Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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          <p>
            <s xml:id="echoid-s14622" xml:space="preserve">
              <pb o="338" file="374" n="375" rhead="Comment in III. Cap. Sphæræ"/>
            tiplicetur ſinus altitudinis poli in ſinum totum, numerusq́; </s>
            <s xml:id="echoid-s14623" xml:space="preserve">productus per ſi-
              <lb/>
              <note position="left" xlink:label="note-374-01" xlink:href="note-374-01a" xml:space="preserve">niãtur dif-
                <lb/>
              ferentiæ a-
                <lb/>
              ſcenſiona-
                <lb/>
              les.</note>
            num complementi altitudinis poli diuidatur. </s>
            <s xml:id="echoid-s14624" xml:space="preserve">Exibit enim ſinus, qui in una
              <lb/>
            eademque regione nunquam uariabitur unde non immerito ſinus regionis
              <lb/>
            dici poterit, qui Romæ talis eſt fere 90041. </s>
            <s xml:id="echoid-s14625" xml:space="preserve">Deinde quoniã, ut demonſtrat 10.
              <lb/>
            </s>
            <s xml:id="echoid-s14626" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s14627" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14628" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14629" xml:space="preserve">Epito. </s>
            <s xml:id="echoid-s14630" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14631" xml:space="preserve">22. </s>
            <s xml:id="echoid-s14632" xml:space="preserve">Talis eſt proportio ſinus complementi decli-
              <lb/>
            nationis puncti eclipticę propoſiti, quod nimirum arcum datum terminat, ad
              <lb/>
            ſinum declinationis, qualis eſt proportio ſinus, quem regionis diximus, ad ſi-
              <lb/>
            num differentiæ aſcen@ionalis propoſiti puncti eclipticæ; </s>
            <s xml:id="echoid-s14633" xml:space="preserve">Si iuxta præceptum
              <lb/>
            regulæ proportionum ſinus declinationis puncti propoſiti multiplicetur in ſi
              <lb/>
            num regionis inuentum, productus deinde numerus in ſinum complementi
              <lb/>
            declinationis diuidatur, habebitur ſinus differentię aſcenſionalis quæſitæ. </s>
            <s xml:id="echoid-s14634" xml:space="preserve">
              <lb/>
              <emph style="sc">Exemplvm</emph>
            . </s>
            <s xml:id="echoid-s14635" xml:space="preserve">Romæ quæro differentiam aſcenſionalem primi Quadrantis ecli
              <lb/>
            pticæ, nempe ultimi puncti ♊. </s>
            <s xml:id="echoid-s14636" xml:space="preserve">Multiplico 39874. </s>
            <s xml:id="echoid-s14637" xml:space="preserve">ſinum deelinationis in ſinũ
              <lb/>
            regionis Romæ, 90041. </s>
            <s xml:id="echoid-s14638" xml:space="preserve">productumq. </s>
            <s xml:id="echoid-s14639" xml:space="preserve">numerũ 3590294834. </s>
            <s xml:id="echoid-s14640" xml:space="preserve">diuido per 91706. </s>
            <s xml:id="echoid-s14641" xml:space="preserve">
              <lb/>
            finum complementi declinationis, & </s>
            <s xml:id="echoid-s14642" xml:space="preserve">proueniet ſinus differentiæ aſcenſionalis
              <lb/>
            quæſitæ 39150. </s>
            <s xml:id="echoid-s14643" xml:space="preserve">cui reſpondet arcus grad. </s>
            <s xml:id="echoid-s14644" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14645" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14646" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14647" xml:space="preserve">ſicut prius.</s>
            <s xml:id="echoid-s14648" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14649" xml:space="preserve">
              <emph style="sc">Hac</emph>
            arte Ioan. </s>
