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-s8877" xml:space="preserve">
              <pb o="219" file="255" n="256" rhead="Ioan. de Sacro Boſco."/>
            re arenulas 10000. </s>
            <s xml:id="echoid-s8878" xml:space="preserve">cõplectetur eadẽ ſdhæra diametrum habens digito æqualẽ
              <lb/>
            arenulas 640000000. </s>
            <s xml:id="echoid-s8879" xml:space="preserve">immo multo maior erit hic numer
              <emph style="sub">9</emph>
            numero arenularũ,
              <lb/>
            quæ in ſphæra diametiũ digito ęqualem habente includitur: </s>
            <s xml:id="echoid-s8880" xml:space="preserve">propterea quòd
              <lb/>
            & </s>
            <s xml:id="echoid-s8881" xml:space="preserve">pauciora grana papaueris, quàm 40. </s>
            <s xml:id="echoid-s8882" xml:space="preserve">digitũ conſtituunt, & </s>
            <s xml:id="echoid-s8883" xml:space="preserve">arenulæ maiores
              <lb/>
            ſunt, quàm ut 10000. </s>
            <s xml:id="echoid-s8884" xml:space="preserve">unum granum papaueris efficere poſſint. </s>
            <s xml:id="echoid-s8885" xml:space="preserve">Nos tamen,
              <lb/>
            ut ſupputatio ſit expeditior, ponamus ſphæram, cuius diameter ſit digito
              <lb/>
            æqualis, compre hendere arenulas non ſolum 640000000. </s>
            <s xml:id="echoid-s8886" xml:space="preserve">ſed 1000000000.</s>
            <s xml:id="echoid-s8887" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8888" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            quia accepimus, digitos 100000. </s>
            <s xml:id="echoid-s8889" xml:space="preserve">conſtituere unum milliare,
              <lb/>
            licet milliare multo minus ſit; </s>
            <s xml:id="echoid-s8890" xml:space="preserve">habebit ſphæra diametrum habens milliari æ-
              <lb/>
            qualem ad ſphæram, quæ diametrum digito æqualem habeat, proportionem,
              <lb/>
            quam 1000000000000000. </s>
            <s xml:id="echoid-s8891" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s8892" xml:space="preserve">propterea quod ſphærę habent triplicatam
              <lb/>
            proportionem diametrorum: </s>
            <s xml:id="echoid-s8893" xml:space="preserve">ut in quatuor his nu-
              <lb/>
              <note position="right" xlink:label="note-255-01" xlink:href="note-255-01a" xml:space="preserve">18. duod.</note>
              <note position="right" xlink:label="note-255-02" xlink:href="note-255-02a" xml:space="preserve">
                <lb/>
              1
                <lb/>
              100000
                <lb/>
              10000000000
                <lb/>
              1000000000000000
                <lb/>
              </note>
            meris appatet, qui continue proportionales ſunt
              <lb/>
            in proportione 100000. </s>
            <s xml:id="echoid-s8894" xml:space="preserve">digitorum, hoc eſt, in pro-
              <lb/>
            portione unius milliarij, ad 1. </s>
            <s xml:id="echoid-s8895" xml:space="preserve">Cum ergo ſphęra dia
              <lb/>
            metrum habens digito ęqualem poſita ſit cõtinere
              <lb/>
            arenulas 1000000000. </s>
            <s xml:id="echoid-s8896" xml:space="preserve">quamuis lõge pauciores cõ-
              <lb/>
            tineat, ut oſtenſum eſt: </s>
            <s xml:id="echoid-s8897" xml:space="preserve">continebit ſphæra, cuius diameter milliario ſit æqua-
              <lb/>
            lis, has omnes arenulas 1000000000000000000000000. </s>
            <s xml:id="echoid-s8898" xml:space="preserve">immo hic numerus
              <lb/>
            multo maior erit numero arenularum, quæ in ſphæra diametrum milliario
              <lb/>
            æqualem habente continetur; </s>
            <s xml:id="echoid-s8899" xml:space="preserve">propterea quòd & </s>
            <s xml:id="echoid-s8900" xml:space="preserve">pauciores arenulæ, quàm
              <lb/>
            1000000000. </s>
            <s xml:id="echoid-s8901" xml:space="preserve">ſphæram replent, cuius diameter digito ſit æqualis, & </s>
            <s xml:id="echoid-s8902" xml:space="preserve">pauciores
              <lb/>
            digiti, quàm 100000. </s>
            <s xml:id="echoid-s8903" xml:space="preserve">milliarium efficiunt. </s>
            <s xml:id="echoid-s8904" xml:space="preserve">Nos tamen, ob cauſam paulo ante
              <lb/>
            dictam, recipiamus arenulas 1000000000000000000000000. </s>
            <s xml:id="echoid-s8905" xml:space="preserve">replere ſphęrã,
              <lb/>
            cuius diameter milliario ſit ęqualis.</s>
            <s xml:id="echoid-s8906" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8907" xml:space="preserve">
              <emph style="sc">Postremo</emph>
            cum poſitũ à nobis ſit, diametrũ cõcaui Firmamẽti cõplecti
              <lb/>
            milliaria 1000000000. </s>
            <s xml:id="echoid-s8908" xml:space="preserve">quãuis re ipſa multo minor ſit: </s>
            <s xml:id="echoid-s8909" xml:space="preserve">habebit ſphęra, cuius
              <lb/>
            diameter ęqualis ſit diametro cõcaui Firmamẽti, ad ſpherã, quę diametrũ mil
              <lb/>
            liario ęqualẽ habeat proportionem, ꝗ̃ 1000000000000000000000000000.
