Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

Table of contents

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[81.] PRONVNCIATVM LXIX.
Page: 68
[82.] PRONVNCIATVM LXX.
Page: 69
[83.] PRONVNCIATVM LXXI.
Page: 69
[84.] PRONVNCIATVM LXXII.
Page: 69
[85.] PRONVNCIATVM LXXIII.
Page: 70
[86.] PRONVNCIATVM LXXIIII.
Page: 70
[87.] PRONVNCIATVM LXXV.
Page: 71
[88.] PRONVNCIATVM LXXVI.
Page: 72
[89.] PRONVNCIATVM LXXVII.
Page: 73
[90.] PRONVNCIATVM LXXVIII.
Page: 74
[91.] PRONVNCIATVM LXXIX.
Page: 76
[92.] PRONVNCIATVM LXXX.
Page: 76
[93.] PRONVNCIATVM LXXXI.
Page: 77
[94.] PRONVNCIATVM LXXXII.
Page: 77
[95.] PRONVNCIATVM LXXXIII.
Page: 77
[96.] PRONVNCIATVM LXXXIIII.
Page: 78
[97.] PRONVNCIATVM LXXXV.
Page: 78
[98.] PRONVNCIATVM LXXXVI.
Page: 79
[99.] PRONVNCIATVM LXXXVII.
Page: 80
[100.] PRONVNCIATVM LXXXVIII.
Page: 80
[101.] PRONVNCIATVM LXXXIX.
Page: 81
[102.] PRONVNCIATVM XC.
Page: 82
[103.] PRONVNCIATVM XCI.
Page: 82
[104.] PRONVNCIATVM XCII.
Page: 83
[105.] PRONVNCIATVM XCIII.
Page: 83
[106.] PRONVNCIATVM XCIIII.
Page: 85
[107.] PRONVNCIATVM XCV.
Page: 85
[108.] PRONVNCIATVM XCVI.
Page: 86
[109.] PRONVNCIATVM XCVII.
Page: 87
[110.] PRONVNCIATVM XCVIII.
Page: 88
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        <div xml:id="echoid-div211" type="section" level="1" n="107">
          <p>
            <s xml:id="echoid-s7264" xml:space="preserve">
              <pb file="0086" n="86" rhead="GENVINVS VSVS"/>
            incipit apparere uel occultari, quære angulum eclypticæ & </s>
            <s xml:id="echoid-s7265" xml:space="preserve">horizontis iuxta iſtud pun-
              <lb/>
            ctum eclypticæ, per 31, pronunciatum in parte orientis, ſi ſcire cupis apparitionem uel
              <lb/>
            occultationem matutinam, ſinus eius eſt ipſe diuiſor, deinde duc ſinum arcus uiſionis in
              <lb/>
              <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">
                <emph style="it">Hocper a-</emph>
                <lb/>
                <emph style="it">realcm in-</emph>
                <lb/>
                <emph style="it">greſſum</emph>
                <lb/>
                <emph style="it">quœrenti</emph>
                <lb/>
                <emph style="it">apparet.</emph>
              </note>
            ſinum totum, productum diuide in diuiſorem, arcus quotientis oſtendet arcum eclypti-
              <lb/>
            cæ: </s>
            <s xml:id="echoid-s7266" xml:space="preserve">ſi locum ſtellæ redigam ad horizontem, & </s>
            <s xml:id="echoid-s7267" xml:space="preserve">tantum numerem ſecundum ordinem ſi-
              <lb/>
            gnorum, quantum ipſe quotiẽs habet, & </s>
            <s xml:id="echoid-s7268" xml:space="preserve">umc ſi numerus hic gradum Solis non attingit,
              <lb/>
            ſtella iſta uidetur adhuc ante ortum Solis, ſcilicet aut arcus quotientis gradum Solis ap
              <lb/>
            præhendi, ſtella hæc amplius uiderinon poteſt: </s>
            <s xml:id="echoid-s7269" xml:space="preserve">ſimili quo modo operaberis in parte
              <lb/>
            occidua, niſi quòd ibi arcum quotientis numerabis contra ordinem ſignorum, quòd ſi
              <lb/>
            arcus iſte præciſe locum Solis appræhendit, eo ipſo die incipit ſtella iſta occultari, uel ex
              <lb/>
            radijs ſolaribus emergit & </s>
            <s xml:id="echoid-s7270" xml:space="preserve">apparetprimum. </s>
            <s xml:id="echoid-s7271" xml:space="preserve">Quando autem planeta aliquis non præciſe
              <lb/>
            eſt in eclyptica, tunc quære per 93. </s>
            <s xml:id="echoid-s7272" xml:space="preserve">gradum, cum quo oritur in parte orientis, & </s>
            <s xml:id="echoid-s7273" xml:space="preserve">angu-
              <lb/>
              <note position="left" xlink:label="note-0086-02" xlink:href="note-0086-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            lum eclypticæ cũ horizonte per 32. </s>
            <s xml:id="echoid-s7274" xml:space="preserve">& </s>
            <s xml:id="echoid-s7275" xml:space="preserve">33. </s>
            <s xml:id="echoid-s7276" xml:space="preserve">deinde operare modo piædicto. </s>
            <s xml:id="echoid-s7277" xml:space="preserve">?</s>
            <s xml:id="echoid-s7278" xml:space="preserve">? Videa-
              <lb/>
            mus iam an ☿ die intronizationis etiam ante ortum Solis uideri oportuerit, aut an ſur-
              <lb/>
            tiuus (uti ſolet) & </s>
            <s xml:id="echoid-s7279" xml:space="preserve">tacitus ad hanc uenerit intronizationem. </s>
            <s xml:id="echoid-s7280" xml:space="preserve">Inuentum habeo gradum e-
              <lb/>
            clypticæ cum quo euaſit ille ſuper horizontem per 93. </s>
            <s xml:id="echoid-s7281" xml:space="preserve">pronunciatum, is fuit 19. </s>
            <s xml:id="echoid-s7282" xml:space="preserve">gia. </s>
            <s xml:id="echoid-s7283" xml:space="preserve">43.
