Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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            <s xml:id="echoid-s13794" xml:space="preserve">
              <pb o="400" file="412" n="412" rhead=""/>
            ſubtendentia angulos, per conſtructionem, æqualia; </s>
            <s xml:id="echoid-s13795" xml:space="preserve">erunt quoque arcus GL,
              <lb/>
              <note position="left" xlink:label="note-412-01" xlink:href="note-412-01a" xml:space="preserve">21. huius.</note>
            DF, æquales, ac propterea & </s>
            <s xml:id="echoid-s13796" xml:space="preserve">eorum ſinus æquales erunt, necnon & </s>
            <s xml:id="echoid-s13797" xml:space="preserve">ſinus ar-
              <lb/>
            cuum æqualium AG, AD, erunt æquales. </s>
            <s xml:id="echoid-s13798" xml:space="preserve">Eadem ergo eſt proportio ſinus
              <lb/>
            arcus AG, ad ſinum arcus GL, quæ ſinus arcus AD, ad ſinum arcus DF: </s>
            <s xml:id="echoid-s13799" xml:space="preserve">Vt
              <lb/>
            autem ſinus arcus AG, ad ſinum arcus GL, ita demonſtratum eſt, eſſe ſinum
              <lb/>
            arcus AB, vel CB, ad ſinum arcus BI, vel BK, propterea quòd puncta B, G,
              <lb/>
            in eodem ſemicirculo ſumpta ſunt. </s>
            <s xml:id="echoid-s13800" xml:space="preserve">Igitur erit quoque, vt ſinus arcus AB, vel
              <lb/>
            CB, ad ſinum arcus BI, vel BK, ita ſinus arcus AD, ad ſinum arcus DF, &</s>
            <s xml:id="echoid-s13801" xml:space="preserve">c.</s>
            <s xml:id="echoid-s13802" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13803" xml:space="preserve">POSTREMO ſumatur in ſemicirculo ABC, punctum B, & </s>
            <s xml:id="echoid-s13804" xml:space="preserve">in alterius
              <lb/>
            circuli ſemicirculo vtrouis
              <lb/>
            nempe in AEC, aliud pun
              <lb/>
            ctum L: </s>
            <s xml:id="echoid-s13805" xml:space="preserve">Et per B, & </s>
            <s xml:id="echoid-s13806" xml:space="preserve">polum
              <lb/>
              <figure xlink:label="fig-412-01" xlink:href="fig-412-01a" number="260">
                <image file="412-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/412-01"/>
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            circuli AEC, arcus maxi-
              <lb/>
              <note position="left" xlink:label="note-412-02" xlink:href="note-412-02a" xml:space="preserve">20. 1 Theod.</note>
            mi circuli ducatur IBK:
              <lb/>
            </s>
            <s xml:id="echoid-s13807" xml:space="preserve">Item per L, & </s>
            <s xml:id="echoid-s13808" xml:space="preserve">per polum
              <lb/>
            circuli ABC, arcus LGM,
              <lb/>
            maximi circuli; </s>
            <s xml:id="echoid-s13809" xml:space="preserve">eruntq́ue
              <lb/>
            anguli I, G, recti. </s>
            <s xml:id="echoid-s13810" xml:space="preserve">Dico rur-
              <lb/>
              <note position="left" xlink:label="note-412-03" xlink:href="note-412-03a" xml:space="preserve">25. 1 Theod.</note>
            ſus, vt eſt ſinus arcus AB,
              <lb/>
            ad ſinum arcus BI, ita eſſe
              <lb/>
            ſinum arcus AL, ad ſinum
              <lb/>
            arcus LG, &</s>
            <s xml:id="echoid-s13811" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13812" xml:space="preserve">Per po-
              <lb/>
            los enim vtriusque circuli
              <lb/>
              <note position="left" xlink:label="note-412-04" xlink:href="note-412-04a" xml:space="preserve">20. 1 Theod.</note>
            ABCD, AECF, arcus cir
              <lb/>
            culi maximi ducatur RE;
              <lb/>
            </s>
            <s xml:id="echoid-s13813" xml:space="preserve">eruntq́ue anguli R, E, re-
              <lb/>
              <note position="left" xlink:label="note-412-05" xlink:href="note-412-05a" xml:space="preserve">15. 1. Theod.</note>
            cti, diuidenturq́ue ſemicir-
              <lb/>
            culi ABC, AEC, bifa-
              <lb/>
              <note position="left" xlink:label="note-412-06" xlink:href="note-412-06a" xml:space="preserve">9. 2. Theod.</note>
            riam in punctis R, E; </s>
            <s xml:id="echoid-s13814" xml:space="preserve">atque
              <lb/>
            adeo ſinus quadrantum AR, AE, æquales erunt; </s>
            <s xml:id="echoid-s13815" xml:space="preserve">Eademq́ue proportio erit
              <lb/>
              <note position="left" xlink:label="note-412-07" xlink:href="note-412-07a" xml:space="preserve">7. quinti.</note>
            ſinus arcus AR, ad ſinum arcus RE, quæ ſinus arcus AE, ad ſinum arcus ER.
