Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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        <div xml:id="echoid-div115" type="section" level="1" n="62">
          <pb file="0057" n="57" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
        </div>
        <div xml:id="echoid-div117" type="section" level="1" n="63">
          <head xml:id="echoid-head67" xml:space="preserve">PRONVNCIATVM LI.</head>
          <p>
            <s xml:id="echoid-s3801" xml:space="preserve">Arcum circuli maioris, qui per utrun polũ mundi & </s>
            <s xml:id="echoid-s3802" xml:space="preserve">corpus ſolare duci-
              <lb/>
            citur, at alio nomine circulus horarius dicitur, quantus ille ſit à polo mũdi
              <lb/>
            arctico uſ ad horizontem, per ſupputationem triangularem cognoſcere.</s>
            <s xml:id="echoid-s3803" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3804" xml:space="preserve">Et ſi arcus ille per ſe magnopere neceſſarius non eſt, ad ſequens tamen pronunc. </s>
            <s xml:id="echoid-s3805" xml:space="preserve">plu
              <lb/>
            rimum conducet, operatio ita iſta ſic habet. </s>
            <s xml:id="echoid-s3806" xml:space="preserve">Propone tibi ſinum complementi altitudi
              <lb/>
              <note position="right" xlink:label="note-0057-01" xlink:href="note-0057-01a" xml:space="preserve">
                <emph style="it">Introitu la-</emph>
                <lb/>
                <emph style="it">terali qua-</emph>
                <lb/>
                <emph style="it">drantem in</emph>
                <lb/>
                <emph style="it">grediaris,</emph>
                <lb/>
                <emph style="it">deinde are-</emph>
                <lb/>
                <emph style="it">li.</emph>
              </note>
            nis poli, eum duc in ſinum diſtantiæ Solis à meridie, productum diuide in ſinum totum,
              <lb/>
            & </s>
            <s xml:id="echoid-s3807" xml:space="preserve">quotientis arcum ſubtrahe à 90. </s>
            <s xml:id="echoid-s3808" xml:space="preserve">ſinum reſidui rurſus tibi propone, ſimul cum ſinu alti
              <lb/>
            tudinis poli, uter illorum fuerit minor, eum ducito in totum ſinum, hinc productum diui
              <lb/>
            de in maiorem, & </s>
            <s xml:id="echoid-s3809" xml:space="preserve">arcus quotientis monſtrabit tibi arcum circuli maioris ducti per polos
              <lb/>
            mundi, & </s>
            <s xml:id="echoid-s3810" xml:space="preserve">per locum Solis, ipſa hora conſiderationis inter polum mundi arcticum & </s>
            <s xml:id="echoid-s3811" xml:space="preserve">ho
              <lb/>
            rizontem compræhenſum. </s>
            <s xml:id="echoid-s3812" xml:space="preserve">?</s>
            <s xml:id="echoid-s3813" xml:space="preserve">?Non erit (opinor) moleſtum hic tibi, ſi exemplo ſubie-
              <lb/>
              <note position="right" xlink:label="note-0057-02" xlink:href="note-0057-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              Epiſcopi.</note>
            cto rem tibi conemur planius oſtendere, propono hic tibi 2. </s>
            <s xml:id="echoid-s3814" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3815" xml:space="preserve">26. </s>
            <s xml:id="echoid-s3816" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3817" xml:space="preserve">II, ubi Sol fuit
              <lb/>
            ipſa hora intronizationis, ſimul etiam horam tibi præſcribo intronizationis 9. </s>
            <s xml:id="echoid-s3818" xml:space="preserve">ante me
              <lb/>
            ridiem. </s>
            <s xml:id="echoid-s3819" xml:space="preserve">diſtantia igitur Solis à meridie eſt trium horarum, quarum ſinus eſt 70710. </s>
            <s xml:id="echoid-s3820" xml:space="preserve">ſiqui
              <lb/>
            dem horæ 3. </s>
            <s xml:id="echoid-s3821" xml:space="preserve">gradus conſiciunt 45. </s>
            <s xml:id="echoid-s3822" xml:space="preserve">ſemper 15. </s>
            <s xml:id="echoid-s3823" xml:space="preserve">gradus pro hora computando. </s>
            <s xml:id="echoid-s3824" xml:space="preserve">Et quia in-
              <lb/>
              <note position="right" xlink:label="note-0057-03" xlink:href="note-0057-03a" xml:space="preserve">
