Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

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[251.] DE ORTV, ET OCC ASV SIGNO-rum in ſphæra recta.
Page: 360 (323)
[252.] COMMENTARIVS.
Page: 360 (323)
[253.] COMMENTARIVS.
Page: 361 (324)
[254.] COMMENTARIVS.
Page: 361 (324)
[255.] COMMENTARIVS.
Page: 364 (327)
[256.] QVOMODO ASCENSIO RECTA cuiuſlibet arcus Zodiaci a Verna ſectione inchoati ſupputetur.
Page: 365 (328)
[257.] TABVLA ASCENSIONVM Rectarum.
Page: 367 (330)
[258.] RESIDVVM TABVLAE ASCEN ſionum rectarum.
Page: 368 (331)
[259.] VSVS TABVLÆ ASCESIONVM RECTARVM.
Page: 369 (332)
[260.] DE ORTV, ET OCCASV SIGNORVM in ſphæraobliqua.
Page: 369 (332)
[261.] COMMENTARIVS.
Page: 370 (333)
[262.] COMMENTARIVS.
Page: 371 (334)
[263.] COMMENTARIVS.
Page: 371 (334)
[264.] COMMENTARIVS.
Page: 373 (336)
[265.] QVA RATIONE ASCENSIO OBLIQVA cuiuslibet arcus Zodiaci à Verna ſectione nu-merati inueniatur.
Page: 374 (337)
[266.] Sequuntur Tabulæ.
Page: 376 (339)
[267.] TABVLA DIFFERENTIARVM Aſcenſionalium.
Page: 377 (340)
[268.] RESIDVVM TABVLAE Differentiarum Aſcenſionalium. # Poli
Page: 378 (341)
[269.] TABVLA DIFFERENTIARVM Aſcenſionalium.
Page: 379 (342)
[270.] RESIDVVM TABVLAE Differentiarum Aſcenſionalium.
Page: 380 (343)
[271.] RESIDVVM TABVLAE Differentiarum Aſcenſionalium.
Page: 381 (344)
[272.] RESIDVVM TABVLAE Differentiarum Aſcenſionalium.
Page: 382 (345)
[273.] RESIDVVM TABVLAE Differentiarum Aſcenſionalium.
Page: 383 (346)
[274.] RESIDVVM TABVLAE Differentiarum Aſcenſionalium.
Page: 384 (347)
[275.] TABVLA ASCENSIONVM Obliquarum.
Page: 385 (348)
[276.] AD LATITV DINEM Graduum 36.
Page: 386 (349)
[277.] TABVLA ASCENSIONVM Obliquarum.
Page: 387 (350)
[278.] AD LATITVDINEM Graduum 37.
Page: 388 (351)
[279.] TABVLA ASCENSIONVM Obliquarum.
Page: 389 (352)
[280.] AD LATITVDINEM Graduum 38.
Page: 390 (353)
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          <p>
            <s xml:id="echoid-s14561" xml:space="preserve">
              <pb o="337" file="373" n="374" rhead="Ioan. de Sacro Boſco."/>
            aſcẽſio huius ſigni poſterioris ęqualis eſſet deſcẽſioni eiuſdẽ, haberẽt ſigna
              <lb/>
              <note position="right" xlink:label="note-373-01" xlink:href="note-373-01a" xml:space="preserve">inęqualis
                <unsure/>
                <lb/>
              eſt deſcẽſi@
                <lb/>
              ni eiuſdem
                <lb/>
              ſigni.</note>
            oppoſita ęquales aſcẽſiones, qđ eſt contra ea, q̃ dicta ſunt in 2. </s>
            <s xml:id="echoid-s14562" xml:space="preserve">regula. </s>
            <s xml:id="echoid-s14563" xml:space="preserve">Aſcen-
              <lb/>
            ſio tamen cuiuſuis ſigni, & </s>
            <s xml:id="echoid-s14564" xml:space="preserve">deſcenſio eiuſdem in obliqua ſphæra ſimul ſumptæ
              <lb/>
            æquales ſunt aſcenſioni, & </s>
            <s xml:id="echoid-s14565" xml:space="preserve">deſcenſioni eiuſdem in ſph ęra recta ſimul ſumptis;
              <lb/>
            </s>
            <s xml:id="echoid-s14566" xml:space="preserve">quia quanto obliquius, uel rectius aliquod ſignum oritur in ſphæra obliqua,
              <lb/>
              <note position="right" xlink:label="note-373-02" xlink:href="note-373-02a" xml:space="preserve">@ſcẽſio, &c
                <lb/>
              deſcenſio
                <lb/>
              eiuſdem ſi-
                <lb/>
              gni in ſphę
                <lb/>
              ra obliqua
                <lb/>
              ſimul æquæ
                <lb/>
              les sũt aſe@
                <lb/>
              ſioni, & de-
                <lb/>
              ſcenſioni
                <lb/>
              eiuſde@@ ſi
