Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

Table of contents

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[51.] PRONVNCIATVM XXXIX.
Page: 51
[52.] PRONVNCIATVM XL.
Page: 52
[53.] PRONVNCIATVM XLI.
Page: 52
[54.] PRONVNCIATVM XLII.
Page: 53
[55.] PRONVNCIATVM XLIII.
Page: 54
[56.] PRONVNCIATVM XLIIII.
Page: 54
[57.] PRONVNCIATVM XLV.
Page: 54
[58.] PRONVNCIATVM XLVI.
Page: 55
[59.] PRONVNCIATVM XLVII.
Page: 55
[60.] PRONVNCIATVM XLVIII.
Page: 55
[61.] PRONVNCIATVM XLIX.
Page: 56
[62.] PRONVNCIATVM L.
Page: 56
[63.] PRONVNCIATVM LI.
Page: 57
[64.] PRONVNCIATVM LII.
Page: 57
[65.] PRONVNCIATVM LIII.
Page: 57
[66.] PRONVNCIATVM LIIII.
Page: 58
[67.] PRONVNCIATVM LV.
Page: 58
[68.] PRONVNCIATVM LVI.
Page: 59
[69.] PRONVNCIATVM LVII.
Page: 59
[70.] PRONVNCIATVM LVIII.
Page: 61
[71.] PRONVNCIATVM LIX.
Page: 62
[72.] PRONVNCIATVM LX.
Page: 63
[73.] PRONVNCIATVM LXI.
Page: 64
[74.] PRONVNCIATVM LXII.
Page: 64
[75.] PRONVNCIATVM LXIII.
Page: 64
[76.] PRONVNCIATVM LXIIII.
Page: 65
[77.] PRONVNCIATVM LXV.
Page: 66
[78.] PRONVNCIATVM LXVI.
Page: 66
[79.] PRONVNCIATVM LXVII.
Page: 67
[80.] PRONVNCIATVM LXVIII.
Page: 68
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        <div xml:id="echoid-div91" type="section" level="1" n="50">
          <p>
            <s xml:id="echoid-s3086" xml:space="preserve">
              <pb file="0051" n="51" rhead="TABVLARVM SINVVM."/>
            li, minorem duc in totum, ꝓductũ diuide in maiorem, & </s>
            <s xml:id="echoid-s3087" xml:space="preserve">arcũ quotientis ſubtrahe à 90,
              <lb/>
              <note position="right" xlink:label="note-0051-01" xlink:href="note-0051-01a" xml:space="preserve">
                <emph style="it">Areatim.</emph>
              </note>
            ad reſiduũ adde declinationẽ ☉(sun), ſi Borealis fuerit, uel ſubtrahe, ſi extiterit meridionalis,
              <lb/>
            reſiduũ uel ꝓductũ illud, ſi quadrante minus fuerit, oſtendet inuentũ ſecundũ: </s>
            <s xml:id="echoid-s3088" xml:space="preserve">ſin maius,
              <lb/>
              <note position="right" xlink:label="note-0051-02" xlink:href="note-0051-02a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">ſecundum.</emph>
              </note>
            ſubtrahendũ erit à 90. </s>
            <s xml:id="echoid-s3089" xml:space="preserve">& </s>
            <s xml:id="echoid-s3090" xml:space="preserve">reliquũ q̊d manſerit, dicetur inuentũ ſecundũ. </s>
            <s xml:id="echoid-s3091" xml:space="preserve">Vtrun illud in-
              <lb/>
            uentum propone tibi, & </s>
            <s xml:id="echoid-s3092" xml:space="preserve">alterius ſinũ itidem duc in ſinũ alterius, productũ diuide in ſinũ
              <lb/>
              <note position="right" xlink:label="note-0051-03" xlink:href="note-0051-03a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
              </note>
            totũ, & </s>
            <s xml:id="echoid-s3093" xml:space="preserve">arcus quotientis dabit altitudinẽ Solis optatã. </s>
            <s xml:id="echoid-s3094" xml:space="preserve">?</s>
            <s xml:id="echoid-s3095" xml:space="preserve">? Exemplũ, rurſus adſumo il-
              <lb/>
              <note position="right" xlink:label="note-0051-04" xlink:href="note-0051-04a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            lud per q̊d operationem hãc ſemꝑ hactenus abſolui, id´ eo maxime, ut uideas tam diuer
              <lb/>
            ſas uias in eundem ſemper tendere finẽ. </s>
            <s xml:id="echoid-s3096" xml:space="preserve">Eſto ergo, ut Sol fuerit in 2. </s>
            <s xml:id="echoid-s3097" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3098" xml:space="preserve">26. </s>
            <s xml:id="echoid-s3099" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3100" xml:space="preserve">II, ego
              <lb/>
            uero iam ſcire cupio altitudinẽ Solis ſupra horizontẽ hora 9. </s>
            <s xml:id="echoid-s3101" xml:space="preserve">ante meridiẽ, qñ introniza
              <lb/>
            tio facta eſt, diſtãtia ꝗdem eſt 45. </s>
            <s xml:id="echoid-s3102" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3103" xml:space="preserve">ſinus eius 70710. </s>
            <s xml:id="echoid-s3104" xml:space="preserve">ſinus aũt cõplementi altitudinis
              <lb/>
            poli 42. </s>
            <s xml:id="echoid-s3105" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3106" xml:space="preserve">eſt 66913. </s>
            <s xml:id="echoid-s3107" xml:space="preserve">iã ſi alte℞ in alterum ducã, ꝓductũ in totũ diuidã, prouenient in q̊
