Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

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[71.] IIII.
Page: 119 (82)
[72.] V.
Page: 119 (82)
[73.] THEOR. 1. PROPOS. 1.
Page: 119 (82)
[74.] THEOR. 2. PROPOS. 2.
Page: 120 (83)
[75.] THEOR. 3. PROPOS. 3.
Page: 121 (84)
[76.] THEOR. 4. PROPOS. 4.
Page: 122 (85)
[77.] THEOR. 5. PROPOS. 5.
Page: 122 (85)
[78.] THEOR. 6. PROPOS. 6.
Page: 123 (86)
[79.] THEOR. 1. PROPOS. 7.
Page: 124 (87)
[80.] SCHOLIVM.
Page: 125 (88)
[81.] THEOR. 7. PROPOS. 8.
Page: 125 (88)
[82.] THEOR. 8. PROPOS. 9.
Page: 126 (89)
[83.] PROBL. 2. PROPOS. 10.
Page: 127 (90)
[84.] THEOR. 9. PROPOS. 11.
Page: 128 (91)
[85.] THEOR. 10. PROPOS. 52
Page: 130 (93)
[86.] SCHOLIVM.
Page: 132 (95)
[87.] THEOR. 11. PROPOS. 13.
Page: 134 (97)
[88.] COROLLARIVM.
Page: 135 (98)
[89.] THEOR. 12. PROPOS. 14.
Page: 135 (98)
[90.] THEOR. 13. PROPOS. 15.
Page: 136 (99)
[91.] THEOR. 14. PROPOS. 16.
Page: 137 (100)
[92.] THEOR. 15. PROPOS. 17.
Page: 139 (102)
[93.] THEOR. 16. PROPOS. 18.
Page: 139 (102)
[94.] COMMENTARIVS.
Page: 142 (105)
[95.] COMMENTARIVS.
Page: 143 (106)
[96.] COMMENTARIVS.
Page: 145 (108)
[97.] TERRAM, ET AQVAM ESSE ROTVNDAS.
Page: 147 (110)
[98.] COMMENTARIVS.
Page: 147 (110)
[99.] COMMENTARIVS.
Page: 150 (113)
[100.] COMMENTARIVS.
Page: 151 (114)
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              <pb o="122" file="158" n="159" rhead="Comment. in I Cap. Sphæræ"/>
            ſionis ſit C, linea autẽ perpendiculi in eodẽ corpore notata CD, ſecãs priorem
              <lb/>
            A B, in puncto E, quod aſſerimus centrũ grauitatis indicare. </s>
            <s xml:id="echoid-s5701" xml:space="preserve">Sic igitur dicũt au
              <lb/>
            ctores illi centrũ totius Vniue@ſi eſſe centrũ grauitat@s terræ & </s>
            <s xml:id="echoid-s5702" xml:space="preserve">aquæ: </s>
            <s xml:id="echoid-s5703" xml:space="preserve">quando
              <lb/>
            quidẽ, ut experientia docet, ad illud tendũt, ſuntq́; </s>
            <s xml:id="echoid-s5704" xml:space="preserve">d@fformis grauitatis; </s>
            <s xml:id="echoid-s5705" xml:space="preserve">at cen-
              <lb/>
            trũ magnitudinis terræ aliud eſſe à centro magn@udinis aquæ, immo utrumq;
              <lb/>
            </s>
            <s xml:id="echoid-s5706" xml:space="preserve">centrũ magnitudinis tã terræ, quã aquæ diuerſum eſſe poſſe à cẽtro totius mũ
              <lb/>
            di, quod eſt centrum grauitatis, ut uolebat ſecunda opinio, ponens tria centra.</s>
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          <p>
            <s xml:id="echoid-s5708" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            hæc reſponſio nulla eſt. </s>
            <s xml:id="echoid-s5709" xml:space="preserve">Nam tam in terra, quàm in aqua neceſ-
              <lb/>
              <note position="left" xlink:label="note-158-01" xlink:href="note-158-01a" xml:space="preserve">Confutatio
                <lb/>
              reſpõſionis
                <lb/>
              aucto@um
                <lb/>
              contrariæ
                <lb/>
              ſententiæ.</note>
            ſario ponendum eſt idem centrum grauitatis, & </s>
            <s xml:id="echoid-s5710" xml:space="preserve">magnitudinis. </s>
            <s xml:id="echoid-s5711" xml:space="preserve">Cum igirur in
              <lb/>
            utro que elemento centrum totius Vniuerſi, ad quod nimirum ex omni loco
              <lb/>
            demiſſa feruntur, ut ex ratione probatum relinquitur, centrũ ſit grauitatis, per-
              <lb/>
            ſpicuum euadit, idem eſſe centrum magnitudinis, nempe centrum Vniuerſi, in
              <lb/>
            terra, & </s>
            <s xml:id="echoid-s5712" xml:space="preserve">aqua; </s>
            <s xml:id="echoid-s5713" xml:space="preserve">ac proinde duo hæc elementa unum globum conſtituere. </s>
            <s xml:id="echoid-s5714" xml:space="preserve">Quod
              <lb/>
              <note position="left" xlink:label="note-158-02" xlink:href="note-158-02a" xml:space="preserve">Idem eſſe
                <lb/>
              centrũ gra-
                <lb/>
              uitatis &
                <lb/>
              magnitudi
                <lb/>
              @is tam in
                <lb/>
              terra, quàm
                <lb/>
              in aqua.</note>
            uero idem ſit centrum grauitatis, & </s>
            <s xml:id="echoid-s5715" xml:space="preserve">magnitudinis in terra, ita demoſtrabimus.