                <lb/>
              gniſimuli@
                <lb/>
              ſphæra re-
                <lb/>
              cta.</note>
            quàm in recta, tanto rectius, uel obliqui
              <unsure/>
            us occidit, ut conſtat ex triangulis ſphę
              <lb/>
            ricis, & </s>
            <s xml:id="echoid-s14567" xml:space="preserve">manifeſtum erit ex tabulis aſcenſionum obliquarum.</s>
            <s xml:id="echoid-s14568" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div752" type="section" level="1" n="265">
          <head xml:id="echoid-head276" xml:space="preserve">QVA RATIONE ASCENSIO OBLIQVA
            <lb/>
          cuiuslibet arcus Zodiaci à Verna ſectione nu-
            <lb/>
          merati inueniatur.</head>
          <p>
            <s xml:id="echoid-s14569" xml:space="preserve">
              <emph style="sc">Qvia</emph>
            dictum eſt in 1. </s>
            <s xml:id="echoid-s14570" xml:space="preserve">regula, aſcenſiones obliquas arcuum Eclipticæ in
              <lb/>
            medietate Septentrionali cõtentorum, initio ſemper facto à primo puncto ♈,
              <lb/>
            tanto minores eſſe aſcenſionibus rectis eorundem arcuũ, quanto maiores ſunt
              <lb/>
            aſcẽſiones obliquæ arcuũ Eclipticæ in medietate Auſtrali comprehenſorum,
              <lb/>
            initio quoque ſemper facto à principio ♎, aſcẽſionibus rectis eorundẽ arcuũ;
              <lb/>
            </s>
            <s xml:id="echoid-s14571" xml:space="preserve">Manifeſtũ eſt, ſi ab aſcenſionibus rectis arcũ prioris medietatis Eclipticæ de-
              <lb/>
              <note position="right" xlink:label="note-373-03" xlink:href="note-373-03a" xml:space="preserve">Quo pact@@
                <lb/>
              ex differe@
                <lb/>
              tijs aſcẽſi@-
                <lb/>
              libus repe-
                <lb/>
              riãtur aſcẽ-
                <lb/>
              ſiones obli
                <unsure/>
                <lb/>
              quæ.</note>
            trahantur differentię aſcenſionales, quibus nimir
              <unsure/>
            ũ differũt aſcenſiones rectæ
              <lb/>
            ab obliquis, relinqui eorundem arcuum aſcenſiones ob liquas; </s>
            <s xml:id="echoid-s14572" xml:space="preserve">Si uero eædem
              <lb/>
            differentiæ aſcenſionales adijciantur aſcenſionibus rectis arcuum Eclipticæ
              <lb/>
            poſterioris medietatis, effici aſcenſiones obliquas eorũdem arcuum, initio ſem
              <lb/>
            per facto à principijs ♈, & </s>
            <s xml:id="echoid-s14573" xml:space="preserve">♎. </s>
            <s xml:id="echoid-s14574" xml:space="preserve">Hanc autem aſcenſionalem differentiã hac arte
              <lb/>
            inuenies ex doctrina Sinuũ. </s>
            <s xml:id="echoid-s14575" xml:space="preserve">Vt demonſtrat Geber, & </s>
            <s xml:id="echoid-s14576" xml:space="preserve">nos etiam demonſtraui-
              <lb/>
            mus in ſcholio propoſ. </s>
            <s xml:id="echoid-s14577" xml:space="preserve">9. </s>
            <s xml:id="echoid-s14578" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14579" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14580" xml:space="preserve">Gnomonices, ita ſe habet ſinus complementi
              <lb/>
              <note position="right" xlink:label="note-373-04" xlink:href="note-373-04a" xml:space="preserve">Qua rati@
                <lb/>
              ne ꝑ ſinus
                <lb/>
              di
                <unsure/>
              fferentiæ
                <lb/>
              aſcenſiona.