              <lb/>
              <note position="right" xlink:label="note-0051-05" xlink:href="note-0051-05a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
                <lb/>
                <emph style="it">idem inue-</emph>
                <lb/>
                <emph style="it">nies.</emph>
              </note>
            tiente 473 14. </s>
            <s xml:id="echoid-s3108" xml:space="preserve">arcus eius eſt 28. </s>
            <s xml:id="echoid-s3109" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3110" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3111" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3112" xml:space="preserve">quo ſubtracto à quadrãte, remanent 61. </s>
            <s xml:id="echoid-s3113" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s3114" xml:space="preserve">46. </s>
            <s xml:id="echoid-s3115" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3116" xml:space="preserve">at id uocamus inuentũ primũ. </s>
            <s xml:id="echoid-s3117" xml:space="preserve">Deinde ſinũ eius propono ſcilicet 88102. </s>
            <s xml:id="echoid-s3118" xml:space="preserve">cum ſi
              <lb/>
              <note position="right" xlink:label="note-0051-06" xlink:href="note-0051-06a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">primum.</emph>
              </note>
            nu altitudinis poli 48. </s>
            <s xml:id="echoid-s3119" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3120" xml:space="preserve">743 14. </s>
            <s xml:id="echoid-s3121" xml:space="preserve">eum duco in totũ, ꝓductũ diuido in primũ illud inuen
              <lb/>
            ti primi, & </s>
            <s xml:id="echoid-s3122" xml:space="preserve">in quotiente ꝓuenient 84349. </s>
            <s xml:id="echoid-s3123" xml:space="preserve">arcus eſt 57. </s>
            <s xml:id="echoid-s3124" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3125" xml:space="preserve">31 mi. </s>
            <s xml:id="echoid-s3126" xml:space="preserve">Cõplementũ uero 32.
              <lb/>
            </s>
            <s xml:id="echoid-s3127" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3128" xml:space="preserve">29. </s>
            <s xml:id="echoid-s3129" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3130" xml:space="preserve">& </s>
            <s xml:id="echoid-s3131" xml:space="preserve">quia Sol eſt ſeptentrionalis, addo declinationẽ ipſius, & </s>
            <s xml:id="echoid-s3132" xml:space="preserve">ſimul 20. </s>
            <s xml:id="echoid-s3133" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3134" xml:space="preserve">42. </s>
            <s xml:id="echoid-s3135" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0051-07" xlink:href="note-0051-07a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">ſecundum.</emph>
              </note>
            mi. </s>
            <s xml:id="echoid-s3136" xml:space="preserve">unde prouenient 53. </s>
            <s xml:id="echoid-s3137" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3138" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3139" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3140" xml:space="preserve">inuentũ illud ſecundũ, cuius ſinus eſt 80055. </s>
            <s xml:id="echoid-s3141" xml:space="preserve">Ad ex-
              <lb/>
            tremum quũ iam ſinum alterius inuenti duxeris in alterũ, productũ quo in ſinũ totum
              <lb/>
            diuiſeris, prouenient in quotiente 70530. </s>
            <s xml:id="echoid-s3142" xml:space="preserve">arcus eius eſt 44 gra. </s>
            <s xml:id="echoid-s3143" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3144" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3145" xml:space="preserve">quæ & </s>
            <s xml:id="echoid-s3146" xml:space="preserve">altitudo eſt
              <lb/>
            Solis ad ipſum momentũ intronizationis, quã nunc quinta ratione adinueni. </s>
            <s xml:id="echoid-s3147" xml:space="preserve">Si aũt di-
              <lb/>
            ſtantia Solis data hora maior fuerit ̈ 90, tunc ſubtrahe eam à ſemicirculo, & </s>
            <s xml:id="echoid-s3148" xml:space="preserve">reſidui ſi-
              <lb/>
              <note position="right" xlink:label="note-0051-08" xlink:href="note-0051-08a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">ingreſſus</emph>
              </note>
            num duc in ſinum cõplementi altitudinis poli, & </s>
            <s xml:id="echoid-s3149" xml:space="preserve">diuide in totũ, arcũ quotientis ſubtrahe
              <lb/>
            ex quadrante, reſiduũ dicetur inuentũ primũ. </s>
