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

Table of contents

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[331.] Gradus Quadrantis pro tangentibus
Page: 244 (232)
[332.] arcuum eiuſdem Quadrantis
Page: 245 (233)
[333.] complementorum arcuum eiuſdem Quadrantis
Page: 245 (233)
[334.] Gradus Quadrantis pro tangentibus
Page: 246 (234)
[335.] Gradus Quadrantis pro tangentibus
Page: 246 (234)
[336.] arcuum eiuſdem Quadrantis
Page: 247 (235)
[337.] complementorum arcuum eiuſdem Quadrantis
Page: 247 (235)
[338.] Gradus Quadrantis pro tangentibus
Page: 248 (236)
[339.] Gradus Quadrantis pro tangentibus
Page: 248 (236)
[340.] arcuum eiuſdem Quadrantis
Page: 249 (237)
[341.] complementorum arcuum eiuſdem Quadrantis
Page: 249 (237)
[342.] Gradus Quadrantis pro tangentibus
Page: 250 (238)
[343.] Gradus Quadrantis pro tangentibus
Page: 250 (238)
[344.] arcuum eiuſdem Quadrantis.
Page: 251 (239)
[345.] complementorum arcuum eiuſdem Quadrantis.
Page: 251 (239)
[346.] Gradus Quadrantis pro tangentibus
Page: 252 (240)
[347.] Gradus Quadrantis pro tangentibus
Page: 252 (240)
[348.] arcuum eiuſdem Quadrantis.
Page: 253 (241)
[349.] complementorum arcuum eiuſdem Quadrantis.
Page: 253 (241)
[350.] Gradus Quadrantis pro tangentibus
Page: 254 (242)
[351.] Gradus Quadrantis pro tangentibus
Page: 254 (242)
[352.] arcuum eiuſdem Quadrantis.
Page: 255 (243)
[353.] complementorum arcuum eiuſdem Quadrantis.
Page: 255 (243)
[354.] LINEARVM SECANTIVM, SIVE BENEFICA.
Page: 257
[355.] Gradus Quadrantis pro ſecantibus
Page: 258 (246)
[356.] Gradus Quadrantis pro ſecantibus
Page: 258 (246)
[357.] arcuum eiuſdem Quadrantis
Page: 259 (247)
[358.] complementorum arcuum eiuſdem Quadrantis
Page: 259 (247)
[359.] Gradus Quadrantis pro ſecantibus
Page: 260 (248)
[360.] Gradus Quadrantis pro ſecantibus
Page: 260 (248)
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            <s xml:id="echoid-s10098" xml:space="preserve">
              <pb o="319" file="331" n="331" rhead=""/>
            BEF, grad. </s>
            <s xml:id="echoid-s10099" xml:space="preserve">_120._ </s>
            <s xml:id="echoid-s10100" xml:space="preserve">Ipſa vero ſemiſſis erit arcus minor DF, vel angulus
              <lb/>
            DEF, grad. </s>
            <s xml:id="echoid-s10101" xml:space="preserve">_60._ </s>
            <s xml:id="echoid-s10102" xml:space="preserve">Ita ſi differentia data complectatur grad. </s>
            <s xml:id="echoid-s10103" xml:space="preserve">_104._ </s>
            <s xml:id="echoid-s10104" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s10105" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s10106" xml:space="preserve">detrahemus eam ex grad. </s>
            <s xml:id="echoid-s10107" xml:space="preserve">_180._ </s>
            <s xml:id="echoid-s10108" xml:space="preserve">& </s>
            <s xml:id="echoid-s10109" xml:space="preserve">reliqui arcus grad. </s>
            <s xml:id="echoid-s10110" xml:space="preserve">_75._ </s>
            <s xml:id="echoid-s10111" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10112" xml:space="preserve">_40._ </s>
            <s xml:id="echoid-s10113" xml:space="preserve">
              <lb/>
            ſemiſſem, nempe grad. </s>
            <s xml:id="echoid-s10114" xml:space="preserve">_37._ </s>
            <s xml:id="echoid-s10115" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10116" xml:space="preserve">_50._ </s>
            <s xml:id="echoid-s10117" xml:space="preserve">datæ differentiæ addemus, vt com-
              <lb/>
            ponatur maior arcus, ſeu angulus propoſitus, grad. </s>
            <s xml:id="echoid-s10118" xml:space="preserve">_142._ </s>
            <s xml:id="echoid-s10119" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10120" xml:space="preserve">_10._ </s>
            <s xml:id="echoid-s10121" xml:space="preserve">Minor
              <lb/>
            enim erit ioſa differentiæ ſemiſſis grad. </s>
            <s xml:id="echoid-s10122" xml:space="preserve">_37._ </s>
            <s xml:id="echoid-s10123" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10124" xml:space="preserve">_50._</s>
            <s xml:id="echoid-s10125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10126" xml:space="preserve">QVOCIRCA, data diſſerentia duorum arcuum, quorum ſinguli ſe-