            <s xml:id="echoid-s14650" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s14651" xml:space="preserve">ſupputauit differẽtias aſcenſionales omniũ pun-
              <lb/>
            ctorũ, quæ declinant ab Aequatore, incipiendo à gradu 1. </s>
            <s xml:id="echoid-s14652" xml:space="preserve">declinationis uſque
              <lb/>
            ad grad. </s>
            <s xml:id="echoid-s14653" xml:space="preserve">32 Nã nullus Planeta, quorum gratia tabulas conſcripſit, maiorem un
              <lb/>
            quam habuit declinationem. </s>
            <s xml:id="echoid-s14654" xml:space="preserve">Si igitur deſideras aſcenſionalem differentiã cu-
              <lb/>
              <note position="left" xlink:label="note-374-02" xlink:href="note-374-02a" xml:space="preserve">Qũo ex ta-
                <lb/>
              bula diffe-
                <lb/>
              rentiarum
                <lb/>
              aſcenſi@na-
                <lb/>
              liũ differẽ-
                <lb/>
              tiæ aſceſio-
                <lb/>
              nales repe-
                <lb/>
              riantur.</note>
            iuſuis arcus eclipticæ, quære in uertice tabulæ differentiarũ aſcenſionaliũ ele-
              <lb/>
            uationem poli, & </s>
            <s xml:id="echoid-s14655" xml:space="preserve">in latere ſiniſtro declinationem extremi puncti arcus pro-
              <lb/>
            poſiti. </s>
            <s xml:id="echoid-s14656" xml:space="preserve">Nam in angulo communis concurſus reperies differentiam quæſitã. </s>
            <s xml:id="echoid-s14657" xml:space="preserve">Vt
              <lb/>
            Romæ, ubi eleuatur polus 42. </s>
            <s xml:id="echoid-s14658" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s14659" xml:space="preserve">punctum eclipticæ, quod declinat 18. </s>
            <s xml:id="echoid-s14660" xml:space="preserve">grad.
              <lb/>
            </s>
            <s xml:id="echoid-s14661" xml:space="preserve">ab Aequatore, habet differentiam aſcenſionalem grad. </s>
            <s xml:id="echoid-s14662" xml:space="preserve">17. </s>
            <s xml:id="echoid-s14663" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14664" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14665" xml:space="preserve">&</s>
            <s xml:id="echoid-s14666" xml:space="preserve">c.</s>
            <s xml:id="echoid-s14667" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14668" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi declinatio puncti non reperiatur in ſiniſtro latere, quærendus
              <lb/>
            eſt exceſſus inter aſcenſionalem differentiam declinationis proxime maioris,
              <lb/>
            & </s>
            <s xml:id="echoid-s14669" xml:space="preserve">differentiam aſcenſionem declinationis proxime minoris. </s>
            <s xml:id="echoid-s14670" xml:space="preserve">Deinde elicien-
              <lb/>
            da pars proportionalis minutis propoſitę declinationis reſpondens. </s>
            <s xml:id="echoid-s14671" xml:space="preserve">Hęc enim
              <lb/>
            adiecta diſſerentiæ aſcenſionali declinationis proxime minoris dabit aſcenſio-
              <lb/>
            nalem differentiam quęſitam. </s>
            <s xml:id="echoid-s14672" xml:space="preserve">
              <emph style="sc">Exemplvm</emph>
            . </s>
            <s xml:id="echoid-s14673" xml:space="preserve">Romæ inuenienda ſit differentia
              <lb/>
            aſcenſionalis ultimi puncti ♊, uel primi grad. </s>
            <s xml:id="echoid-s14674" xml:space="preserve">♋, hoc eft primi Quadrantis
              <lb/>
            eclipticę. </s>
            <s xml:id="echoid-s14675" xml:space="preserve">Quoniam igitur declinatio primi gradus ♋, eſt grad. </s>
            <s xml:id="echoid-s14676" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14677" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14678" xml:space="preserve">30.
