Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of figures

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            <s xml:id="echoid-s4494" xml:space="preserve">
              <pb o="92" file="128" n="129" rhead="Comment. in I. Cap. Sphæræ"/>
            C F K, & </s>
            <s xml:id="echoid-s4495" xml:space="preserve">angulus A F K, angulo C F K, æqualis, vt probatum eſt, erunt ba-
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            ſes A K, K C, æquales, & </s>
            <s xml:id="echoid-s4496" xml:space="preserve">anguli ad K, æquales quoque, hoc eſt, recti. </s>
            <s xml:id="echoid-s4497" xml:space="preserve">Eadem
              <lb/>
              <note position="left" xlink:label="note-128-01" xlink:href="note-128-01a" xml:space="preserve">4. primi.</note>
            ratiocinatione concludemus rectam C E, in puncto H, diuidi bifariam; </s>
            <s xml:id="echoid-s4498" xml:space="preserve">angu-
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            losq́ue ad H, eſſe rectos. </s>
            <s xml:id="echoid-s4499" xml:space="preserve">Producatur recta D H, ad partes H, ſumaturq́; </s>
            <s xml:id="echoid-s4500" xml:space="preserve">H L,
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            æqualis rectæ D H, & </s>
            <s xml:id="echoid-s4501" xml:space="preserve">extendatur à puncto L, per punctum C, recta L C N.
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            </s>
            <s xml:id="echoid-s4502" xml:space="preserve">Quoniam uero latera D H, H C, trianguli D C H, æqualia ſunt lateribus
              <lb/>
            L H, H C, trianguli L C H, anguli ad H, æquales, vtpote recti, erunt baſes
              <lb/>
              <note position="left" xlink:label="note-128-02" xlink:href="note-128-02a" xml:space="preserve">4. primi.</note>
            D C, L C, æquales, & </s>
            <s xml:id="echoid-s4503" xml:space="preserve">anguli D C H, L C H, æquales etiam: </s>
            <s xml:id="echoid-s4504" xml:space="preserve">At qui angulus
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            D C H, maior eſt angulo G C H, & </s>
            <s xml:id="echoid-s4505" xml:space="preserve">angulus G C H, æqualis eſt angulo F A K,
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            propter ſimilitudinem triangulorum G C E, & </s>
            <s xml:id="echoid-s4506" xml:space="preserve">F A C, hoc eſt, angulo F C A,
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            qui angulo F A C, æqualis eſt, Erit igitur angulus D C H, hoc eſt, angulus
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            L C H, qui illi oſtenſus eſt æqualis, hoc eſt angulus N C K, qui angulo L C H,
              <lb/>
              <note position="left" xlink:label="note-128-03" xlink:href="note-128-03a" xml:space="preserve">5. primi.</note>
            ad uerticem eſt æqualis, maior etiam angulo F C A; </s>
            <s xml:id="echoid-s4507" xml:space="preserve">& </s>
            <s xml:id="echoid-s4508" xml:space="preserve">ob id C N, recta extra
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            rectam CF, cadet neceſſario; </s>
            <s xml:id="echoid-s4509" xml:space="preserve">& </s>
            <s xml:id="echoid-s4510" xml:space="preserve">rectæ L C, C B, propterea comprehendent ad
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              <note position="left" xlink:label="note-128-04" xlink:href="note-128-04a" xml:space="preserve">15. primi.</note>
            partes K, angulum BCL. </s>
            <s xml:id="echoid-s4511" xml:space="preserve">Quare ſi ducatur recta B L, ſecabit ea lineam C K,
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            in aliquo puncto inter puncta C, & </s>
            <s xml:id="echoid-s4512" xml:space="preserve">K, quod ſit M. </s>
            <s xml:id="echoid-s4513" xml:space="preserve">Quoniam uero rectæ A B,
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            B C, C D, D E, ſimul æquales ſunt rectis A F, F C, C G, G E, ſimul, propter
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            triangula iſoperimetra, erunt quoque dimidia earum æqualia inter ſe, ni-
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            mirum rectæ B C, C D, hoc eſt, B C, C L, ſimul æquales ipſis F C, C G, ſi-
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            mul: </s>
            <s xml:id="echoid-s4514" xml:space="preserve">Sunt autem rectæ B C, C L, ſimul maiores recta B L. </s>
            <s xml:id="echoid-s4515" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s4516" xml:space="preserve">F C, C G,
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              <note position="left" xlink:label="note-128-05" xlink:href="note-128-05a" xml:space="preserve">20. primi.</note>
            ſimul maiores erunt eadem recta B L: </s>
            <s xml:id="echoid-s4517" xml:space="preserve">ideoq́ue quadratum ex F C, C G, tan-
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              <figure xlink:label="fig-128-01" xlink:href="fig-128-01a" number="30">
                <image file="128-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/128-01"/>
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            quam ex una linea, de
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            ſcriptum maius erit
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            quadrato BL. </s>
            <s xml:id="echoid-s4518" xml:space="preserve">Quod
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            autem ex F C, C G,
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            tanquam ex una linea,
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            deſcribitur quadratum,
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            æquale eſt (per pro-
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            poſ. </s>
            <s xml:id="echoid-s4519" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4520" xml:space="preserve">huius) quadrato
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            ex F K, G H, tan quam
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            ex una linea deſcripto,
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            vnà cum quadrato,
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            quod ex K C, C H,
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            tanquam ex una linea,
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            deſcribitur: </s>
            <s xml:id="echoid-s4521" xml:space="preserve">Quadratum
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            uero ex L B, deſcriptum
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            æquale eſt (per eandem
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            9. </s>
            <s xml:id="echoid-s4522" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4523" xml:space="preserve">huius) qna-
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            drato ex B K, L H,
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            hoc eſt, ex B K, D H,
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            tanquam ex una linea,
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            deſcripto, unà cum qua-
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            drato, quod ex K M, M H, tanquam ex una linea, deſcribitur; </s>
            <s xml:id="echoid-s4524" xml:space="preserve">eò quòd trian-
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            gula rectangula B K M, L H M, ſint ſimilia inter ſe. </s>
            <s xml:id="echoid-s4525" xml:space="preserve">Sunt enim anguli M, ad
              <lb/>
              <note position="left" xlink:label="note-128-06" xlink:href="note-128-06a" xml:space="preserve">15. primi.</note>
            uerticem æquales, & </s>
            <s xml:id="echoid-s4526" xml:space="preserve">anguli K, H, recti, ideoq́ue & </s>
            <s xml:id="echoid-s4527" xml:space="preserve">reliqui K B N, H L M, æ-
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              <note position="left" xlink:label="note-128-07" xlink:href="note-128-07a" xml:space="preserve">32. primi.</note>
            quales. </s>
            <s xml:id="echoid-s4528" xml:space="preserve">Igitur quadratum ex F K, G H, tanquam ex una linea, deſcriptum, & </s>
            <s xml:id="echoid-s4529" xml:space="preserve">
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            quadratum ex K C, C H, tanquam ex una linea, deſcriptum, hoc eſt, quadra-
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            tum K H, utraque ſimul, maiora ſunt quadrato ex B K, D H, tanquam </s>
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