                <emph style="it">Intronizd-</emph>
                <lb/>
                <emph style="it">tio facta eſt</emph>
                <lb/>
                <emph style="it">in 48. gra.</emph>
                <lb/>
                <emph style="it">eleuationis</emph>
                <lb/>
                <emph style="it">poli.</emph>
              </note>
            tronizatio facta eſt in 48. </s>
            <s xml:id="echoid-s3825" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3826" xml:space="preserve">polaris eleuationis, complementum eius eſt 42. </s>
            <s xml:id="echoid-s3827" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3828" xml:space="preserve">ſinũ
              <lb/>
            igitur ipſius 66913. </s>
            <s xml:id="echoid-s3829" xml:space="preserve">ducin ſinum trium horarum, productum diuide in ſinum totum, & </s>
            <s xml:id="echoid-s3830" xml:space="preserve">
              <lb/>
            in quotiente prouenient 74314. </s>
            <s xml:id="echoid-s3831" xml:space="preserve">arcus eius eſt 28. </s>
            <s xml:id="echoid-s3832" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3833" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3834" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3835" xml:space="preserve">quibus ſubtractis à 90. </s>
            <s xml:id="echoid-s3836" xml:space="preserve">rema
              <lb/>
            nent 61. </s>
            <s xml:id="echoid-s3837" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3838" xml:space="preserve">46. </s>
            <s xml:id="echoid-s3839" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3840" xml:space="preserve">ſinus illius diuiſor efficitur, quietiam quum ſit maior ſinu altitudi-
              <lb/>
            nis poli 48. </s>
            <s xml:id="echoid-s3841" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3842" xml:space="preserve">ideo ducendus tibi eſt ſinus altitudinis poli, ſcilicet 74314. </s>
            <s xml:id="echoid-s3843" xml:space="preserve">in totum ſinũ
              <lb/>
            productum uero diuidendũ in diuiſorem iam ſeruatum. </s>
            <s xml:id="echoid-s3844" xml:space="preserve">In quotiente comperies 84349.
              <lb/>
            </s>
            <s xml:id="echoid-s3845" xml:space="preserve">cuius arcus eſt 57. </s>
            <s xml:id="echoid-s3846" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3847" xml:space="preserve">31. </s>
            <s xml:id="echoid-s3848" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3849" xml:space="preserve">ille nimirum quem hactemus inquirebas, planè enim tan-
              <lb/>
            tus eſt etiam arcus huius circuli inter horizontem & </s>
            <s xml:id="echoid-s3850" xml:space="preserve">polum arcticum.</s>
            <s xml:id="echoid-s3851" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div119" type="section" level="1" n="64">
          <head xml:id="echoid-head68" xml:space="preserve">PRONVNCIATVM LII.</head>
          <p>
            <s xml:id="echoid-s3852" xml:space="preserve">Locum ſiue punctũ horizontis, ubi linea horaria in plano horizontali, ſi-
              <lb/>
            militer & </s>
            <s xml:id="echoid-s3853" xml:space="preserve">circulus horarius in corpore ſphærico tangit horizontẽ, inuenire.</s>
            <s xml:id="echoid-s3854" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3855" xml:space="preserve">Attendenda quæ nũc docebimus tibi erũt diligenter, maxime aũt ſi te delectant cõpo
              <lb/>
            ſitiones inſtrumentorũ quæ ſolaria uocantur horizõtalia, hoc eſt, ſi in ſuperficie aliqua
              <lb/>
            plana horizonti tuo æquidiſtante cupis diuidere horas. </s>
            <s xml:id="echoid-s3856" xml:space="preserve">Adſume ita arcũ huius circu-
              <lb/>
            li horarij â polo mundi uſ in horizontẽ, quem ex antecedente propoſitione cognoui-
              <lb/>
            ſti, ſinum eius duc in ſinũ diſtantiæ Solis horariæ â meridie, ſiue ante ſiue poſt meridiem,
              <lb/>
              <note position="right" xlink:label="note-0057-04" xlink:href="note-0057-04a" xml:space="preserve">
                <emph style="it">Illud babe-</emph>
                <lb/>
                <emph style="it">tur per qua</emph>
