Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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    <echo version="1.0RC">
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        <div xml:id="echoid-div83" type="section" level="1" n="46">
          <p>
            <s xml:id="echoid-s2842" xml:space="preserve">
              <pb file="0049" n="49" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
            traho à 90. </s>
            <s xml:id="echoid-s2843" xml:space="preserve">& </s>
            <s xml:id="echoid-s2844" xml:space="preserve">reliqui ſunt gradus 45. </s>
            <s xml:id="echoid-s2845" xml:space="preserve">ſinus eſt 70710. </s>
            <s xml:id="echoid-s2846" xml:space="preserve">quo ſubtracto à ſinu toto, manent
              <lb/>
            29290. </s>
            <s xml:id="echoid-s2847" xml:space="preserve">ſinus ille uerſus trium horarum, quos etiam conuertere oportet, ſicut in differẽtia
              <lb/>
            aſcenſionali factum eſt, ſic enim regula cõſtituenda eſt proportionũ, 100000 dant 93544
              <lb/>
            quid igitur proueniet ex 29290? </s>
            <s xml:id="echoid-s2848" xml:space="preserve">iuxta operationem inuenio 27399. </s>
            <s xml:id="echoid-s2849" xml:space="preserve">ea ſubtraho à ſinu to
              <lb/>
            to huius operationis, & </s>
            <s xml:id="echoid-s2850" xml:space="preserve">remanent 105406. </s>
            <s xml:id="echoid-s2851" xml:space="preserve">At ſic rurſus propo@o regulam, 100000.
              <lb/>
            </s>
            <s xml:id="echoid-s2852" xml:space="preserve">dant 66913. </s>
            <s xml:id="echoid-s2853" xml:space="preserve">(qui ſinus eſt complementi altitudinis poli) quid da@unt 105406? </s>
            <s xml:id="echoid-s2854" xml:space="preserve">inde aũt
              <lb/>
            per multiplicationem & </s>
            <s xml:id="echoid-s2855" xml:space="preserve">diuiſionem reſultant in quotiente 70530. </s>
            <s xml:id="echoid-s2856" xml:space="preserve">arcus illius 44. </s>
            <s xml:id="echoid-s2857" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2858" xml:space="preserve">
              <lb/>
            52. </s>
            <s xml:id="echoid-s2859" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2860" xml:space="preserve">quibus manifeſta fit altitudo Solis tantopere quæſita.</s>
            <s xml:id="echoid-s2861" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div85" type="section" level="1" n="47">
          <head xml:id="echoid-head51" xml:space="preserve">PRONVNCIATVM XXXV.</head>
          <p>
            <s xml:id="echoid-s2862" xml:space="preserve">Eandem Solis altitudinem ſuper horizõtem quacun hora, & </s>
            <s xml:id="echoid-s2863" xml:space="preserve">ubiuis gen
              <lb/>
            tium diuerſaratione indagare.</s>
            <s xml:id="echoid-s2864" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2865" xml:space="preserve">Vbi iã ex 31. </s>
            <s xml:id="echoid-s2866" xml:space="preserve">& </s>
            <s xml:id="echoid-s2867" xml:space="preserve">32. </s>
            <s xml:id="echoid-s2868" xml:space="preserve">pronunc. </s>
            <s xml:id="echoid-s2869" xml:space="preserve">angulũ didiciſti aſcẽdentis, deinde & </s>
            <s xml:id="echoid-s2870" xml:space="preserve">aſcendentis gradũ
              <lb/>
              <note position="right" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
                <lb/>
                <emph style="it">in quadran</emph>
                <lb/>
                <emph style="it">te hoc perſi</emph>
                <lb/>
                <emph style="it">aes.</emph>
              </note>
            ex pronunc. </s>
            <s xml:id="echoid-s2871" xml:space="preserve">30, mox à gradu Solis numera uſ ad gradũ aſcendentis, ſinũ eius duc in ſi-
              <lb/>
            num anguli eclypticæ & </s>
            <s xml:id="echoid-s2872" xml:space="preserve">horizontis, ꝓductũ diuide in ſinũ totũ, hinc ſi quæras quotiẽtis
              <lb/>
            arcũ, is ipſe arguit altitudinẽ Solis quã quærebas. </s>
            <s xml:id="echoid-s2873" xml:space="preserve">Atqui etiã hoc tibi obſeruandum eſt, ꝙ
              <lb/>
            ſemper duæ horæ, altera ante, altera poſt meridiem æ qualẽ habent altitudinẽ, puta ante
              <lb/>
            & </s>
            <s xml:id="echoid-s2874" xml:space="preserve">poſt meridiẽ æqualiter cõputãdo, ſic em̃ 11. </s>
            <s xml:id="echoid-s2875" xml:space="preserve">ante meridiẽ & </s>
            <s xml:id="echoid-s2876" xml:space="preserve">prima pomeridiana eandẽ
              <lb/>
            habent altitudinẽ, ſimiliter & </s>
            <s xml:id="echoid-s2877" xml:space="preserve">10. </s>
            <s xml:id="echoid-s2878" xml:space="preserve">ante & </s>
            <s xml:id="echoid-s2879" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2880" xml:space="preserve">poſt meridiẽ &</s>
            <s xml:id="echoid-s2881" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2882" xml:space="preserve">Inuenta igitur altitudine una
              <lb/>
            quacũ tandem, ſiue ante ſiue poſt meridiem, alterã amplius quærere neceſſe nõ eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2883" xml:space="preserve">?</s>
            <s xml:id="echoid-s2884" xml:space="preserve">? Vis & </s>
            <s xml:id="echoid-s2885" xml:space="preserve">hic exemplũ dari tibi, ne fruſtra laboraſſe uideamur? </s>
            <s xml:id="echoid-s2886" xml:space="preserve">Ecce ex propoſitione 30. </s>
            <s xml:id="echoid-s2887" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0049-02" xlink:href="note-0049-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            inueni ſub ipſam horã intronizationis 5. </s>
            <s xml:id="echoid-s2888" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2889" xml:space="preserve">25. </s>
            <s xml:id="echoid-s2890" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2891" xml:space="preserve">♌ fuiſſe in aſcendente, deinde ꝑ 31.
