Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

Table of Notes

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        <div xml:id="echoid-div111" type="section" level="1" n="60">
          <pb file="0056" n="56" rhead="GENVINVS VSVS"/>
          <p>
            <s xml:id="echoid-s3650" xml:space="preserve">Primũ hic adſume ſinũ rectũ ſecundũ diſtãtiæ Solis à gradu aſcẽdẽtis, & </s>
            <s xml:id="echoid-s3651" xml:space="preserve">ſinũrectũ ſe-
              <lb/>
              <note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">
                <emph style="it">Hoc latera</emph>
                <lb/>
                <emph style="it">tim aſſeque</emph>
                <lb/>
                <emph style="it">ris.</emph>
              </note>
            cundũ altitudinis ☉(sun), minorẽ duc in ſinũ ꝓfectũ, ꝓductũ diuide in maiorẽ, & </s>
            <s xml:id="echoid-s3652" xml:space="preserve">arcu quotiẽ-
              <lb/>
            tis à 90. </s>
            <s xml:id="echoid-s3653" xml:space="preserve">ſubtracto, ſinũ reſidui adhuc tibi denuo ꝓpone, & </s>
            <s xml:id="echoid-s3654" xml:space="preserve">ſinũ diſtãtiæ Solis ab abſcẽden
              <lb/>
            te, deinde minorem illũ ex ijs duobus duc in ſinũ totũ, ꝓductũ diuide in maiorẽ, & </s>
            <s xml:id="echoid-s3655" xml:space="preserve">arcus
              <lb/>
            quotientis mõſtrabit angulũ quæſitũ. </s>
            <s xml:id="echoid-s3656" xml:space="preserve">?</s>
            <s xml:id="echoid-s3657" xml:space="preserve">?V is exemplo rem magis ob oculos poni? </s>
            <s xml:id="echoid-s3658" xml:space="preserve">Ec-
              <lb/>
              <note position="left" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſcopi.</emph>
              </note>
            ce in ſaꝑiori perſiſtẽdo, dico in ipſa hora intronizationis Solẽ abfuiſſe ab aſcendente 62
              <lb/>
            gra. </s>
            <s xml:id="echoid-s3659" xml:space="preserve">59. </s>
            <s xml:id="echoid-s3660" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3661" xml:space="preserve">iã ita cõplementũ eius eſt 27. </s>
            <s xml:id="echoid-s3662" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3663" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3664" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3665" xml:space="preserve">ſinus uero 45424. </s>
            <s xml:id="echoid-s3666" xml:space="preserve">illũ ꝗa minor eſt
              <lb/>
            duc in ſinũ totũ, ꝓductũ diu de ꝗ 70875. </s>
            <s xml:id="echoid-s3667" xml:space="preserve">at is eſt ſinus cõplemẽti altitudinis Solis ipſa
              <lb/>
            hora intronizationis, in quotiẽte ꝓueniũt 64090. </s>
            <s xml:id="echoid-s3668" xml:space="preserve">arcũ eius 39. </s>
            <s xml:id="echoid-s3669" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3670" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3671" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3672" xml:space="preserve">ſubtrahe à 90.
