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

Table of contents

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[301.] complementorum arcuum eiuſdem Quadrantis.
Page: 229 (217)
[302.] Gradus Quadrantis pro tangentibus
Page: 230 (218)
[303.] Gradus Quadrantis pro tangentibus
Page: 230 (218)
[304.] arcuum eiuſdem Quadrantis.
Page: 231 (219)
[305.] complementorum arcuum eiuſdem Quadrantis.
Page: 231 (219)
[306.] Gradus Qudrantis pro tangentibus
Page: 232 (220)
[307.] Gradus Quadrantis pro tangentibus
Page: 232 (220)
[308.] arcuum eiuſdem Quadrantis
Page: 233 (221)
[309.] complementorum arcuum eiuſdem Quadrantis
Page: 233 (221)
[310.] Gradus Quadrantis pro tangentibus
Page: 234 (222)
[311.] Gradus Quadrantis pro tangentibus
Page: 234 (222)
[312.] arcuum eiuſdem Quadrantis
Page: 235 (223)
[313.] complementorum arcuum eiuſdem Quadrantis
Page: 235 (223)
[314.] Gradus Quadrantis pro tangentibus
Page: 236 (224)
[315.] Gradus Quadrantis pro tangentibus
Page: 236 (224)
[316.] arcuum eiuſdem Quadrantis
Page: 237 (225)
[317.] complementorum arcuum eiuſdem Quadrantis
Page: 237 (225)
[318.] Gradus Quadrantis pro tangentibus
Page: 238 (226)
[319.] Gradus Quadrantis pro tangentibus
Page: 238 (226)
[320.] arcuum eiuſdem Quadrantis
Page: 239 (227)
[321.] complementorum arcuum eiuſdem Quadrantis
Page: 239 (227)
[322.] Gradus Quadrantis pro tangentibus
Page: 240 (228)
[323.] Gradus Quadrantis pro tangentibus
Page: 240 (228)
[324.] arcuum eiuſdem Quadrantis.
Page: 241 (229)
[325.] complementorum arcuum eiuſdem Quadrantis.
Page: 241 (229)
[326.] Gradus Quadrantis pro tangentibus
Page: 242 (230)
[327.] Gradus Quadrantis pro tangentibus
Page: 242 (230)
[328.] arcuum eiuſdem Quadrantis.
Page: 243 (231)
[329.] complementorum arcuum eiuſdem Quadrantis.
Page: 243 (231)
[330.] Gradus Quadrantis pro tangentibus
Page: 244 (232)
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            <s xml:id="echoid-s12625" xml:space="preserve">
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            C, duobus angulis E, F, æquales, vtrumque vtrique, & </s>
            <s xml:id="echoid-s12626" xml:space="preserve">latera AC, DF, ſub-
              <lb/>
            tendentia angulos æquales B, E, inter ſe æqualia, reliqua verò latera AB,
              <lb/>
            DE, ſubtendentia alios æquales angulos C,F, non æqualia ſint ſemicirculo,
              <lb/>
            ſed vel maiora, vel minora. </s>
            <s xml:id="echoid-s12627" xml:space="preserve">Dico reliqua latera
              <lb/>
              <figure xlink:label="fig-387-01" xlink:href="fig-387-01a" number="223">
                <image file="387-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/387-01"/>
              </figure>
            CB, BA, reliquis lateribus FE, ED, eſſe æqua-
              <lb/>
            lia, vtrumque vtrique, & </s>
            <s xml:id="echoid-s12628" xml:space="preserve">reliquos quoque an-
              <lb/>
            gulos A, D, eſſe æquales. </s>
            <s xml:id="echoid-s12629" xml:space="preserve">Si enim CB, & </s>
            <s xml:id="echoid-s12630" xml:space="preserve">FE,
              <lb/>
            non ſunt æqualia, ſit CB, maius, & </s>
            <s xml:id="echoid-s12631" xml:space="preserve">abſcindatur
              <lb/>
            CG, arcus arcui FE, æqualis, & </s>
            <s xml:id="echoid-s12632" xml:space="preserve">per A, G, ar-
              <lb/>
              <note position="right" xlink:label="note-387-01" xlink:href="note-387-01a" xml:space="preserve">1. huius.</note>
            cus circuli maximi ducatur AG. </s>
            <s xml:id="echoid-s12633" xml:space="preserve">Quoniam igi-
              <lb/>
              <note position="right" xlink:label="note-387-02" xlink:href="note-387-02a" xml:space="preserve">10. 1. Theo.</note>
