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

Table of contents

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[371.] Gradus Quadrantis pro ſecantibus
Page: 266 (254)
[372.] Gradus Quadrantis pro ſecantibus
Page: 266 (254)
[373.] arcuum eiuſdem Quadrantis
Page: 267 (255)
[374.] complementorum arcuum eiuſdem Quadrantis
Page: 267 (255)
[375.] Gradus Quadrantis pro ſecantibus
Page: 268 (256)
[376.] Gradus Quadrantis pro ſecantibus
Page: 268 (256)
[377.] arcuum eiuſdem Quadrantis.
Page: 269 (257)
[378.] complementorum arcuum eiuſdem Quadrantis.
Page: 269 (257)
[379.] Gradus Quadrantis pro ſecantibus
Page: 270 (258)
[380.] Gradus Quadrantis pro ſecantibus
Page: 270 (258)
[381.] arcuum eiuſdem Quadrantis.
Page: 271 (259)
[382.] complementorum arcuum eiuſdem Quadrantis.
Page: 271 (259)
[383.] Gradus Quadrantis pro ſecantibus
Page: 272 (260)
[384.] Gradus Quadrantis pro ſecantibus
Page: 272 (260)
[385.] arcuum eiuſdem Quadrantis
Page: 273 (261)
[386.] complementorum arcuum eiuſdem Quadrantis
Page: 273 (261)
[387.] Gradus Quadrantis pro ſecantibus
Page: 274 (262)
[388.] Gradus Quadrantis pro ſecantibus
Page: 274 (262)
[389.] arcuum eiuſdem Quadrantis
Page: 275 (263)
[390.] complementorum arcuum eiuſdem Quadrantis
Page: 275 (263)
[391.] Gradus Quadrantis pro ſecantibus
Page: 276 (264)
[392.] Gradus Quadrantis pro ſecantibus
Page: 276 (264)
[393.] arcuum eiuſdem Quadrantis.
Page: 277 (265)
[394.] complementorum arcuum eiuſdem Quadrantis.
Page: 277 (265)
[395.] Gradus Quadrantis pro ſecantibus
Page: 278 (266)
[396.] Gradus Quadrantis pro ſecantibus
Page: 278 (266)
[397.] arcuum eiuſdem Quadrantis.
Page: 279 (267)
[398.] complementorum arcuum eiuſdem Quadrantis.
Page: 279 (267)
[399.] Gradus Quadrantis pro ſecantibus
Page: 280 (268)
[400.] Gradus Quadrantis pro ſecantibus
Page: 280 (268)
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            <s xml:id="echoid-s12299" xml:space="preserve">
              <pb o="368" file="380" n="380" rhead=""/>
            AC, æquales ponuntur ſemicirculo BAD; </s>
            <s xml:id="echoid-s12300" xml:space="preserve">dempto communi arcu BA, erunt
              <lb/>
            reliqui arcus AC, AD, æquales. </s>
            <s xml:id="echoid-s12301" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s12302" xml:space="preserve">angulus ACD, angulo D, æqua-
              <lb/>
              <note position="left" xlink:label="note-380-01" xlink:href="note-380-01a" xml:space="preserve">8. huius.</note>
            lis erit. </s>
            <s xml:id="echoid-s12303" xml:space="preserve">Cum igitur anguli B, & </s>
            <s xml:id="echoid-s12304" xml:space="preserve">D, ſint quoque æquales, æqualis quoque erit
              <lb/>
              <note position="left" xlink:label="note-380-02" xlink:href="note-380-02a" xml:space="preserve">13. huius.</note>
            angulus ACD, angulo B. </s>
            <s xml:id="echoid-s12305" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s12306" xml:space="preserve"/>
          </p>
          <figure number="214">
            <image file="380-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/380-01"/>
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          <p>
            <s xml:id="echoid-s12307" xml:space="preserve">SINT deinde duo latera AB, AC, mi-
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            nora ſemicirculo BAD. </s>
            <s xml:id="echoid-s12308" xml:space="preserve">Dempto ergo com
              <lb/>
            muniarcu AB, erit reliquus AC, reliquo
              <lb/>
            AD, minor; </s>
            <s xml:id="echoid-s12309" xml:space="preserve">ac propterea angulus ACD,
              <lb/>
              <note position="left" xlink:label="note-380-03" xlink:href="note-380-03a" xml:space="preserve">11. huius.</note>
            maior angulo D, hoc eſt, angulo B, qui an-
              <lb/>
              <note position="left" xlink:label="note-380-04" xlink:href="note-380-04a" xml:space="preserve">13. huius.</note>
            gulo D, æqualis eſt. </s>
            <s xml:id="echoid-s12310" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12311" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12312" xml:space="preserve">SINT poſtremo latera AB, AC, ma-
              <lb/>
            iora ſemicirculo BAD. </s>
            <s xml:id="echoid-s12313" xml:space="preserve">Dempto igitur cõ-
              <lb/>
            muni arcu AB, erit reliquus AC, reliquo
              <lb/>
            AD, maior; </s>
            <s xml:id="echoid-s12314" xml:space="preserve">ac propterea angulus D, maior erit angulo ACD. </s>