              <lb/>
            </s>
            <s xml:id="echoid-s3673" xml:space="preserve">& </s>
            <s xml:id="echoid-s3674" xml:space="preserve">remanebũt 50. </s>
            <s xml:id="echoid-s3675" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3676" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3677" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3678" xml:space="preserve">Reſidui huius iterũ quære ſinũ ſcilicet 76753. </s>
            <s xml:id="echoid-s3679" xml:space="preserve">eũ duc in totũ,
              <lb/>
            diuide aũt productũ in ſinum diſtantiæ Solis ab aſcendente 89087. </s>
            <s xml:id="echoid-s3680" xml:space="preserve">in quotiente proue-
              <lb/>
            niunt 86155. </s>
            <s xml:id="echoid-s3681" xml:space="preserve">arcus illius eſt 59, gra. </s>
            <s xml:id="echoid-s3682" xml:space="preserve">30. </s>
            <s xml:id="echoid-s3683" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3684" xml:space="preserve">angulus. </s>
            <s xml:id="echoid-s3685" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3686" xml:space="preserve">quæſitus, & </s>
            <s xml:id="echoid-s3687" xml:space="preserve">iã triplici uia inuẽtus.</s>
            <s xml:id="echoid-s3688" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div113" type="section" level="1" n="61">
          <head xml:id="echoid-head65" xml:space="preserve">PRONVNCIATVM XLIX.</head>
          <p>
            <s xml:id="echoid-s3689" xml:space="preserve">Angulũ illũ, de qq̊ hactenus diſputatũ eſt, etiamnũ diuerſa uia inquirere.</s>
            <s xml:id="echoid-s3690" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3691" xml:space="preserve">Iam nunc ſinũ cõplementi altitudinis meridianæ (gra dũ illũ uolo zodiaci, qui ſub ho-
              <lb/>
            ram huius cõſiderationis mediũ cœli attingit, cuius etiã cõplementũ nihil aliud eſt niſi
              <lb/>
            diſtãtia gradus illius à uertice capitis) duc in ſinũ anguli, quem facit eclyptica cũ meridia
              <lb/>
              <note position="left" xlink:label="note-0056-03" xlink:href="note-0056-03a" xml:space="preserve">
                <emph style="it">Lateralcm</emph>
                <lb/>
                <emph style="it">animaduer</emph>
                <lb/>
                <emph style="it">
                  <gap/>
                ingreſ-</emph>
                <lb/>
                <emph style="it">ſum.</emph>
              </note>
            no iuxta punctũ illud medij cœli, unde cõplementũ ſumitur, productũ diuide in ſinũ totũ
              <lb/>
            quotientem ſerua in locũ aliquem ſeorſim, & </s>
            <s xml:id="echoid-s3692" xml:space="preserve">ei adiunge ſinũ altitudinis Solis, minorem
              <lb/>
            ducin totũ, ꝓductũ in maiorẽ diuide, & </s>
            <s xml:id="echoid-s3693" xml:space="preserve">arcus quotientis oſtẽdet quantitatẽ anguli quæſi
              <lb/>
            ti. </s>
            <s xml:id="echoid-s3694" xml:space="preserve">?</s>
            <s xml:id="echoid-s3695" xml:space="preserve">? Adcõmodemus huc etiã exemplũ ſuꝗius. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">In die & </s>
            <s xml:id="echoid-s3697" xml:space="preserve">hora intronizatiõis fuit in me
              <lb/>
              <note position="left" xlink:label="note-0056-04" xlink:href="note-0056-04a" xml:space="preserve">
                <emph style="it">Arealis bic</emph>
                <lb/>
                <emph style="it">conſideran</emph>
                <lb/>
                <emph style="it">dus eſt in-</emph>
                <lb/>
                <emph style="it">troitus.</emph>
              </note>
            dio cœli 16. </s>
            <s xml:id="echoid-s3698" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3699" xml:space="preserve">40. </s>
            <s xml:id="echoid-s3700" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3701" xml:space="preserve">♈, ſicut in 25. </s>
            <s xml:id="echoid-s3702" xml:space="preserve">ꝓnunc. </s>
            <s xml:id="echoid-s3703" xml:space="preserve">declinationẽ eius inueni ꝑ ꝓnunc. </s>
            <s xml:id="echoid-s3704" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3705" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3706" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s3707" xml:space="preserve">35. </s>
            <s xml:id="echoid-s3708" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3709" xml:space="preserve">hãc adde ad cõplemẽtũ altitudinis poli 48. </s>
            <s xml:id="echoid-s3710" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3711" xml:space="preserve">illu@ eſt 42. </s>
            <s xml:id="echoid-s3712" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3713" xml:space="preserve">ſumma igitur erit
