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

Table of contents

< >
[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)
[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)
< >
page |< < (311) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div817" type="section" level="1" n="459">
          <p>
            <s xml:id="echoid-s9590" xml:space="preserve">
              <pb o="311" file="323" n="323" rhead=""/>
            quauis ad eandem partem producta; </s>
            <s xml:id="echoid-s9591" xml:space="preserve">erit eadem
              <lb/>
              <note position="right" xlink:label="note-323-01" xlink:href="note-323-01a" xml:space="preserve">producta,
                <lb/>
              & cũ dia-
                <lb/>
              metro pro-
                <lb/>
              ducta con-
                <lb/>
              ueniens, ad
                <lb/>
              ſegmẽtum
                <lb/>
              exterius.</note>
            proportio totius chordæ productæ ad ſegmẽtum
              <lb/>
            exterius, quæ ſinus arcus inter punctú, per quod
              <lb/>
            diameter producta eſt, & </s>
            <s xml:id="echoid-s9592" xml:space="preserve">remotius punctum ex-
              <lb/>
            tremum dictæ chordæ, ad ſinum arcus inter idem
              <lb/>
            punctum diametri, & </s>
            <s xml:id="echoid-s9593" xml:space="preserve">propinquius punctum ex-
              <lb/>
            tremum eiuſdem chordæ.</s>
            <s xml:id="echoid-s9594" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9595" xml:space="preserve">IN circulo ABCD, chorda AD, arcus AD, ad partes D, producta con-
              <lb/>
            ueniat cum diametro BC, ad eaſdem partes producta in puncto E; </s>
            <s xml:id="echoid-s9596" xml:space="preserve">demittan-
              <lb/>
            turq́ue AF, DG, ad diametrum BC, perpendiculares; </s>
            <s xml:id="echoid-s9597" xml:space="preserve">quarum AF, ſinus eſt
              <lb/>
            arcus AC: </s>
            <s xml:id="echoid-s9598" xml:space="preserve">& </s>
            <s xml:id="echoid-s9599" xml:space="preserve">DG, ſinus arcus CD. </s>
            <s xml:id="echoid-s9600" xml:space="preserve">Dico ita eſ-
              <lb/>
              <figure xlink:label="fig-323-01" xlink:href="fig-323-01a" number="171">
                <image file="323-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/323-01"/>
              </figure>
            ſe AE, ad DE, ut AF, ad DG. </s>
            <s xml:id="echoid-s9601" xml:space="preserve">Quoniam enim
              <lb/>
            AF, DG, parallelæ ſunt obangulos rectos F,
              <lb/>
              <note position="right" xlink:label="note-323-02" xlink:href="note-323-02a" xml:space="preserve">28. primi.
                <lb/>
              Coroll. 4.
                <lb/>
              ſexti.</note>
            G; </s>
            <s xml:id="echoid-s9602" xml:space="preserve">ſimilia erunt triangula AEF, DEG. </s>
            <s xml:id="echoid-s9603" xml:space="preserve">Qua-
              <lb/>
            re erit, ut AE, ad AF, ita DE, ad DG: </s>
            <s xml:id="echoid-s9604" xml:space="preserve">Et per-
              <lb/>
            mutando, ut AE, ad DE, ita AF, ad DG. </s>
            <s xml:id="echoid-s9605" xml:space="preserve">Si
              <lb/>
            igitur in circulo chorda cuiuſlibet arcus ad
              <lb/>
            unam partem producatur, conueniatq́ue cum
              <lb/>
            diametro quauis, &</s>
            <s xml:id="echoid-s9606" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9607" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s9608" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div820" type="section" level="1" n="460">
          <head xml:id="echoid-head492" xml:space="preserve">PROBL. 3. PROPOS. 6.</head>
          <note position="right" xml:space="preserve">Ex ſumma
            <lb/>
          data duorũ
            <lb/>
          arcuũ, quo
            <lb/>
          rum quili-
            <lb/>
          bet ſemicir
            <lb/>
          culo minor
            <lb/>
          ſit, vel duo-
            <lb/>
          rum angu-
            <lb/>
          lotum, vna
            <lb/>
          cũ propor-
            <lb/>
          ticne, quã
            <lb/>
          eorũ ſinus
            <lb/>
          habẽ@, vter-
            <lb/>
          que cogno
            <lb/>
          ſcitur.</note>
          <p>
            <s xml:id="echoid-s9609" xml:space="preserve">DATO aggregato duorum arcuum, quo-
              <lb/>
            rum ſinguli ſemicirculo ſint minores, vel duorum
              <lb/>
            angulorum rectilineorum, ſiue minus illud ſit, ſi
              <lb/>
            ue maius, quàm grad. </s>
            <s xml:id="echoid-s9610" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9611" xml:space="preserve">vnà cum proportione,
              <lb/>
            quam eorum ſinus habent: </s>
            <s xml:id="echoid-s9612" xml:space="preserve">vtrum queillorum ſi
              <lb/>
            gillatim exhibere notum.</s>
            <s xml:id="echoid-s9613" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9614" xml:space="preserve">IN circulo ABCD, cuius centrum E, datum ſit primo aggregatum ar-
              <lb/>
              <note position="right" xlink:label="note-323-04" xlink:href="note-323-04a" xml:space="preserve">Quãdo ag
                <lb/>
              gregatũ ar-
                <lb/>
              cuum, vel
                <lb/>
              angulorũ
                <lb/>
              minus eſt,
                <lb/>
              quã grad.
                <lb/>
              180.</note>
            cuum BF, FD, quorum ſinguli ſint ſemicirculo minores, uel angulorũ BEF,
              <lb/>
            FED, & </s>
            <s xml:id="echoid-s9615" xml:space="preserve">aggregatum tam arcuum, quàm angulorum minus, quàm grad. </s>
            <s xml:id="echoid-s9616" xml:space="preserve">180.
              <lb/>
            </s>
            <s xml:id="echoid-s9617" xml:space="preserve">nimirum datum ſit grad. </s>
            <s xml:id="echoid-s9618" xml:space="preserve">130. </s>
            <s xml:id="echoid-s9619" xml:space="preserve">Data quoque ſit proportio ſinus arcus BF, vel
              <lb/>
            anguli BEF, ad ſinum arcus FD, uel anguli FED, eadẽ, quæ 10.</s>
            <s xml:id="echoid-s9620" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9621" xml:space="preserve">Opor-
              <lb/>
            tet ex his utrumque arcum BF, FD, uel utrumque angulum BEF, FED,
              <lb/>
            notum efficere. </s>
            <s xml:id="echoid-s9622" xml:space="preserve">Ducta chorda BD, ducatur ex puncto F, ubi dati arcus con-
              <lb/>
            iunguntur, diameter FC, ſecans chordam BD, in G. </s>
            <s xml:id="echoid-s9623" xml:space="preserve">Diuiſo quoque toto </s>
          </p>
        </div>
      </text>
    </echo>
Impressum