Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of figures

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          <p>
            <s xml:id="echoid-s3339" xml:space="preserve">
              <pb o="66" file="102" n="103" rhead="Comment. in I. Cap. Sphæræ"/>
            duo latera H A, A B, trianguli A B H, æqualia duobus lateribus O A, A B,
              <lb/>
              <note position="left" xlink:label="note-102-01" xlink:href="note-102-01a" xml:space="preserve">27. tertij.</note>
            trianguli A B O, & </s>
            <s xml:id="echoid-s3340" xml:space="preserve">anguli dictis lateribus comprehenſi æquales, quòd arcus
              <lb/>
            O M, H M, æquales ſint, propter æqualitatem arcuum M H, M O, diſtantias di-
              <lb/>
              <note position="left" xlink:label="note-102-02" xlink:href="note-102-02a" xml:space="preserve">4. primi.</note>
            ctorum aſtrorum a uertice M, metientium. </s>
            <s xml:id="echoid-s3341" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s3342" xml:space="preserve">baſes B H, B O, & </s>
            <s xml:id="echoid-s3343" xml:space="preserve">anguli
              <lb/>
            H, O, qui oſtendunt quantitatem diuerſitatis aſpectus, æquales erunt.</s>
            <s xml:id="echoid-s3344" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3345" xml:space="preserve">
              <emph style="sc">Pari</emph>
            ratione ſequitur, aſtrum idem, quò propinquius fuerit Horizonti,
              <lb/>
            eo maiorem habere diuerſitatem aſpectus, adeo ut in Horizonte exiſtens maxi
              <lb/>
            mam habeat: </s>
            <s xml:id="echoid-s3346" xml:space="preserve">quò uerò remotius fuerit ab Horizonte, eo minorẽ habere, adeo
              <lb/>
            vt in uertice capitis exiſtens, vbi maxime ab Horizonte remouetur, nullã pror-
              <lb/>
            ſus habeat aſpectus diuerſitatem: </s>
            <s xml:id="echoid-s3347" xml:space="preserve">quæ omnia ordinatim demonſtrabimus. </s>
            <s xml:id="echoid-s3348" xml:space="preserve">Exi
              <lb/>
              <note position="left" xlink:label="note-102-03" xlink:href="note-102-03a" xml:space="preserve">Aſtrũ, quõ
                <lb/>
              uicinius eſt
                <lb/>
              Morizonti,
                <lb/>
              eo maiorẽ
                <lb/>
              habet aſpe-
                <lb/>
              ctus diuerſi
                <lb/>
              tatem.</note>
            ſtat unum & </s>
            <s xml:id="echoid-s3349" xml:space="preserve">idem aſtrum modo in puncto M, id eſt, in uertice, modo in puncto
              <lb/>
            K, accedens ad Horizontem, modo in puncto H, quod uicinius eſt Horizonti,
              <lb/>
              <figure xlink:label="fig-102-01" xlink:href="fig-102-01a" number="12">
                <image file="102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/102-01"/>
              </figure>
            modo deniq. </s>
            <s xml:id="echoid-s3350" xml:space="preserve">in
              <lb/>
            puncto F, id eſt,
              <lb/>
            in Horizonte, du
              <lb/>
            canturq́ue a cen-
              <lb/>
            tro terræ A, & </s>
            <s xml:id="echoid-s3351" xml:space="preserve">
              <lb/>
            ex oculo B, per
              <lb/>
            centrũ huius ſtel-
              <lb/>
            lę, vbicunque exi
              <lb/>
            ſtat, lineæ rectæ:
              <lb/>
            </s>
            <s xml:id="echoid-s3352" xml:space="preserve">ſumatur quoque
              <lb/>
            arcus M O, æqua-
              <lb/>
            lis arcui M H,
              <lb/>
            ita ut duo aſtra
              <lb/>
            in punctis H,
              <lb/>
            & </s>
            <s xml:id="echoid-s3353" xml:space="preserve">O, exiſtentia,
              <lb/>
            & </s>
            <s xml:id="echoid-s3354" xml:space="preserve">ęqualiter a uertice M, remota, æquales habeant altitudines ſupra Horizon-
              <lb/>
            tem; </s>
            <s xml:id="echoid-s3355" xml:space="preserve">atq. </s>
            <s xml:id="echoid-s3356" xml:space="preserve">adeo, ut proxime demonſtratum eſt, aſpectus diuerſitatem eandem. </s>
            <s xml:id="echoid-s3357" xml:space="preserve">
              <lb/>
            Connectantur puncta K, & </s>
            <s xml:id="echoid-s3358" xml:space="preserve">O, linea recta K O. </s>
            <s xml:id="echoid-s3359" xml:space="preserve">Quoniam igitur B O, æqualis
              <lb/>
              <note position="left" xlink:label="note-102-04" xlink:href="note-102-04a" xml:space="preserve">7. tertij.</note>