              <lb/>
            </s>
            <s xml:id="echoid-s13816" xml:space="preserve">Quoniam vero eſt, vt ſinus arcus AR, ad ſinũ arcus RE, ita ſinus arcus AB,
              <lb/>
            ad ſinum arcus BI, vt demonſtratum eſt; </s>
            <s xml:id="echoid-s13817" xml:space="preserve">(ſumpta ſunt enim duo puncta R,
              <lb/>
            B, in eodem ſemicirculo) erit quoque, vt ſinus arcus AE, ad ſinum arcus ER,
              <lb/>
            ita ſinus arcus AB, ad ſinum arcus BI: </s>
            <s xml:id="echoid-s13818" xml:space="preserve">Sed eadem ratione eſt, vt ſinus arcus
              <lb/>
            AE, ad ſinum arcus ER, ita ſinus arcus AL, ad ſinum arcus LG. </s>
            <s xml:id="echoid-s13819" xml:space="preserve">Igitur erit
              <lb/>
            quoque, vt ſinus arcus AB, ad ſinum arcus BI, ita ſinus arcus AL, ad ſinum
              <lb/>
            arcus LG, &</s>
            <s xml:id="echoid-s13820" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13821" xml:space="preserve">Quòd ſi loco puncti L, ſumatur in altero ſemicirculo AFC,
              <lb/>
            eiuſdem circuli AECF, aliud punctum, nempe F, & </s>
            <s xml:id="echoid-s13822" xml:space="preserve">arcus FD, faciat angu-
              <lb/>
            lum D, rectum, erit adhuc, vt ſinus arcus AB, ad linum arcus BI, ita ſinus ar-
              <lb/>
            cus AF, ad ſinum arcus FD, &</s>
            <s xml:id="echoid-s13823" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13824" xml:space="preserve">Vt enim proxime oſtendimus, vt ſinus ar-
              <lb/>
            cus AB, ad ſinum arcus BI, ita eſt arcus ſinus AL, ad ſinum arcus LG: </s>
            <s xml:id="echoid-s13825" xml:space="preserve">Vt
              <lb/>
            autem ſinus arcus AL, ad ſinum arcus LG ita demonſtratum eſt, eſſe ſinum
              <lb/>
            arcus AF, ad ſinum arcus FD, quòd puncta L, F, ſumantur in duobus ſemi-
              <lb/>
            circulis eiuſdem circuli. </s>
            <s xml:id="echoid-s13826" xml:space="preserve">Igitur erit quoque, vt ſinus arcus AB, ad ſinum ar-
              <lb/>
            cus BI, ita ſinus arcus AF, ad ſinum arcus FD: </s>
            <s xml:id="echoid-s13827" xml:space="preserve">Atque ita in vniuerſum vera
              <lb/>
            eſt propoſitio, quomodocunq; </s>
            <s xml:id="echoid-s13828" xml:space="preserve">duo puncta ſumãtur, quando circuli ABCD,
              <lb/>
            AECF, ſe mutuo ſecantad angulos non rectos.</s>
            <s xml:id="echoid-s13829" xml:space="preserve"/>
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