            <s xml:id="echoid-s3150" xml:space="preserve">Primihuius inuenti ſinũ tibi propone, & </s>
            <s xml:id="echoid-s3151" xml:space="preserve">
              <lb/>
            ſinũ altitudinis poli, minorẽ duc in ſinũ totũ, productũ diuide in maiorẽ, de arcu quotien-
              <lb/>
              <note position="right" xlink:label="note-0051-09" xlink:href="note-0051-09a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">ingreſſus.</emph>
              </note>
            tis ſubtrahe complementũ declinationis, & </s>
            <s xml:id="echoid-s3152" xml:space="preserve">reliquũ manebit inuentũ ſecundum. </s>
            <s xml:id="echoid-s3153" xml:space="preserve">Deinde
              <lb/>
            ſi ſinum primi ducas in ſinum inuenti ſecundi, & </s>
            <s xml:id="echoid-s3154" xml:space="preserve">in totũ diuidas, arcus quotientis mon-
              <lb/>
            ſtrabit altitudinem quæſitã. </s>
            <s xml:id="echoid-s3155" xml:space="preserve">?</s>
            <s xml:id="echoid-s3156" xml:space="preserve">? Accipe & </s>
            <s xml:id="echoid-s3157" xml:space="preserve">hic exemplũ tibi. </s>
            <s xml:id="echoid-s3158" xml:space="preserve">Volo ſcire altitudinẽ Solis
              <lb/>
              <note position="right" xlink:label="note-0051-10" xlink:href="note-0051-10a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            ſupra horizontem adhorã quintã ante meridianã ipſo die intronizationis, ideo´ gradũ
              <lb/>
            & </s>
            <s xml:id="echoid-s3159" xml:space="preserve">minutũ Solis relinquo ita, ut fuerunt antea. </s>
            <s xml:id="echoid-s3160" xml:space="preserve">diſtãtia Solis à meridiano eſt 105. </s>
            <s xml:id="echoid-s3161" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3162" xml:space="preserve">dũ
              <lb/>
              <note position="right" xlink:label="note-0051-11" xlink:href="note-0051-11a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">introitus.</emph>
              </note>
            ſubtraho à ſemicirculo & </s>
            <s xml:id="echoid-s3163" xml:space="preserve">manent 75. </s>
            <s xml:id="echoid-s3164" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3165" xml:space="preserve">in reſiduo, quo℞ ſinus eſt 96592. </s>
            <s xml:id="echoid-s3166" xml:space="preserve">& </s>
            <s xml:id="echoid-s3167" xml:space="preserve">hunc duco
              <lb/>
            in ſinũ cõplementi altitudinis poli, ſcilicet 66913. </s>
            <s xml:id="echoid-s3168" xml:space="preserve">producto diuiſo per ſinũ totũ, proueni-
              <lb/>
            ent in quotiente 64632. </s>
            <s xml:id="echoid-s3169" xml:space="preserve">arcus erit 40. </s>
            <s xml:id="echoid-s3170" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3171" xml:space="preserve">16. </s>
            <s xml:id="echoid-s3172" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3173" xml:space="preserve">quẽ ſi ſubtraho à quadrante, reliqui ma-
              <lb/>
              <note position="right" xlink:label="note-0051-12" xlink:href="note-0051-12a" xml:space="preserve">
                <emph style="it">Inucntum</emph>
                <lb/>
                <emph style="it">primum.</emph>
              </note>
            nent 49. </s>
            <s xml:id="echoid-s3174" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3175" xml:space="preserve">cum 44. </s>
            <s xml:id="echoid-s3176" xml:space="preserve">minutis, inuentum puta primũ, cuius ſinũ mihi deinceps propono,
              <lb/>
            ſimiliter & </s>
            <s xml:id="echoid-s3177" xml:space="preserve">ſinum altitudinis poli 74314. </s>
            <s xml:id="echoid-s3178" xml:space="preserve">eum tanquam minorẽ duco in ſinũ totũ, & </s>
            <s xml:id="echoid-s3179" xml:space="preserve">in ſi
              <lb/>
              <note position="right" xlink:label="note-0051-13" xlink:href="note-0051-13a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">ingreſſus</emph>
              .</note>
            num primi inuenti diuido, unde ꝓdeunt in quotiente 97272. </s>
            <s xml:id="echoid-s3180" xml:space="preserve">arcus illius quotientis eſt
              <lb/>
            76. </s>
            <s xml:id="echoid-s3181" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3182" xml:space="preserve">35. </s>
            <s xml:id="echoid-s3183" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3184" xml:space="preserve">hinc ſnbtraho complementũ declinationis Solis, ſcilicet 69. </s>