            eſt ipſi B H, ut proxime demonſtratum eſt: </s>
            <s xml:id="echoid-s3360" xml:space="preserve">Eſt autem B H, maior quam B K; </s>
            <s xml:id="echoid-s3361" xml:space="preserve">e-
              <lb/>
              <note position="left" xlink:label="note-102-05" xlink:href="note-102-05a" xml:space="preserve">18. primi.</note>
            rit quoq. </s>
            <s xml:id="echoid-s3362" xml:space="preserve">B O, maior quam B K; </s>
            <s xml:id="echoid-s3363" xml:space="preserve">& </s>
            <s xml:id="echoid-s3364" xml:space="preserve">ob id angulus B K O, maior angulo B O K;
              <lb/>
            </s>
            <s xml:id="echoid-s3365" xml:space="preserve">
              <note position="left" xlink:label="note-102-06" xlink:href="note-102-06a" xml:space="preserve">5. primi.</note>
            Su nt autem anguli toti A K O, & </s>
            <s xml:id="echoid-s3366" xml:space="preserve">A O K, ęquales. </s>
            <s xml:id="echoid-s3367" xml:space="preserve">Reliquus igitur A O B, ma-
              <lb/>
            ior erit reliquo A K B, & </s>
            <s xml:id="echoid-s3368" xml:space="preserve">idcirco aſtrum in O, exiſtens, ac proinde & </s>
            <s xml:id="echoid-s3369" xml:space="preserve">in puncto
              <lb/>
            H, maiorẽ habebit diuerſitatẽ aſpectus, quã in puncto K. </s>
            <s xml:id="echoid-s3370" xml:space="preserve">Quare conſtat, aſtrum
              <lb/>
              <note position="left" xlink:label="note-102-07" xlink:href="note-102-07a" xml:space="preserve">Aſtrum in
                <lb/>
              Horizonte
                <lb/>
              maximam
                <lb/>
              habetdiuer
                <lb/>
              ſitatẽ aſpe-
                <lb/>
              ctũs.</note>
            quodcunq;</s>
            <s xml:id="echoid-s3371" xml:space="preserve">, quo uicinius fuerit Horizonti, eo maiorẽ hẽre diuerſitatẽ aſpect
              <emph style="sub">9</emph>
            .</s>
            <s xml:id="echoid-s3372" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3373" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            exiſtat aliquod aſtrum in Horizonte, nempe in G, & </s>
            <s xml:id="echoid-s3374" xml:space="preserve">aliud in eo-
              <lb/>
            dem cælo in puncto L, ſupra Horizontem; </s>
            <s xml:id="echoid-s3375" xml:space="preserve">& </s>
            <s xml:id="echoid-s3376" xml:space="preserve">producatur Horizon G B, uſque
              <lb/>
            ad R, & </s>
            <s xml:id="echoid-s3377" xml:space="preserve">connectantur rectæ A G, A R, A L, B L, L R, eruntq́ue baſes B G,
              <lb/>
            B R, & </s>
            <s xml:id="echoid-s3378" xml:space="preserve">duo anguli A G B, A R B, ęquales: </s>
            <s xml:id="echoid-s3379" xml:space="preserve">Sed angulus A R B, maior eſt, an-
              <lb/>
              <note position="left" xlink:label="note-102-08" xlink:href="note-102-08a" xml:space="preserve">4. primi.</note>
            gulo A L B, quod quidem eodem pacto demonſtrari poteſt, quemadmodum
              <lb/>
            oſtenſum fuit, angulum A O B, maiorem eſſe angulo A K B. </s>
            <s xml:id="echoid-s3380" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3381" xml:space="preserve">angu-
              <lb/>
              <note position="left" xlink:label="note-102-09" xlink:href="note-102-09a" xml:space="preserve">Aſtrum in
                <lb/>
              uertice exi-
                <lb/>
              ſtens nullã
                <lb/>
              habet diuer
                <lb/>
              ſitatẽ aſpe-
                <lb/>
              ctus: Inter
                <lb/>
              duo uero
                <lb/>
              aſtra eũdẽ.</note>
            lus A G B, maior erit eodem angulo A L B, & </s>
            <s xml:id="echoid-s3382" xml:space="preserve">propterea aſtrum in Horizonte
              <lb/>
            exiſtens maximam habebit diuerſitatem aſpectus. </s>
            <s xml:id="echoid-s3383" xml:space="preserve">Eadem enim ratione demon
              <lb/>
            ſtrabitur angulum A G B, maiorem eſſe quocunque alio. </s>
            <s xml:id="echoid-s3384" xml:space="preserve">Facile autem perſpi
              <lb/>
            cis, aſtrum in puncto M, exiſtens nullam habere diuerſitatem aſpectus, cum idẽ
              <lb/>
            ſit eius locus uiſus & </s>
            <s xml:id="echoid-s3385" xml:space="preserve">uerus.</s>
            <s xml:id="echoid-s3386" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3387" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            ex eadem figura colligitur, inter duo aſtra, quę eundem </s>
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