              <lb/>
            </s>
            <s xml:id="echoid-s2892" xml:space="preserve">& </s>
            <s xml:id="echoid-s2893" xml:space="preserve">32. </s>
            <s xml:id="echoid-s2894" xml:space="preserve">propoſitiones inueni etiã angulũ eclypticæ & </s>
            <s xml:id="echoid-s2895" xml:space="preserve">horizontis 52. </s>
            <s xml:id="echoid-s2896" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2897" xml:space="preserve">21. </s>
            <s xml:id="echoid-s2898" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2899" xml:space="preserve">Nũc por-
              <lb/>
            rò accipienda mihi eſt diſtantia gradus Solis à gradu aſcendẽtis, ea´ eſt 62. </s>
            <s xml:id="echoid-s2900" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2901" xml:space="preserve">59. </s>
            <s xml:id="echoid-s2902" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2903" xml:space="preserve">
              <lb/>
            Contingit etiam interdum, ꝙ diſtantia Solis ab aſcendente maior ſit 90. </s>
            <s xml:id="echoid-s2904" xml:space="preserve">gradibus, & </s>
            <s xml:id="echoid-s2905" xml:space="preserve">tũc
              <lb/>
            ſanè diſtantia illa ſubtrahenda tibi eſt à ſemicirculo, & </s>
            <s xml:id="echoid-s2906" xml:space="preserve">remanebit arcus uerus huius ope
              <lb/>
            rationis. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">Iam propono mihi ſinũ anguli 52. </s>
            <s xml:id="echoid-s2908" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2909" xml:space="preserve">21. </s>
            <s xml:id="echoid-s2910" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2911" xml:space="preserve">ſcilicet 79175. </s>
            <s xml:id="echoid-s2912" xml:space="preserve">eũ duco in ſinũ ar-
              <lb/>
            cus à gradu Solis ad gradũ aſcendentis, qui fuit 62. </s>
            <s xml:id="echoid-s2913" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2914" xml:space="preserve">59. </s>
            <s xml:id="echoid-s2915" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2916" xml:space="preserve">89087. </s>
            <s xml:id="echoid-s2917" xml:space="preserve">ſi ergo unũ in alte
              <lb/>
            rũ duxero, productũ in ſinũ totũ diuiſero, prouenient in quotiente 70534. </s>
            <s xml:id="echoid-s2918" xml:space="preserve">arcus eius eſt
              <lb/>
            44. </s>
            <s xml:id="echoid-s2919" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2920" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2921" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2922" xml:space="preserve">altitudo nimirũ Solis ad horam, imò & </s>
            <s xml:id="echoid-s2923" xml:space="preserve">minutum ipſius intronizationis.</s>
            <s xml:id="echoid-s2924" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div87" type="section" level="1" n="48">
          <head xml:id="echoid-head52" xml:space="preserve">PRONVNCIATVM XXXVI.</head>
          <p>
            <s xml:id="echoid-s2925" xml:space="preserve">Rurſus alio modo cognoſcere altitudinem Solis ſuper horizontem, omni
              <lb/>
            die & </s>
            <s xml:id="echoid-s2926" xml:space="preserve">momento per uniuerſum terrarum orbem.</s>
            <s xml:id="echoid-s2927" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2928" xml:space="preserve">Operæpreciũ hic principio fuerit noſſe cõplemẽtũ altitudinis poli & </s>
            <s xml:id="echoid-s2929" xml:space="preserve">declinatiõem So
              <lb/>
            lis, deinde q̊ diſtantiã Solis à meridiano, hoc eſt diſtantiã horariã, puta q̊t horis ante uel
              <lb/>
              <note position="right" xlink:label="note-0049-03" xlink:href="note-0049-03a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">introitus.</emph>
              </note>
            poſt meridiẽ altitudo illa Solis debeat ſupputari. </s>