              <lb/>
            micirculo ſint minores, vel duorum angulorum rectilineorum, &</s>
            <s xml:id="echoid-s10127" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10128" xml:space="preserve">vtrumq;
              <lb/>
            </s>
            <s xml:id="echoid-s10129" xml:space="preserve">illorum ſigillatim notum effecimus. </s>
            <s xml:id="echoid-s10130" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s10131" xml:space="preserve"/>
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          <head xml:id="echoid-head495" xml:space="preserve">THEOR. 4. PROPOS. 8.</head>
          <p>
            <s xml:id="echoid-s10132" xml:space="preserve">SI ab angulo trianguli cuiuſuis duobus lateri-
              <lb/>
              <note position="right" xlink:label="note-331-01" xlink:href="note-331-01a" xml:space="preserve">Quãto ma
                <lb/>
              ius ſit qua-
                <lb/>
              dratũ ma-
                <lb/>
              ioris late-
                <lb/>
              ris. quàm
                <lb/>
              minoris in
                <lb/>
              quouis triã
                <lb/>
              gulo.</note>
            bus inæqualibus comprehenſo linea perpendicu-
              <lb/>
            laris ad baſim ducatur, ſi quidem intra triangu-
              <lb/>
            lum cadit, erit quadratum maioris laterum dictum
              <lb/>
            angulum ambientium maius, quam quadratum
              <lb/>
            minoris, rectangulo ſub baſe, & </s>
            <s xml:id="echoid-s10133" xml:space="preserve">differentia ſeg-
              <lb/>
            mentorum à perpẽdiculari factorum comprehen-
              <lb/>
            ſo: </s>
            <s xml:id="echoid-s10134" xml:space="preserve">ſi vero extra cadit, erit quadratum maioris la-
              <lb/>
            teris maius, quam quadratum minoris, rectangu-
              <lb/>
            lo ſub baſe, & </s>
            <s xml:id="echoid-s10135" xml:space="preserve">recta linea, quæ ex baſe, & </s>
            <s xml:id="echoid-s10136" xml:space="preserve">duplo ex-
              <lb/>
            terioris lineæ inter perpendicularem, & </s>
            <s xml:id="echoid-s10137" xml:space="preserve">angulum
              <lb/>
            trianguli componitur, comprehenſo.</s>
            <s xml:id="echoid-s10138" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10139" xml:space="preserve">IN triangulo ABC, cuius duo latera AB,
              <lb/>
              <figure xlink:label="fig-331-01" xlink:href="fig-331-01a" number="176">
                <image file="331-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/331-01"/>
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            AC, inæqualia ſint, AC, maius, & </s>
            <s xml:id="echoid-s10140" xml:space="preserve">AB, minus,
              <lb/>
            ducatur ex angulo A, ad baſim BC, perpendicu-
              <lb/>
            laris AD, cadens primùm intra triangulum, vt
              <lb/>
            in priori figura. </s>
            <s xml:id="echoid-s10141" xml:space="preserve">Et quoniam tam quadrata re-
              <lb/>
            ctarum AD, DB, quadrato rectæ AB, quàm
              <lb/>
              <note position="right" xlink:label="note-331-02" xlink:href="note-331-02a" xml:space="preserve">47. primi.</note>
            quadrata rectarum AD, DC, quadrato rectæ
              <lb/>
            AC, æqualia ſunt; </s>
            <s xml:id="echoid-s10142" xml:space="preserve">eſt autem quadratum rectæ
              <lb/>
            AB, minus quadrato rectæ AC, quòd minor po
              <lb/>
            natur recta AB, quam AC: </s>
            <s xml:id="echoid-s10143" xml:space="preserve">erunt quoque duo
              <lb/>
            quadrata rectarum AD, DB, ſimul; </s>
            <s xml:id="echoid-s10144" xml:space="preserve">minora
              <lb/>
            duobus quadratis AD, DC, ſimul; </s>
            <s xml:id="echoid-s10145" xml:space="preserve">ablato-
              <lb/>
            que propterea communi quadrato rectæ AD,
              <lb/>
            quadratum rectæ BD, quadrato rectæ </s>
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