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            </s>
            <s xml:id="echoid-s5716" xml:space="preserve">Pondera, & </s>
            <s xml:id="echoid-s5717" xml:space="preserve">omnia grauia, quæ ex edito loco ad ſuperficiem terræ feruntur, ef
              <lb/>
            ſiciunt ſimiles, ac æquales angulos in ipſa, & </s>
            <s xml:id="echoid-s5718" xml:space="preserve">non ad æquidiſtantiam feruntur,
              <lb/>
            ut ſenſus iudicat, quandoquidem in centro Vniuerſi, quod eſt centrũ grauita-
              <lb/>
            tis, coeunt. </s>
            <s xml:id="echoid-s5719" xml:space="preserve">Igitur unum & </s>
            <s xml:id="echoid-s5720" xml:space="preserve">idem centrum eſt magnitudinis terræ, & </s>
            <s xml:id="echoid-s5721" xml:space="preserve">grauitatis
              <lb/>
            eiuſdẽ, ſeu Vniuerſi. </s>
            <s xml:id="echoid-s5722" xml:space="preserve">Antecedens communi experientia eſt comprobatũ, ut ui-
              <lb/>
            dere eſt in perpendiculis, quibus utuntur artifices in conſtru ctionibus ędificio
              <lb/>
            rum, quę nec in hanc, nec in illam @artem flectuntur, ſed ęqualibiter terrę ſu-
              <lb/>
            perficiei iuſiſtunt: </s>
            <s xml:id="echoid-s5723" xml:space="preserve">Ex quocunq. </s>
            <s xml:id="echoid-s5724" xml:space="preserve">enim loco demittantur in terram, ſimiles ſem-
              <lb/>
            per, & </s>
            <s xml:id="echoid-s5725" xml:space="preserve">ęquales angulos cum ea conſtituunt, ſuntq́ue ſemper fila illorum per-
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            pendiculorum in diametro cœli & </s>
            <s xml:id="echoid-s5726" xml:space="preserve">terrę; </s>
            <s xml:id="echoid-s5727" xml:space="preserve">Aliàs ędificia diu conſiſtere non poſ-
              <lb/>
            ſent. </s>
            <s xml:id="echoid-s5728" xml:space="preserve">Idem antecedens eſt Ariſtotelis in 2. </s>
            <s xml:id="echoid-s5729" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5730" xml:space="preserve">de cœlo. </s>
            <s xml:id="echoid-s5731" xml:space="preserve">Conſequentia uero cla-
              <lb/>
            riſſima eſt apud Geometras: </s>
            <s xml:id="echoid-s5732" xml:space="preserve">Ex oppoſito namque conſequentis infertur op-
              <lb/>
            poſitum antecedentis. </s>
            <s xml:id="echoid-s5733" xml:space="preserve">Sit enim, ſi fieri poteſt, centrum grauitatis, ſiue Vniuer-
              <lb/>
            ſi E, terrę uero centrum magnitudinis ſit aliud, nempe F, feraturq́; </s>
            <s xml:id="echoid-s5734" xml:space="preserve">è ſublimi
              <lb/>
            pondus aliquod ad centrum E, totius Vniuerſi per lineam B G E, non autem
              <lb/>
            ad centrũ terræ F. </s>
            <s xml:id="echoid-s5735" xml:space="preserve">Dico hoc pondus terrę incidens non efficere angulos ęqua
              <lb/>
            les, aut ſimiles cum ſuperficie terræ
              <lb/>
              <figure xlink:label="fig-158-01" xlink:href="fig-158-01a" number="51">
                <image file="158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/158-01"/>
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            ſed prorſus inęquales, diſſimileſue.
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            </s>
            <s xml:id="echoid-s5736" xml:space="preserve">Ducta enim ſemidiametro terrę F G,
              <lb/>
            protractaque uſque ad H, erunt duo
              <lb/>
            anguli F G D, F G L, ęquales, cum
              <lb/>
            ſint ſemicirculorum ęqualium; </s>
            <s xml:id="echoid-s5737" xml:space="preserve">& </s>
            <s xml:id="echoid-s5738" xml:space="preserve">ex
              <lb/>
            conſequenti eadẽ ratione erunt duo
              <lb/>
            anguli exteriores D G H, L G Hęqua
              <lb/>
            les, ut patet, ſi unus angulus alteri ſu-
              <lb/>
            perponeretur. </s>
            <s xml:id="echoid-s5739" xml:space="preserve">Cõgrueret enim arcus
              <lb/>
            G D, arcui G L, & </s>
            <s xml:id="echoid-s5740" xml:space="preserve">communis eſſer re-
              <lb/>
            cta H F. </s>
            <s xml:id="echoid-s5741" xml:space="preserve">Cum igitur angulus D G B,
              <lb/>
            minor ſit angulo D G H, & </s>
            <s xml:id="echoid-s5742" xml:space="preserve">angulus
              <lb/>
            B G L maior angulo L G H; </s>
            <s xml:id="echoid-s5743" xml:space="preserve">erir an-
              <lb/>
            gulus D G B, multis partibus minor
              <lb/>
            angulo B G L. </s>
            <s xml:id="echoid-s5744" xml:space="preserve">Quocirca pondus per
              <lb/>
            lineam rectam B G E, demiſſu@m non feretur ad angulos ęquales, ſimilesue in
              <lb/>
            ſuperficiem terrę. </s>
            <s xml:id="echoid-s5745" xml:space="preserve">quod erat demonſtrandum. </s>
            <s xml:id="echoid-s5746" xml:space="preserve">Idem dices, ſi per lineam </s>
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