            <s xml:id="echoid-s2930" xml:space="preserve">Primũ ita oĩm duc ſinũ cõplemẽti de
              <lb/>
            clinatiõis Solis in ſinũ diſtãtiæ ante uel poſt meridiẽ, ꝓductũ diuide in ſinũ totũ, & </s>
            <s xml:id="echoid-s2931" xml:space="preserve">quo-
              <lb/>
            tientẽ ſepone ſeorſim, qm̃ is eſt ſinus arcus diſtãtiæ Solis ab ortu æquatoris, quotiẽti op-
              <lb/>
              <note position="right" xlink:label="note-0049-04" xlink:href="note-0049-04a" xml:space="preserve">
                <emph style="it">Arealis.</emph>
              </note>
            pone ſinũ declinationis minorẽ, & </s>
            <s xml:id="echoid-s2932" xml:space="preserve">duc in ſinũ totũ, ꝓductũ in maiorẽ diuide, & </s>
            <s xml:id="echoid-s2933" xml:space="preserve">arcũ quo
              <lb/>
            tientis adde ad cõplementũ altitudinis poli, Sole exiſtente in ſigno aliquo ſeptentrionali
              <lb/>
            uel ſubtrahe ab eo ubi Sol fuerit in aliquo ſignorũ meridionaliũ, quicꝗd ex hac ſiue addi-
              <lb/>
            tione ſiue ſubtractione ꝓuenerit, uel reliquũ manſerit, dicet̃ angulus operationis, ꝗ ſi fue-
              <lb/>
            erit quadrãs circuli, iã ipſe ꝑ ſe oſtẽdit altitudinẽ Solis quæſitã, quã antea altitudinẽ Solis
              <lb/>
            uerticalẽ diximus. </s>
            <s xml:id="echoid-s2934" xml:space="preserve">Qđ ſi autẽ angulus operatiõis maior fuerit ̈ 90. </s>
            <s xml:id="echoid-s2935" xml:space="preserve">ſubtrahe eũ à ſemicir
              <lb/>
            culo, & </s>
            <s xml:id="echoid-s2936" xml:space="preserve">tunc tandẽ remanebit angulus uerus operatiõis, ſinũ anguli huius duc in ſinũ pri
              <lb/>
              <note position="right" xlink:label="note-0049-05" xlink:href="note-0049-05a" xml:space="preserve">
                <emph style="it">Lateralis.</emph>
              </note>
            mi q̊tientis, ꝓductũ diuide cum ſinu toto, & </s>
            <s xml:id="echoid-s2937" xml:space="preserve">arcus quotientis mõſtrabit altitudinem Solis
              <lb/>
            quã quærebas, ſed exemplo adiuncto melius operationẽ hanc intelliges. </s>
            <s xml:id="echoid-s2938" xml:space="preserve">?</s>
            <s xml:id="echoid-s2939" xml:space="preserve">? Iterũ hic
              <lb/>
              <note position="right" xlink:label="note-0049-06" xlink:href="note-0049-06a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            mihi ꝓpono horã intronizationis ampliſsimi patris & </s>
            <s xml:id="echoid-s2940" xml:space="preserve">ornatiſsimi Præſulis Auguſtẽſis
              <lb/>
            quæ fuit hora 9. </s>
            <s xml:id="echoid-s2941" xml:space="preserve">ante meridiẽ, eius diſtãtia à meridie eſt 3. </s>
            <s xml:id="echoid-s2942" xml:space="preserve">horarũ, ꝗ ſunt gradus 45. </s>
            <s xml:id="echoid-s2943" xml:space="preserve">ſemꝑ
              <lb/>
            em̃ in una hora oriunt̃ 15. </s>
            <s xml:id="echoid-s2944" xml:space="preserve">gradus æquino ctialis ſuꝑ horizontẽ ab ortu uerſus occaſum, ſi
              <lb/>
            nus illius eſt 70710. </s>
            <s xml:id="echoid-s2945" xml:space="preserve">declinatio Solis 20. </s>
            <s xml:id="echoid-s2946" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">42. </s>
            <s xml:id="echoid-s2948" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2949" xml:space="preserve">cõplementũ eius 69. </s>
            <s xml:id="echoid-s2950" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2951" xml:space="preserve">18. </s>
            <s xml:id="echoid-s2952" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2953" xml:space="preserve">ſinus
              <lb/>
            uero 93544. </s>
            <s xml:id="echoid-s2954" xml:space="preserve">ſinũ iſto℞ ſi duxero in alterũ, productũ autem diuiſero in ſinum totum, </s>
          </p>
        </div>
      </text>
    </echo>
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