplo ſuperioris propoſitionis.</s>
            <s xml:id="echoid-s3647" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div111" type="section" level="1" n="60">
          <head xml:id="echoid-head64" xml:space="preserve">PRONVNCIATVM XLVIII.</head>
          <p>
            <s xml:id="echoid-s3648" xml:space="preserve">Angulum eum ipſum quem duabus propoſitionibus oſtendimus, adhuc
              <lb/>
            alia ratione indicare.</s>
            <s xml:id="echoid-s3649" xml:space="preserve"/>
          </p>
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