              <lb/>
            </s>
            <s xml:id="echoid-s8910" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s8911" xml:space="preserve">propterea quod ſphęrę proportionem habent triplicatam diametrorum. </s>
            <s xml:id="echoid-s8912" xml:space="preserve">
              <lb/>
            ut patet in his quatuor numeris, qui
              <lb/>
              <note position="right" xlink:label="note-255-03" xlink:href="note-255-03a" xml:space="preserve">18. duod.</note>
            continuam proportionem habent in
              <lb/>
              <note position="right" xlink:label="note-255-04" xlink:href="note-255-04a" xml:space="preserve">
                <lb/>
              1000000000
                <lb/>
              1000000000000000000
                <lb/>
              1000000000000000000000000000
                <lb/>
              </note>
            proportione 1000000000. </s>
            <s xml:id="echoid-s8913" xml:space="preserve">milliario
              <lb/>
            rum, ideſt, in proportione diametri
              <lb/>
            concaui Firmamenti, ad 1. </s>
            <s xml:id="echoid-s8914" xml:space="preserve">Quare eũ
              <lb/>
            ſphęra diametrum habens milliario
              <lb/>
            ęqualem poſita ſit continere arenulas 1000000000000000000000000. </s>
            <s xml:id="echoid-s8915" xml:space="preserve">li-
              <lb/>
            cet multo pauciores re ipſa includat, ut demonſtrauimus: </s>
            <s xml:id="echoid-s8916" xml:space="preserve">continebit ſphæra
              <lb/>
              <note position="right" xlink:label="note-255-05" xlink:href="note-255-05a" xml:space="preserve">Qui nume
                <lb/>
              rus maior
                <lb/>
              ſit numero
                <lb/>
              arenularũ,
                <lb/>
              q̃@ũ 10000.
                <lb/>
              grano papa
                <lb/>
              ueris æqua
                <lb/>
              les ſint re-
                <lb/>
              plentiũ to-
                <lb/>
              tuni mũ dũ
                <lb/>
              uſque ad
                <lb/>
              concauum
                <lb/>
              Firmamẽt@</note>
            initra concauum Firmamenti tõprehenſa, ipſumq; </s>
            <s xml:id="echoid-s8917" xml:space="preserve">prorſus att ngens, arenulas
              <lb/>
            000000000000000000000000000000000000000000000000000
              <lb/>
            . </s>
            <s xml:id="echoid-s8918" xml:space="preserve">. </s>
            <s xml:id="echoid-s8919" xml:space="preserve">. </s>
            <s xml:id="echoid-s8920" xml:space="preserve">. </s>
            <s xml:id="echoid-s8921" xml:space="preserve">. </s>
            <s xml:id="echoid-s8922" xml:space="preserve">. </s>
            <s xml:id="echoid-s8923" xml:space="preserve">. </s>
            <s xml:id="echoid-s8924" xml:space="preserve">. </s>
            <s xml:id="echoid-s8925" xml:space="preserve">.
              <lb/>
            </s>
            <s xml:id="echoid-s8926" xml:space="preserve">immo numerus hic longe maior erit numero arenularum, quę in toto mun-
              <lb/>
            do uſque ad concauum Firmamenti continentur: </s>
            <s xml:id="echoid-s8927" xml:space="preserve">propterea quòd & </s>
            <s xml:id="echoid-s8928" xml:space="preserve">paucio-
              <lb/>
            res arenulæ, quàm 1000000000000000000000000. </s>
            <s xml:id="echoid-s8929" xml:space="preserve">ſphęram replent haben-
              <lb/>
            tem diametrũ mill iario ęqualem, & </s>
            <s xml:id="echoid-s8930" xml:space="preserve">pauciora milliaria, quàm 1000000000. </s>
            <s xml:id="echoid-s8931" xml:space="preserve">
              <lb/>
            in diametro concaui Firmamenti continentur. </s>
            <s xml:id="echoid-s8932" xml:space="preserve">Numerus ergo ultimo loco in
              <lb/>
            uentus, qui nimirum poſt figuram 1. </s>
            <s xml:id="echoid-s8933" xml:space="preserve">habet 51. </s>
            <s xml:id="echoid-s8934" xml:space="preserve">cifras, longe maior eſt numero
              <lb/>
            arenularum totum mundum uſque ad concauum Firmamenti </s>
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