                <lb/>
              les inueni@
                <lb/>
              tur.</note>
            declinationis puncti Eclipticæ propoſiti ad ſinum complementi latitudinis
              <lb/>
            ortiuæ, ſiue occiduæ eiuſdem puncti Eclipticæ, ut ſinus totus ad ſinum cõple-
              <lb/>
            menti differentiæ aſcenſionalis. </s>
            <s xml:id="echoid-s14581" xml:space="preserve">Quamobrem ſi ſinus complementi latitudi-
              <lb/>
            nis ortiuæ in ſinum totum multiplicetur, & </s>
            <s xml:id="echoid-s14582" xml:space="preserve">productus numerus in ſinum cõ
              <lb/>
            plementi declina
              <unsure/>
            tionis puncti propoſiti diuidatur, ut pręcipit regula propor-
              <lb/>
            tionũ, habebitur ſinus complementi differentiæ aſcenſionalis. </s>
            <s xml:id="echoid-s14583" xml:space="preserve">Quare cogno-
              <lb/>
            ſcetur ex tabula finuum differentia aſcenſionalis. </s>
            <s xml:id="echoid-s14584" xml:space="preserve">
              <emph style="sc">Exemplvm</emph>
            . </s>
            <s xml:id="echoid-s14585" xml:space="preserve">Quærenda ſit
              <lb/>
            differentia Romæ, qua differt aſcenſ@o obliqua arcus Eclipticæ ab ♈, uſque ad
              <lb/>
            finem ♊, ab aſcenſioni recta. </s>
            <s xml:id="echoid-s14586" xml:space="preserve">Quoniam igitur declinatio puncti extremi ♊, eſt
              <lb/>
            grad. </s>
            <s xml:id="echoid-s14587" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14588" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14589" xml:space="preserve">30. </s>
            <s xml:id="echoid-s14590" xml:space="preserve">& </s>
            <s xml:id="echoid-s14591" xml:space="preserve">latitudo ortiua grad. </s>
            <s xml:id="echoid-s14592" xml:space="preserve">32. </s>
            <s xml:id="echoid-s14593" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14594" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14595" xml:space="preserve">Multiplico ſinum comple
              <lb/>
            menti latitudinis ortiuę, nempe 84386. </s>
            <s xml:id="echoid-s14596" xml:space="preserve">in ſinum totum, uidelicet in 100000.
              <lb/>
            </s>
            <s xml:id="echoid-s14597" xml:space="preserve">productũ deinde numerum 8438600000. </s>
            <s xml:id="echoid-s14598" xml:space="preserve">diuido per 91706. </s>
            <s xml:id="echoid-s14599" xml:space="preserve">ſinum comple-
              <lb/>
            menti declinationis extremi puncti ♊, & </s>
            <s xml:id="echoid-s14600" xml:space="preserve">exibit ſinus complementi differen-
              <lb/>
              <note position="right" xlink:label="note-373-05" xlink:href="note-373-05a" xml:space="preserve">Satis eſt, ſ@
                <lb/>
              inueſtigen-
                <lb/>
              tur differe@
                <lb/>
              tię aſcẽſio-
                <lb/>
              nales pun-
                <lb/>
              ctorũ vnius
                <lb/>
              quadrantis
                <lb/>
              Eclipticæ.</note>
            tiæ aſcenſionalis fere 92018. </s>
            <s xml:id="echoid-s14601" xml:space="preserve">cui reſpondent in tabula ſinuum grad. </s>
            <s xml:id="echoid-s14602" xml:space="preserve">66. </s>
            <s xml:id="echoid-s14603" xml:space="preserve">min.
              <lb/>
            </s>
            <s xml:id="echoid-s14604" xml:space="preserve">57. </s>
            <s xml:id="echoid-s14605" xml:space="preserve">Igitur differentia aſcenſionalis erit grad. </s>
            <s xml:id="echoid-s14606" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14607" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14608" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14609" xml:space="preserve">Quia ablata ex aſcenſio
              <lb/>
            ne recta arcus propoſiti, nempe ex grad. </s>
            <s xml:id="echoid-s14610" xml:space="preserve">90. </s>
            <s xml:id="echoid-s14611" xml:space="preserve">quia eſt in priori medietate Ecli-
              <lb/>
            pticæ, relinquetur aſcenſio obliqua dictiarcus Romæ grad. </s>
            <s xml:id="echoid-s14612" xml:space="preserve">66. </s>
            <s xml:id="echoid-s14613" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14614" xml:space="preserve">57.</s>
            <s xml:id="echoid-s14615" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14616" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            vero ſupra docuimus, & </s>
            <s xml:id="echoid-s14617" xml:space="preserve">declinationes, & </s>
            <s xml:id="echoid-s14618" xml:space="preserve">latitudines ortiuas
              <lb/>
            punctorum oium unius Quadrantis ęquales eſſe declinationibus, latitudini-
              <lb/>
            busque, quas habent omnia puncta reliquorũ Quadrantũ, perſpicuum eſt, ſatis
              <lb/>
            eſſe, ſi @@ueſtigétur differẽtiæ aſcẽſionales unius dũtaxat Quadr
              <unsure/>
            ãtis Eclipticę.</s>
            <s xml:id="echoid-s14619" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quo pacto
            <lb/>
          a@ter per
            <lb/>
          anus inue-</note>
          <p>
            <s xml:id="echoid-s14620" xml:space="preserve">
              <emph style="sc">Alio</emph>
            modo reperietur differentia aſcenſionalis cuiusuis arcus, ſeu pun-
              <lb/>
            cti Eclipticæ abſq. </s>
            <s xml:id="echoid-s14621" xml:space="preserve">cognitione latitudinis ortiuæ, uel occiduę, hac arte. </s>
            <s xml:id="echoid-s14622" xml:space="preserve"/>
          </p>
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