              <lb/>
            </s>
            <s xml:id="echoid-s14679" xml:space="preserve">Accipio differentiam aſcenſionalem grad. </s>
            <s xml:id="echoid-s14680" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14681" xml:space="preserve">declinationis, nempe gr. </s>
            <s xml:id="echoid-s14682" xml:space="preserve">22. </s>
            <s xml:id="echoid-s14683" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14684" xml:space="preserve">
              <lb/>
            28. </s>
            <s xml:id="echoid-s14685" xml:space="preserve">Item differentiam aſcenſionalem debitam declinationi grad. </s>
            <s xml:id="echoid-s14686" xml:space="preserve">24. </s>
            <s xml:id="echoid-s14687" xml:space="preserve">nimirum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s14688" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14689" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14690" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14691" xml:space="preserve">quarum differentia eſt grad. </s>
            <s xml:id="echoid-s14692" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14693" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14694" xml:space="preserve">10. </s>
            <s xml:id="echoid-s14695" xml:space="preserve">quę debetur tunc inte-
              <lb/>
            gro gradui declinationis: </s>
            <s xml:id="echoid-s14696" xml:space="preserve">Igitur iuxta regulam proportionum minutis 30. </s>
            <s xml:id="echoid-s14697" xml:space="preserve">de-
              <lb/>
            bentur min. </s>
            <s xml:id="echoid-s14698" xml:space="preserve">35. </s>
            <s xml:id="echoid-s14699" xml:space="preserve">quæ adiecta differentiæ aſcenſionali, quę debetur declinatio-
              <lb/>
            ni grad. </s>
            <s xml:id="echoid-s14700" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14701" xml:space="preserve">nempe gradibus 22. </s>
            <s xml:id="echoid-s14702" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14703" xml:space="preserve">28. </s>
            <s xml:id="echoid-s14704" xml:space="preserve">habebitur differentia aſcenſionalis
              <lb/>
            grad. </s>
            <s xml:id="echoid-s14705" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14706" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14707" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14708" xml:space="preserve">ueluti prius, debita declinationi grad. </s>
            <s xml:id="echoid-s14709" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14710" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14711" xml:space="preserve">30. </s>
            <s xml:id="echoid-s14712" xml:space="preserve">nempe princi
              <lb/>
            pio ♋. </s>
            <s xml:id="echoid-s14713" xml:space="preserve">Atque ita cæteris.</s>
            <s xml:id="echoid-s14714" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14715" xml:space="preserve">
              <emph style="sc">Constat</emph>
            igitur ex his, qua arte conſtruenda ſit tabula differentia-
              <lb/>
            rum aſcenſionalium ad quamcunque poli eleuationem, & </s>
            <s xml:id="echoid-s14716" xml:space="preserve">conſequenter ex ta
              <lb/>
            bula aſcenſionalium differentiarum tabula aſcenſionum obliquarum. </s>
            <s xml:id="echoid-s14717" xml:space="preserve">Vt ta-
              <lb/>
            men lectorem hoc onere ſubleuarem; </s>
            <s xml:id="echoid-s14718" xml:space="preserve">ſubiunxi ex Ioan. </s>
            <s xml:id="echoid-s14719" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s14720" xml:space="preserve">tabulas diffe-
              <lb/>
            rentiarũ aſcenſionaliũ ad omnes poli eleuationes incipiendo ab 1. </s>
            <s xml:id="echoid-s14721" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s14722" xml:space="preserve">vſq; </s>
            <s xml:id="echoid-s14723" xml:space="preserve">ad
              <lb/>
            60. </s>
            <s xml:id="echoid-s14724" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s14725" xml:space="preserve">Item tabulas aſcenſionum obliquarum ad ſingulas quoque poli alti-
              <lb/>
            tudines, incipiendo à grad. </s>
            <s xml:id="echoid-s14726" xml:space="preserve">36. </s>
            <s xml:id="echoid-s14727" xml:space="preserve">vſq; </s>
            <s xml:id="echoid-s14728" xml:space="preserve">ad grad. </s>
            <s xml:id="echoid-s14729" xml:space="preserve">60. </s>
            <s xml:id="echoid-s14730" xml:space="preserve">quoniam inſignes habent </s>
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