            tur latera AC, CG, lateribus DF, FE, æqua-
              <lb/>
            lia ſunt, angulosq́ue continent æquales C, F;
              <lb/>
            </s>
            <s xml:id="echoid-s12634" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s12635" xml:space="preserve">arcus AG, DE, & </s>
            <s xml:id="echoid-s12636" xml:space="preserve">anguli AGC, & </s>
            <s xml:id="echoid-s12637" xml:space="preserve">E, æquales: </s>
            <s xml:id="echoid-s12638" xml:space="preserve">Poſitus eſt autem an-
              <lb/>
              <note position="right" xlink:label="note-387-03" xlink:href="note-387-03a" xml:space="preserve">7. huius.</note>
            gulus E, angulo B, æqualis. </s>
            <s xml:id="echoid-s12639" xml:space="preserve">Aequalis igitur eſt etiam angulus AGC, angulo
              <lb/>
            B; </s>
            <s xml:id="echoid-s12640" xml:space="preserve">ac propterea arcus AB, AG, ſemicirculo æquales erunt. </s>
            <s xml:id="echoid-s12641" xml:space="preserve">Cum ergo arcus
              <lb/>
              <note position="right" xlink:label="note-387-04" xlink:href="note-387-04a" xml:space="preserve">15. huius.</note>
            AG, arcui DE, oſtenſus ſit æqualis, erunt quoque arcus AB, DE, ſemicir-
              <lb/>
            culo æquales: </s>
            <s xml:id="echoid-s12642" xml:space="preserve">Ponuntur autem & </s>
            <s xml:id="echoid-s12643" xml:space="preserve">non æquales ſemicirculo. </s>
            <s xml:id="echoid-s12644" xml:space="preserve">Quod eſt abſur-
              <lb/>
            dum. </s>
            <s xml:id="echoid-s12645" xml:space="preserve">Non ergo inæquales ſunt arcus CB, FE, ſed æquales. </s>
            <s xml:id="echoid-s12646" xml:space="preserve">Quare cum late-
              <lb/>
            ra AC, CB, ſint æqualia lateribus DF, FE, angulosq́ue æquales contineant
              <lb/>
            C, F; </s>
            <s xml:id="echoid-s12647" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s12648" xml:space="preserve">arcus AB, DE, & </s>
            <s xml:id="echoid-s12649" xml:space="preserve">anguli BAC, & </s>
            <s xml:id="echoid-s12650" xml:space="preserve">D, æquales. </s>
            <s xml:id="echoid-s12651" xml:space="preserve">Siigitur ſue-
              <lb/>
              <note position="right" xlink:label="note-387-05" xlink:href="note-387-05a" xml:space="preserve">7. huius.</note>
            rint duo triangula ſphæica, &</s>
            <s xml:id="echoid-s12652" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12653" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s12654" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div997" type="section" level="1" n="511">
          <head xml:id="echoid-head546" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s12655" xml:space="preserve">_DIXIMVS,_ duo latera ſubtendentia reliquos angulos æquales, non debere
              <lb/>
            eſſe æqualia ſemicirculo. </s>
            <s xml:id="echoid-s12656" xml:space="preserve">Nam alias propoſitio vera non eſſet. </s>
            <s xml:id="echoid-s12657" xml:space="preserve">Sit enim triangulum
              <lb/>
            ſphæricum _ABC,_ quodcunq; </s>
            <s xml:id="echoid-s12658" xml:space="preserve">habens duo latera _AB, AC,_ inæqualia inter ſe, ſed
              <lb/>
              <figure xlink:label="fig-387-02" xlink:href="fig-387-02a" number="224">
                <image file="387-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/387-02"/>
              </figure>
            ſimul ſemicirculo æqualia: </s>
            <s xml:id="echoid-s12659" xml:space="preserve">Producto autem latere _BC,_
              <lb/>