              <lb/>
            </s>
            <s xml:id="echoid-s7284" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s7285" xml:space="preserve">♉. </s>
            <s xml:id="echoid-s7286" xml:space="preserve">Deinde habeo etiam per 31. </s>
            <s xml:id="echoid-s7287" xml:space="preserve">& </s>
            <s xml:id="echoid-s7288" xml:space="preserve">32. </s>
            <s xml:id="echoid-s7289" xml:space="preserve">angulum quam facit eclyptica cum horizon
              <lb/>
            te iuxta gradum occidentis, is eſt 22. </s>
            <s xml:id="echoid-s7290" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7291" xml:space="preserve">41. </s>
            <s xml:id="echoid-s7292" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s7293" xml:space="preserve">ſinus huius anguli eſt 38563. </s>
            <s xml:id="echoid-s7294" xml:space="preserve">& </s>
            <s xml:id="echoid-s7295" xml:space="preserve">quia ar-
              <lb/>
            cus uiſionis eſt 10. </s>
            <s xml:id="echoid-s7296" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7297" xml:space="preserve">ſinus quo ipſius 17364. </s>
            <s xml:id="echoid-s7298" xml:space="preserve">duco ſinum illum in totum, productum
              <lb/>
            diuido in 38563. </s>
            <s xml:id="echoid-s7299" xml:space="preserve">quotiens erit 45028. </s>
            <s xml:id="echoid-s7300" xml:space="preserve">arcus autem eius 26. </s>
            <s xml:id="echoid-s7301" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7302" xml:space="preserve">46. </s>
            <s xml:id="echoid-s7303" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s7304" xml:space="preserve">& </s>
            <s xml:id="echoid-s7305" xml:space="preserve">tantum quidẽ
              <lb/>
            diſtare debet Sol ab horizonte ſecundum eclypticam, ut appareat ille, quod ſi propius ac
              <lb/>
            ceſſerit, non uidebitur, ſi iam à 19. </s>
            <s xml:id="echoid-s7306" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7307" xml:space="preserve">43. </s>
            <s xml:id="echoid-s7308" xml:space="preserve">mi ♉. </s>
            <s xml:id="echoid-s7309" xml:space="preserve">26. </s>
            <s xml:id="echoid-s7310" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7311" xml:space="preserve">46. </s>
            <s xml:id="echoid-s7312" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s7313" xml:space="preserve">numerauero ſecundum
              <lb/>
            ordinem ſignorum, finis iſtius arcuspertinget ad 16. </s>
            <s xml:id="echoid-s7314" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7315" xml:space="preserve">29. </s>
            <s xml:id="echoid-s7316" xml:space="preserve">II, ubi oporteret eſſe So-
              <lb/>
            lem, ſi principio ſtatim uideri deberet ☿, & </s>
            <s xml:id="echoid-s7317" xml:space="preserve">quò magis ☉(sun) inde receſſerit, cò diutius ap-
              <lb/>
            parebit ☿ ante Solis exortum, quia autem arcum eitis non attingit, certum eſt eum occul
              <lb/>
            to ſe proripuiſſe ultra horizontem. </s>
            <s xml:id="echoid-s7318" xml:space="preserve">Nunc uideamus an etiam ſic ſurtim ſeſe ſubduxerit
              <lb/>
            (uti plærun facit) ſub horizontem, uelan poſt Solis occaſum adhuc uideri potuerit,
              <lb/>
            primo conſidero gradum Solis, & </s>
            <s xml:id="echoid-s7319" xml:space="preserve">gradum cum quo occidit ☿, quem inueni per præmiſ-
              <lb/>
            ſam eſſe 9. </s>
            <s xml:id="echoid-s7320" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7321" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7322" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s7323" xml:space="preserve">Ecce iam in aperto eſt, quia ☿ ante ☉(sun) occaſum ſe coniecit ſub hori
              <lb/>
            zontem, exiſtente ☉(sun) in 2. </s>
            <s xml:id="echoid-s7324" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7325" xml:space="preserve">26. </s>
            <s xml:id="echoid-s7326" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s7327" xml:space="preserve">II, unde nec ulla ulteriori inquiſitione opus erit.</s>
            <s xml:id="echoid-s7328" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div213" type="section" level="1" n="108">