            <s xml:id="echoid-s12315" xml:space="preserve">Cum ergo
              <lb/>
              <note position="left" xlink:label="note-380-05" xlink:href="note-380-05a" xml:space="preserve">11. huius.</note>
            angulo D, æqualis ſit angulus B, erit quoque angulus B, maior angulo ACD,
              <lb/>
              <note position="left" xlink:label="note-380-06" xlink:href="note-380-06a" xml:space="preserve">13. huius.</note>
            hoc eſt, angulus ACD, angulo B, minor erit. </s>
            <s xml:id="echoid-s12316" xml:space="preserve">Cuiuſcunque ergo trianguli,
              <lb/>
            &</s>
            <s xml:id="echoid-s12317" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12318" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s12319" xml:space="preserve"/>
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        <div xml:id="echoid-div970" type="section" level="1" n="502">
          <head xml:id="echoid-head537" xml:space="preserve">THEOR. 13. PROPOS. 15.</head>
          <p>
            <s xml:id="echoid-s12320" xml:space="preserve">SI cuiuſcunque trianguli ſphærici vno latere
              <lb/>
            producto, externus angulus æqualis fuerit interno
              <lb/>
            oppoſito ſupra arcum productum, erunt duo reli-
              <lb/>
            qua latera ſimul æqualia ſemicirculo: </s>
            <s xml:id="echoid-s12321" xml:space="preserve">Si verò an-
              <lb/>
            gulus externus maior fuerit interno eodem, & </s>
            <s xml:id="echoid-s12322" xml:space="preserve">op-
              <lb/>
            poſito, erunt duo reliqua latera ſemicirculo mi-
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            nora: </s>
            <s xml:id="echoid-s12323" xml:space="preserve">Si deniq; </s>
            <s xml:id="echoid-s12324" xml:space="preserve">externus angulus interno oppoſi-
              <lb/>
            to dicto minor fuerit, erunt duo latera reliqua ſe-
              <lb/>
            micirculo maiora.</s>
            <s xml:id="echoid-s12325" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12326" xml:space="preserve">POSITO eodem triangulo ſphærico, & </s>
            <s xml:id="echoid-s12327" xml:space="preserve">conſtructione figuræ eadem;
              <lb/>
            </s>
            <s xml:id="echoid-s12328" xml:space="preserve">
              <figure xlink:label="fig-380-02" xlink:href="fig-380-02a" number="215">
                <image file="380-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/380-02"/>
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            Sit primum angulus ACD, externus æqua-
              <lb/>
            lis interno oppoſito B. </s>
            <s xml:id="echoid-s12329" xml:space="preserve">Dico latera AB,
              <lb/>
            AC, ſemicirculo eſſe ęqualia, &</s>
            <s xml:id="echoid-s12330" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12331" xml:space="preserve">Cum enim
              <lb/>
            angulus B, angulo D, æqulis ſit, erit quo-
              <lb/>
              <note position="left" xlink:label="note-380-07" xlink:href="note-380-07a" xml:space="preserve">13. huius.</note>
            que angulus ACD, angulo D, æqualis;
              <lb/>
            </s>
            <s xml:id="echoid-s12332" xml:space="preserve">ideoq̀ & </s>
            <s xml:id="echoid-s12333" xml:space="preserve">arcus AC, AD, æquales erunt. </s>
            <s xml:id="echoid-s12334" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-380-08" xlink:href="note-380-08a" xml:space="preserve">9. huius.</note>
            Addito ergo communi arcu AB, erunt duo
              <lb/>
            arcus AB, AC, ſemicirculo BAD, æqua-
              <lb/>
            les. </s>
            <s xml:id="echoid-s12335" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12336" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12337" xml:space="preserve">SIT deinde angulus ACD, maior angulo B, hoc eſt, angulo D, quian-
              <lb/>
              <note position="left" xlink:label="note-380-09" xlink:href="note-380-09a" xml:space="preserve">13. huius.</note>
            gulo B, æqualis eſt; </s>
            <s xml:id="echoid-s12338" xml:space="preserve">eritq́ arcus AD, maior arcu AC. </s>
            <s xml:id="echoid-s12339" xml:space="preserve">Addito ergo commu-
              <lb/>
              <note position="left" xlink:label="note-380-10" xlink:href="note-380-10a" xml:space="preserve">11. huius.</note>
            </s>
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