Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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          <p>
            <s xml:id="echoid-s14397" xml:space="preserve">
              <pb o="335" file="371" n="372" rhead="Ioan. de Sacro Boſco."/>
            in his numeris, 4. </s>
            <s xml:id="echoid-s14398" xml:space="preserve">9. </s>
            <s xml:id="echoid-s14399" xml:space="preserve">9. </s>
            <s xml:id="echoid-s14400" xml:space="preserve">14. </s>
            <s xml:id="echoid-s14401" xml:space="preserve">Item in his, 20. </s>
            <s xml:id="echoid-s14402" xml:space="preserve">70. </s>
            <s xml:id="echoid-s14403" xml:space="preserve">70. </s>
            <s xml:id="echoid-s14404" xml:space="preserve">120. </s>
            <s xml:id="echoid-s14405" xml:space="preserve">Sic igitur fit in aſcenſioni-
              <lb/>
            bus. </s>
            <s xml:id="echoid-s14406" xml:space="preserve">Nam duæ aſcenſiones duorum arcuum oppoſitorum in ſphæra recta ſunt
              <lb/>
            ęquales, quibus circumponuntur aſcenſiones inæquales eorundem arcuum in
              <lb/>
            ſphæra@ obliqua, ita vt eodem exceſſu ſuperet maior æqualem alteram, quo mi
              <lb/>
            nor ab altera æquali ſuperatur. </s>
            <s xml:id="echoid-s14407" xml:space="preserve">Vt apparet in his quatuor aſcenſionibus, grad.
              <lb/>
            </s>
            <s xml:id="echoid-s14408" xml:space="preserve">17. </s>
            <s xml:id="echoid-s14409" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14410" xml:space="preserve">21. </s>
            <s xml:id="echoid-s14411" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s14412" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14413" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14414" xml:space="preserve">54. </s>
            <s xml:id="echoid-s14415" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s14416" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14417" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14418" xml:space="preserve">54. </s>
            <s xml:id="echoid-s14419" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s14420" xml:space="preserve">38. </s>
            <s xml:id="echoid-s14421" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14422" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14423" xml:space="preserve">Quarum prima
              <lb/>
            eſt Arietis aſcenſio Romæ; </s>
            <s xml:id="echoid-s14424" xml:space="preserve">ſecunda, aſcenſio eiuſdem Ar
              <unsure/>
            ietis in ſphæra recta; </s>
            <s xml:id="echoid-s14425" xml:space="preserve">
              <lb/>
            Tertia, aſcenſio Libræ ſigni oppoſiti in ſphęra recta; </s>
            <s xml:id="echoid-s14426" xml:space="preserve">Quarta denique, aſcenſio
              <lb/>
            eiuſdẽ Libræ Romæ; </s>
            <s xml:id="echoid-s14427" xml:space="preserve">& </s>
            <s xml:id="echoid-s14428" xml:space="preserve">quia tantũ prima ſuperatur à ſecunda, quantum quarta
              <lb/>
            ſuperat tertiã; </s>
            <s xml:id="echoid-s14429" xml:space="preserve">(eſt enim utrobiq; </s>
            <s xml:id="echoid-s14430" xml:space="preserve">exceſſus grad. </s>
            <s xml:id="echoid-s14431" xml:space="preserve">10. </s>
            <s xml:id="echoid-s14432" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14433" xml:space="preserve">33.) </s>
            <s xml:id="echoid-s14434" xml:space="preserve">ideo prima, & </s>
            <s xml:id="echoid-s14435" xml:space="preserve">quar
              <lb/>
            ta ſimul efficiunt tot gradus, & </s>
            <s xml:id="echoid-s14436" xml:space="preserve">minuta, quot conſtituuntur ex medijs duabus,
              <lb/>
            nempe grad. </s>
            <s xml:id="echoid-s14437" xml:space="preserve">55. </s>
            <s xml:id="echoid-s14438" xml:space="preserve">min. </s>