            <s xml:id="echoid-s3185" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3186" xml:space="preserve">18. </s>
            <s xml:id="echoid-s3187" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3188" xml:space="preserve">& </s>
            <s xml:id="echoid-s3189" xml:space="preserve">
              <lb/>
            manent in reſiduo gra. </s>
            <s xml:id="echoid-s3190" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3191" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3192" xml:space="preserve">17. </s>
            <s xml:id="echoid-s3193" xml:space="preserve">inuentũ ſecũdũ. </s>
            <s xml:id="echoid-s3194" xml:space="preserve">Iam ita utriuſ inuenti ſinus ſcilicet
              <lb/>
              <note position="right" xlink:label="note-0051-14" xlink:href="note-0051-14a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">ſecundum</emph>
              .</note>
            76398. </s>
            <s xml:id="echoid-s3195" xml:space="preserve">& </s>
            <s xml:id="echoid-s3196" xml:space="preserve">12677. </s>
            <s xml:id="echoid-s3197" xml:space="preserve">inter ſe multiplico, & </s>
            <s xml:id="echoid-s3198" xml:space="preserve">quotientẽ in totum diuido, at hinc ꝓuenient in
              <lb/>
            quotiẽte 9685. </s>
            <s xml:id="echoid-s3199" xml:space="preserve">arcus eſt 5. </s>
            <s xml:id="echoid-s3200" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3201" xml:space="preserve">33. </s>
            <s xml:id="echoid-s3202" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3203" xml:space="preserve">altitudo nimi℞ Solis quæſita ad horã 5. </s>
            <s xml:id="echoid-s3204" xml:space="preserve">antemeri-
              <lb/>
            dianã in ipſo die intronizationis. </s>
            <s xml:id="echoid-s3205" xml:space="preserve">Fit aliquãdo ut inuentũ ſecundũ præciſe ſit 90. </s>
            <s xml:id="echoid-s3206" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3207" xml:space="preserve">& </s>
            <s xml:id="echoid-s3208" xml:space="preserve">
              <lb/>
            tũc inuentũ illud ꝑ ſe erit altitudo Solis quæſita, ne ulla ulteriori indiget ſupputatiõe.
              <lb/>
            </s>
            <s xml:id="echoid-s3209" xml:space="preserve">Inſuper & </s>
            <s xml:id="echoid-s3210" xml:space="preserve">hoc ſcitu neceſſariũ eſt, ꝙ quũ ☉(sun) eſt in principio ♈ uel ♎, tunc multiplicare
              <lb/>
              <note position="right" xlink:label="note-0051-15" xlink:href="note-0051-15a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
                <lb/>
                <emph style="it">ſimile per</emph>
                <lb/>
                <emph style="it">quadrantë</emph>
                <lb/>
                <emph style="it">reperies.</emph>
              </note>
            debes ſinus utriuſ cõplemẽti, diſtãtiæ ſcilicet Solis à meridie & </s>
            <s xml:id="echoid-s3211" xml:space="preserve">altitudinis poli, produ-
              <lb/>
            ctum uero diuides in ſinũ totum, & </s>
            <s xml:id="echoid-s3212" xml:space="preserve">ſic arcus quotiẽtis ſtatim tibi mõſtrabit altitudinem
              <lb/>
            Solis quã quærebas. </s>
            <s xml:id="echoid-s3213" xml:space="preserve">Præterea quæcun hic te ꝑ Solem docuimus inuenire, puta arcum
              <lb/>
            diurnum, altitudinẽ ab horizõte, & </s>
            <s xml:id="echoid-s3214" xml:space="preserve">id genus ſimilia plura, intelliges etiam de ſtellis, ita
              <lb/>
            ꝙ quæ de eclyptica tradidimus, in reliquorũ etiã ſyderum motibus uſum ſuum retineãt.</s>
            <s xml:id="echoid-s3215" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div93" type="section" level="1" n="51">
          <head xml:id="echoid-head55" xml:space="preserve">PRONVNCIATVM XXXIX.</head>
          <p>
            <s xml:id="echoid-s3216" xml:space="preserve">Diſtantiam Solis ante meridiem per circulum magnum ab ipſo puncto
              <lb/>
            interſectionis æ quatoris & </s>
            <s xml:id="echoid-s3217" xml:space="preserve">horizontis ſolerte inueſtigare.</s>
            <s xml:id="echoid-s3218" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3219" xml:space="preserve">Si quãdo arcum illũ ex ſphærica ratione inuenire cupis, primũ multiplica ſinum cõple
              <lb/>
            menti declinationis Solis cum ſinu diſtantiæ Solis à meridiano (qñ diſtantia illa in </s>
          </p>
        </div>
      </text>
    </echo>
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