            vſque ad _D,_ ita tamen, vt _BD,_ ſemicirculo ſit minor, du-
              <lb/>
            caiur per _A, D,_ arcus circuli maximi _AD._ </s>
            <s xml:id="echoid-s12660" xml:space="preserve">Quoniam igi-
              <lb/>
              <note position="right" xlink:label="note-387-06" xlink:href="note-387-06a" xml:space="preserve">_20. 1. Theo._</note>
            tur arcus _AB, AC,_ ſemicirculo æquales ſunt, erit angu-
              <lb/>
            lus _ACD,_ angulo _B,_ æqualis. </s>
            <s xml:id="echoid-s12661" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s12662" xml:space="preserve">duotriangula _ABD,_
              <lb/>
              <note position="right" xlink:label="note-387-07" xlink:href="note-387-07a" xml:space="preserve">_14. huius._</note>
            _ACD;_ </s>
            <s xml:id="echoid-s12663" xml:space="preserve">duos angulos _B, D,_ duobus angulis _C, D,_ æqua-
              <lb/>
            leshabent, vtrumque vtrique, & </s>
            <s xml:id="echoid-s12664" xml:space="preserve">latus _AD,_ commune,
              <lb/>
            quod æqualibus angulis _B, C,_ ſubtenditur; </s>
            <s xml:id="echoid-s12665" xml:space="preserve">& </s>
            <s xml:id="echoid-s12666" xml:space="preserve">tamen ne-
              <lb/>
            que reliqualatera _AB, BD,_ reliquis lateribus _AC, CD,_
              <lb/>
            æqualia ſunt, vtrumque vtrique, neque reliquus angulus _BAD,_ reliquo angulo
              <lb/>
            _CAD,_ vt perſpicuum eſt. </s>
            <s xml:id="echoid-s12667" xml:space="preserve">Hoc autem ideò contingit, quod latera _AE, AC,_ ſemicir-
              <lb/>
            culo ſunt æqualia.</s>
            <s xml:id="echoid-s12668" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12669" xml:space="preserve">_NICOLAVS_ ergo Copernicus lib. </s>
            <s xml:id="echoid-s12670" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12671" xml:space="preserve">Reuolutionum propoſ. </s>
            <s xml:id="echoid-s12672" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12673" xml:space="preserve">triangulorum
              <lb/>
              <note position="right" xlink:label="note-387-08" xlink:href="note-387-08a" xml:space="preserve">Error Ni-
                <lb/>
              colai Co-
                <lb/>
              pernici.</note>
            ſphæricorum hallucinaiur, cum docet, omne triangulum ſphæricum, cuius duo anguli
              <lb/>
            vtcunque dati fuerint, cum aliquo latere, datorum eſſicv angulorum, & </s>
            <s xml:id="echoid-s12674" xml:space="preserve">laterum.
              <lb/>
            </s>
            <s xml:id="echoid-s12675" xml:space="preserve">Nam in triangulo _ACD,_ licet duo anguli _D,_ & </s>
            <s xml:id="echoid-s12676" xml:space="preserve">_ACD,_ noti ſint cum latere _AD,_
              <lb/>
            non tamen ex hoc perueniemus in notitiam reliquerum laterum, & </s>
            <s xml:id="echoid-s12677" xml:space="preserve">reliquianguli: </s>
            <s xml:id="echoid-s12678" xml:space="preserve">
              <lb/>
            cum reliqua latera eſſe poſsint vel _AC, CD,_ vel _AB, BD,_ &</s>
            <s xml:id="echoid-s12679" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12680" xml:space="preserve">Oportebit ergo
              <lb/>
            præterea aliquid aliud conſtare, antequam reliquus angulus, cumreliquis lateribus
              <lb/>
            cognoſcatur, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s12681" xml:space="preserve">45. </s>
            <s xml:id="echoid-s12682" xml:space="preserve">dicemus.</s>
            <s xml:id="echoid-s12683" xml:space="preserve"/>
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