            <s xml:id="echoid-s14439" xml:space="preserve">48. </s>
            <s xml:id="echoid-s14440" xml:space="preserve">Eademque eſt ratio habenda de cæteris.</s>
            <s xml:id="echoid-s14441" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14442" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            arcus æquales, æqualiterque ab alterutro punctorum ſolſtitia-
              <lb/>
              <note position="right" xlink:label="note-371-01" xlink:href="note-371-01a" xml:space="preserve">Arcus æqu@
                <lb/>
              les, æquali-
                <lb/>
              terq́; ab al-
                <lb/>
              terutro pun
                <lb/>
              ctorum ſol
                <lb/>
              ſtitialiũ re-
                <lb/>
              moti habẽt
                <lb/>
              in ſphæra
                <lb/>
              obliqua a-
                <lb/>
              ſcẽſiones ſi-
                <lb/>
              mul ſum-
                <lb/>
              ptas ęqua-
                <lb/>
              les aſcenſio
                <lb/>
              nibus eorũ-
                <lb/>
              dem ſimul
                <lb/>
              ſ@mptis in
                <lb/>
              ſphæra re-
                <lb/>
              cta.</note>
            lium remoti habent aſcenſiones ſimul ſumptas æquales aſcenſionibus eorun-
              <lb/>
            dem in ſphæra recta ſimul ſumptis, nempe ♉, & </s>
            <s xml:id="echoid-s14443" xml:space="preserve">♌; </s>
            <s xml:id="echoid-s14444" xml:space="preserve">♓, & </s>
            <s xml:id="echoid-s14445" xml:space="preserve">♎, &</s>
            <s xml:id="echoid-s14446" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14447" xml:space="preserve">ut demonſtrãt
              <lb/>
            Geber, & </s>
            <s xml:id="echoid-s14448" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s14449" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s14450" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14451" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14452" xml:space="preserve">Epitomes propoſ. </s>
            <s xml:id="echoid-s14453" xml:space="preserve">20.</s>
            <s xml:id="echoid-s14454" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14455" xml:space="preserve">
              <emph style="sc">Eodem</emph>
            pacto erunt aſcenſiones quorumlibet duorum arcuũ æqualium
              <lb/>
            & </s>
            <s xml:id="echoid-s14456" xml:space="preserve">oppoſitorum, etiamſi non initium ſumant à punctis ęquinoctiorum, ſimul
              <lb/>
            ſumptæ æquales aſcenſionibus eorundem arcuũ in ſphæra recta ſimul ſumptis,
              <lb/>
            quamuis inter ſe ſint inęquales: </s>
            <s xml:id="echoid-s14457" xml:space="preserve">Verum tamen eſt, tunc non ſemper aſcenſio-
              <lb/>
            nem obliquam arcus, qui in medietate Zodiaci Borea comprehenditur, mino-
              <lb/>
            rem eſſe aſcenſione recta eiuſdem arcus, aſcenſionem uero obliquam arcus in
              <lb/>
            medietate Zodiaci Auſtrina contenti maiorem aſcenſione recta eiuſdẽ arcus;
              <lb/>
            </s>
            <s xml:id="echoid-s14458" xml:space="preserve">ſed quandoque illam eſſe maiorem, hanc vero minorem, quandoq; </s>
            <s xml:id="echoid-s14459" xml:space="preserve">vero illam
              <lb/>
            minorem, & </s>
            <s xml:id="echoid-s14460" xml:space="preserve">hanc maiorem. </s>
            <s xml:id="echoid-s14461" xml:space="preserve">Quæ quidem omnia Geometrice poſſunt oſtendi
              <lb/>
            ex doctrina triangulorum ſphæricorum, clariſſimeq́. </s>
            <s xml:id="echoid-s14462" xml:space="preserve">perſpiciuntur in tabulis
              <lb/>
            aſcenſionum obliquar
              <unsure/>
            um. </s>