              <lb/>
            48. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3715" xml:space="preserve">34. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3717" xml:space="preserve">iam ſi cõplementũ eius accepero 41. </s>
            <s xml:id="echoid-s3718" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3719" xml:space="preserve">26. </s>
            <s xml:id="echoid-s3720" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3721" xml:space="preserve">ea ipſa eſt diſtantia medij
              <lb/>
            cœli à zenith capitis, ſinum cõplementi huius 66174. </s>
            <s xml:id="echoid-s3722" xml:space="preserve">duco in ſinũ anguli, quẽ eclyptica
              <lb/>
              <note position="left" xlink:label="note-0056-05" xlink:href="note-0056-05a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              Epiſcopi.</note>
            facit cũ meridiano iuxta illum gradum medij cœli, hunc etiam antea uaiijs rationibus ad
              <lb/>
            inueni, eſt autem 67. </s>
            <s xml:id="echoid-s3723" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3724" xml:space="preserve">23. </s>
            <s xml:id="echoid-s3725" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3726" xml:space="preserve">ſinus eius 92309, productũ diuido in ſinum totũ, & </s>
            <s xml:id="echoid-s3727" xml:space="preserve">quo
              <lb/>
            tiens puta minorẽ duco in totum, productũ diuido in ſinum maiorem, in quotiente pro
              <lb/>
            uenient 86173, arcus eius eſt 49. </s>
            <s xml:id="echoid-s3728" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3729" xml:space="preserve">30. </s>
            <s xml:id="echoid-s3730" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3731" xml:space="preserve">angulus ille quæſitus, quoniam hora intro-
              <lb/>
            nizationis fuit ante meridiem. </s>
            <s xml:id="echoid-s3732" xml:space="preserve">Sin autem hora conſiderationis eſſet pomeridiana, angu
              <lb/>
            lus inuẽtus ſubtrahi deberet à ſemicirculo ad hoc ut remanebit quãtitas anguli quæſiti.</s>
            <s xml:id="echoid-s3733" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div115" type="section" level="1" n="62">
          <head xml:id="echoid-head66" xml:space="preserve">PRONVNCIATVM L.</head>
          <p>
            <s xml:id="echoid-s3734" xml:space="preserve">Cognito iam gradu aſcendentis, adhuc gradum eclypticæ qui mediat
              <lb/>
            cœlum explorare.</s>
            <s xml:id="echoid-s3735" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3736" xml:space="preserve">Quære principio amplitudinem aſcendentis per 12. </s>
            <s xml:id="echoid-s3737" xml:space="preserve">pronunc. </s>
            <s xml:id="echoid-s3738" xml:space="preserve">ſinum eius duc in ſinũ
              <lb/>
            anguli horizontis & </s>
            <s xml:id="echoid-s3739" xml:space="preserve">eclypticæ, productum diuide in totum ſinum, deinde arcum quoti
              <lb/>
              <note position="left" xlink:label="note-0056-06" xlink:href="note-0056-06a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">ingreſſus.</emph>
              </note>
            entis ſubtrahe à 90. </s>
            <s xml:id="echoid-s3740" xml:space="preserve">& </s>
            <s xml:id="echoid-s3741" xml:space="preserve">ſinũ reſidui tibi propone, ſimul´ ſinum complementi altitudinis,
              <lb/>
            minorem ex ijs duc in ſinum totũ
              <emph style="sub">2</emph>
            productũ diuide in maiorẽ, & </s>
            <s xml:id="echoid-s3742" xml:space="preserve">quotientis arcũ ſubtrahe
              <lb/>
              <note position="left" xlink:label="note-0056-07" xlink:href="note-0056-07a" xml:space="preserve">
                <emph style="it">Arealis in-</emph>
                <lb/>
                <emph style="it">greſſus.</emph>
              </note>
            à gra du aſcendentis, hoc eſt numera tot gradus ab aſcendente cõtra ordinẽ ſignorũ, ſi-
              <lb/>
            modo tũc gradus aſcendẽtis fuerit in ſigno aliq̊ meridionali. </s>
            <s xml:id="echoid-s3743" xml:space="preserve">Sed ſi in ſeptentrionali exti
              <lb/>
            terit, accipe cõtrariũ eius, puta gradũ eclypticæ occidentem eo temporis momẽto in par
              <lb/>
            te occidentis, & </s>
            <s xml:id="echoid-s3744" xml:space="preserve">adde arcũ quotientis, ſic´ ꝓueniet gradus ille ꝗ mediat cœlũ. </s>
            <s xml:id="echoid-s3745" xml:space="preserve">?</s>
            <s xml:id="echoid-s3746" xml:space="preserve">? Ex-
              <lb/>
            emplo adiũcto rem plenius intelliges. </s>
            <s xml:id="echoid-s3747" xml:space="preserve">In ipſa intronizatiõis hora fuit in aſcendente 5.