          <head xml:id="echoid-head112" xml:space="preserve">PRONVNCIATVM XCVI.</head>
          <p>
            <s xml:id="echoid-s7329" xml:space="preserve">Ex altitudine ſtellæ fixæ uel planetæ ſupra horizontem etiam noctis ho-
              <lb/>
            ram elicere.</s>
            <s xml:id="echoid-s7330" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7331" xml:space="preserve">Ad hanc rem opus tibi erit declinatione ſtellæ complemento altitudinis poli, aſcenſi
              <lb/>
              <note position="left" xlink:label="note-0086-03" xlink:href="note-0086-03a" xml:space="preserve">
                <emph style="it">Illud depræ</emph>
                <lb/>
                <emph style="it">henditur in</emph>
                <lb/>
                <emph style="it">greſſu a-</emph>
                <lb/>
                <emph style="it">reali.</emph>
              </note>
            one recta ſtellæ, & </s>
            <s xml:id="echoid-s7332" xml:space="preserve">aſcenſione recta Solis, altitudine quo meridiana ſtellæ, altitudine eti
              <lb/>
            am ſtellæ ſuper horizontem, & </s>
            <s xml:id="echoid-s7333" xml:space="preserve">complemento declinationis ſtellæ. </s>
            <s xml:id="echoid-s7334" xml:space="preserve">Duc igitur ſinum al
              <lb/>
            titudinis meridianæ in totum, productum diuide in ſinum complementi altitudinis poli,
              <lb/>
            quotiens iſte erit inuentum primum. </s>
            <s xml:id="echoid-s7335" xml:space="preserve">Duc etiam ſinum altitudinis ſtellæ ſuper horizon-
              <lb/>
              <note position="left" xlink:label="note-0086-04" xlink:href="note-0086-04a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">primum</emph>
                <lb/>
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">ſecundum</emph>
                <lb/>
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">tertium.</emph>
              </note>
            tem tempore obſeruationis in totũ, productum diuide in ſinum com plementi altitudinis
              <lb/>
            poli, quotiens dicetur inuentum ſecundum, & </s>
            <s xml:id="echoid-s7336" xml:space="preserve">hoc ſubtrahe à primo, quia ſemper eſt mi
              <lb/>
            nus, & </s>
            <s xml:id="echoid-s7337" xml:space="preserve">reſiduum rurſus duc in ſinum totum, productũ diuide in ſinum complementi de-
              <lb/>
            clinationis ſtellæ, quotiens uocabitur inuentum tertium. </s>
            <s xml:id="echoid-s7338" xml:space="preserve">Quod ſi minus fuerit ſinu toto,
              <lb/>
            ſubtrahe illud à toto, & </s>
            <s xml:id="echoid-s7339" xml:space="preserve">arcu reſidui iterũ de 90. </s>
            <s xml:id="echoid-s7340" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s7341" xml:space="preserve">ſubducto, remanebit arcus diſtan-
              <lb/>
            tiæ ſtellæ à meridiano. </s>
            <s xml:id="echoid-s7342" xml:space="preserve">Sed ſi tertium illud inuentum maius extiterit ſinu toto, ſubtrahe
              <lb/>
            ſinum totũ ab eo, & </s>
            <s xml:id="echoid-s7343" xml:space="preserve">ad arcum reſidui adde 90. </s>
            <s xml:id="echoid-s7344" xml:space="preserve">gra ſic´ habebis diſtantiã ſtellæ à meridi
              <lb/>
            ano: </s>
            <s xml:id="echoid-s7345" xml:space="preserve">quòd ſi ſtella fuerit in parte orientis, puta à meridiano, tunc ſubtrahe illam diſtantiã
              <lb/>
            ab aſcenſione recta ſtellæ, uerum ſi ſtella apparuerit tempore obſeruationis in medietate
              <lb/>
            cœli occidentall, adde tunc iſtam diſtantiam ſtellæ ad eius aſcenſionem rectam, & </s>
            <s xml:id="echoid-s7346" xml:space="preserve">habe-
              <lb/>
            bis ex aliquo illorum modorum gradum æquatoris, qui tangit medium cœ i ipſa hora ob
              <lb/>
            ſeruationis. </s>
            <s xml:id="echoid-s7347" xml:space="preserve">Hic mihi confer illud etiam ad aſcenſionem rectam nadir Solis, hoc eſt, ſi
              <lb/>
            180. </s>
            <s xml:id="echoid-s7348" xml:space="preserve">addas ad aſcenſionem rectam, iam habes aſcenſionem nadir Solis rectam, </s>
          </p>
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