            <s xml:id="echoid-s14463" xml:space="preserve">Nihilominus hoc ipſum hac ratione confirmatio po
              <lb/>
            terit. </s>
            <s xml:id="echoid-s14464" xml:space="preserve">Sint duo ſigna oppoſita ♌, & </s>
            <s xml:id="echoid-s14465" xml:space="preserve">♒. </s>
            <s xml:id="echoid-s14466" xml:space="preserve">Dico aſcenſiones eorum ſimul ſumptas
              <lb/>
            æquales eſſe aſcenſionibus eorundem ſimul ſumptis in ſphæra recta. </s>
            <s xml:id="echoid-s14467" xml:space="preserve">Quoniã
              <lb/>
            enim aſcenſio ♌ & </s>
            <s xml:id="echoid-s14468" xml:space="preserve">aſcenſio ♉, in ſphæra obliqua ſimul ſumptæ æquales ſunt
              <lb/>
            aſcenſionibus ſimul ſumptis, quas habent in ſphæra recta, vt dictum eſt, quia
              <lb/>
            hæc ſigna ęqualiter recedunt a puncto Solſtitij; </s>
            <s xml:id="echoid-s14469" xml:space="preserve">Et aſcenſio ♉, in ſphæra obli-
              <lb/>
            qua æqualis eſt aſcenſioni ♒, ut ex 3. </s>
            <s xml:id="echoid-s14470" xml:space="preserve">regula conſtabit, quia hæc ſigna ęquali-
              <lb/>
            ter ab æquinoctij puncto remouentur; </s>
            <s xml:id="echoid-s14471" xml:space="preserve">Erunt aſcenſio ♌, & </s>
            <s xml:id="echoid-s14472" xml:space="preserve">aſcenſio ♒, ſimul
              <lb/>
            æquales eorundem ſignorum aſcenſionibus in ſphæra recta. </s>
            <s xml:id="echoid-s14473" xml:space="preserve">Quod aliter ita
              <lb/>
            quoque confirmabitur. </s>
            <s xml:id="echoid-s14474" xml:space="preserve">Quoniam aſcenſio arcus a principio ♈, vſque ad ſinem
              <lb/>
            ♌; </s>
            <s xml:id="echoid-s14475" xml:space="preserve">& </s>
            <s xml:id="echoid-s14476" xml:space="preserve">aſcenſio arcus a principio ♎, uſque ad finem ♒, in ſphæra obliqua ſimul
              <lb/>
            æquales ſunt aſcenſionibus eorundem arcuum ſimul in ſphæra recta, ut ex
              <lb/>
            proximo coroll. </s>
            <s xml:id="echoid-s14477" xml:space="preserve">patet: </s>
            <s xml:id="echoid-s14478" xml:space="preserve">Item aſcenſio arcus à principio ♈, uſque ad princi-
              <lb/>
            pium ♌; </s>
            <s xml:id="echoid-s14479" xml:space="preserve">& </s>
            <s xml:id="echoid-s14480" xml:space="preserve">aſcenſio arcus a principio ♎, uſque ad principium ♒, in ſphæ-
              <lb/>
            ra obliqua ſimul ęquales ſunt aſcenſionibus eorundem arcuum ſimul in ſphæ-
              <lb/>
            ra recta, ut ex eodem coroll. </s>
            <s xml:id="echoid-s14481" xml:space="preserve">manifeſtum eſt: </s>
            <s xml:id="echoid-s14482" xml:space="preserve">fit, ut ſi hæ aſcenſiones poſte-
              <lb/>
            riores ex illis prioribus detrahantur, reliquæ aſcenſiones arcuum ♌, & </s>
            <s xml:id="echoid-s14483" xml:space="preserve">♒, ſi-
              <lb/>
            mul in ſphæra obliqua æquales ſint reliquis aſcenſionibus eorundem arcuum
              <lb/>
            ſimul in ſphæra recta. </s>
            <s xml:id="echoid-s14484" xml:space="preserve">Idem dices de quibuſcunque arcubus oppoſitis, & </s>
            <s xml:id="echoid-s14485" xml:space="preserve">æqua-
              <lb/>
            libus, quia ſemper aſcenſio unius eſt æqualis aſcenſioni alicuius arcus æqua-
              <lb/>
            lis, qui æqualiter cum reliquo a Solſtitiali puncto diſtat, ut patet. </s>
            <s xml:id="echoid-s14486" xml:space="preserve">Ex his patet
              <lb/>
            ueritas 2. </s>
            <s xml:id="echoid-s14487" xml:space="preserve">regulæ propoſitæ. </s>
            <s xml:id="echoid-s14488" xml:space="preserve">Eſt enim eadem ratio arcuum æqualium, & </s>
            <s xml:id="echoid-s14489" xml:space="preserve"/>
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