              <lb/>
            </s>
            <s xml:id="echoid-s3748" xml:space="preserve">
              <note position="left" xlink:label="note-0056-08" xlink:href="note-0056-08a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              Epiſcopi.</note>
            gra. </s>
            <s xml:id="echoid-s3749" xml:space="preserve">25. </s>
            <s xml:id="echoid-s3750" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3751" xml:space="preserve">♌, amplitudo eius eſt 29. </s>
            <s xml:id="echoid-s3752" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3753" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3754" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3755" xml:space="preserve">ſinũ eius 48563. </s>
            <s xml:id="echoid-s3756" xml:space="preserve">duco in ſinũ anguli ecly-
              <lb/>
            pticæ & </s>
            <s xml:id="echoid-s3757" xml:space="preserve">horizõtis, ſiquidẽ intronizatio illa facta eſt in latitudine 48. </s>
            <s xml:id="echoid-s3758" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3759" xml:space="preserve">angulus autẽ
              <lb/>
            erit 52. </s>
            <s xml:id="echoid-s3760" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3761" xml:space="preserve">21. </s>
            <s xml:id="echoid-s3762" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3763" xml:space="preserve">ſinus eius 79175. </s>
            <s xml:id="echoid-s3764" xml:space="preserve">productum ſi diuicã in totũ, proueniẽt in quotiẽte
              <lb/>
            38449 arcũ iplſius. </s>
            <s xml:id="echoid-s3765" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3766" xml:space="preserve">22. </s>
            <s xml:id="echoid-s3767" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3768" xml:space="preserve">37. </s>
            <s xml:id="echoid-s3769" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3770" xml:space="preserve">ſubtraho à 90. </s>
            <s xml:id="echoid-s3771" xml:space="preserve">& </s>
            <s xml:id="echoid-s3772" xml:space="preserve">remanẽt 67. </s>
            <s xml:id="echoid-s3773" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3774" xml:space="preserve">23. </s>
            <s xml:id="echoid-s3775" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3776" xml:space="preserve">ſinum ipſius
              <lb/>
            92309. </s>
            <s xml:id="echoid-s3777" xml:space="preserve">tã̈ maiorẽ adſeruo ꝓ diuiſore, deinde adſumo ſinũ cõplemẽti amplitudinis, q̊d
              <lb/>
            ſanè ſuit 60. </s>
            <s xml:id="echoid-s3778" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3779" xml:space="preserve">56. </s>
            <s xml:id="echoid-s3780" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3781" xml:space="preserve">ſed ſinũ eius 87405. </s>
            <s xml:id="echoid-s3782" xml:space="preserve">duco in ſinũ totũ, ꝓductũ diuido in diuiſorẽ
              <lb/>
            iam ſeruatũ, quotiens dat 94687. </s>
            <s xml:id="echoid-s3783" xml:space="preserve">arcus illius eſt 71. </s>
            <s xml:id="echoid-s3784" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3785" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3786" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3787" xml:space="preserve">tot gra. </s>
            <s xml:id="echoid-s3788" xml:space="preserve">dehinc addo ad
              <lb/>
            gradũ occidentis. </s>
            <s xml:id="echoid-s3789" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3790" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3791" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s3792" xml:space="preserve">25. </s>
            <s xml:id="echoid-s3793" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3794" xml:space="preserve">♒ eò ꝙ aſcendens eſt ſignũ ſeptentrionale, & </s>
            <s xml:id="echoid-s3795" xml:space="preserve">arcus hic
              <lb/>
            attingit 16. </s>
            <s xml:id="echoid-s3796" xml:space="preserve">gra 40. </s>
            <s xml:id="echoid-s3797" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s3798" xml:space="preserve">?</s>
            <s xml:id="echoid-s3799" xml:space="preserve">?, medium ipſum cœli quod hactenus diligenter inquiſiuimus.</s>
            <s xml:id="echoid-s3800" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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