                <lb/>
                <emph style="it">drãtis late-</emph>
                <lb/>
                <emph style="it">ra.</emph>
              </note>
            productum diuide in ſinũ totum, & </s>
            <s xml:id="echoid-s3857" xml:space="preserve">tunc arcus quotientis arguet arcũ horizontis interce
              <lb/>
            ptum inter meridianũ & </s>
            <s xml:id="echoid-s3858" xml:space="preserve">circulũ horariũ, qui tranſit per locũ Solis & </s>
            <s xml:id="echoid-s3859" xml:space="preserve">utrun polũ mun-
              <lb/>
            di. </s>
            <s xml:id="echoid-s3860" xml:space="preserve">Ne uero eſt quòd putes ſimpliciter tibi habendũ ſemper eſſe locum Solis, ſed diſtanti
              <lb/>
            am horariam tibi tantum propone, non conſiderãs, ubicun Sol ſit in zodiaco. </s>
            <s xml:id="echoid-s3861" xml:space="preserve">?</s>
            <s xml:id="echoid-s3862" xml:space="preserve">? Ex
              <lb/>
              <note position="right" xlink:label="note-0057-05" xlink:href="note-0057-05a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              Epiſoo
                <unsure/>
              pi.</note>
            emplum huius rei tibi ſit tale. </s>
            <s xml:id="echoid-s3863" xml:space="preserve">Cupio ſcire, quo tandem intronizationis hora, quæ 3. </s>
            <s xml:id="echoid-s3864" xml:space="preserve">fuit
              <lb/>
            ante meridiẽ, uel ipſa umbra ab axe mũdi pertigerit. </s>
            <s xml:id="echoid-s3865" xml:space="preserve">ne hic opus eſt, ut conſiderem,
              <lb/>
            in quo ſigno ſiue gradu Sol fuerit, ſed tantũ adſumo ſinũ triũ horarũ, qui eſt 45 graduum
              <lb/>
            70710. </s>
            <s xml:id="echoid-s3866" xml:space="preserve">eũ duco in ſinũ arcus circuli horarij inter polũ mundi & </s>
            <s xml:id="echoid-s3867" xml:space="preserve">horizontẽ intercluſum,
              <lb/>
            quẽ iam q̊ ex ſuperiori pronunciat. </s>
            <s xml:id="echoid-s3868" xml:space="preserve">inuentũ habeo, eſt autem 57. </s>
            <s xml:id="echoid-s3869" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3870" xml:space="preserve">31. </s>
            <s xml:id="echoid-s3871" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3872" xml:space="preserve">ſinus ipſe
              <lb/>
            84349. </s>
            <s xml:id="echoid-s3873" xml:space="preserve">Hinc ubi productũ diuido in ſinũ totũ, remanent 59643. </s>
            <s xml:id="echoid-s3874" xml:space="preserve">arcus eſt 36. </s>
            <s xml:id="echoid-s3875" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3876" xml:space="preserve">38. </s>
            <s xml:id="echoid-s3877" xml:space="preserve">mi.
              <lb/>
            </s>
            <s xml:id="echoid-s3878" xml:space="preserve">At hoc eſt, quod hucuſ inueſtigauimus. </s>
            <s xml:id="echoid-s3879" xml:space="preserve">Tantum etiam in plano horizontali diſtat li
              <lb/>
            nea horæ 9 ante meridiẽ uerſus ſeptentrionem à linea meridiana, ex altera quo parte ſi
              <lb/>
            militer tantum diſtat linea horæ 3. </s>
            <s xml:id="echoid-s3880" xml:space="preserve">à linea meridiana. </s>
            <s xml:id="echoid-s3881" xml:space="preserve">Et ad hunc quidem modum ipſe ti
              <lb/>
            bi potes tabulas ſupputare, ad omnes horas & </s>
            <s xml:id="echoid-s3882" xml:space="preserve">ad quaſcun eleuationes poli, ſicut in no-
              <lb/>
            ſtro opere de V mbris ad omnes polares eleuationes clare perſpicies.</s>
            <s xml:id="echoid-s3883" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div121" type="section" level="1" n="65">
          <head xml:id="echoid-head69" xml:space="preserve">PRONVNCIATVM LIII.</head>
          <p>
            <s xml:id="echoid-s3884" xml:space="preserve">Arcũ illũ horizõtis inter meridianũ & </s>
            <s xml:id="echoid-s3885" xml:space="preserve">circulũ horariũ cõprehenſum adhuc
              <lb/>
            alia quadã ratione inueſtigare, iſtũ inquã, qui per locũ Solis protenditur.</s>
            <s xml:id="echoid-s3886" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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