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

List of thumbnails

< >
191
191 (179) 		192
192 (180)
193
193 (181) 		194
194 (182)
195
195 (183) 		196
196 (184)
197
197 (185) 		198
198 (186)
199
199 (187) 		200
200 (188)
< >
page |< < (180) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div508" type="section" level="1" n="247">
          <p>
            <s xml:id="echoid-s6736" xml:space="preserve">
              <pb o="180" file="192" n="192" rhead=""/>
            quod diuiſum per diametrum AD, notam, cognitam faciet chordam BC. </s>
            <s xml:id="echoid-s6737" xml:space="preserve">Ex
              <lb/>
            datis ergo chordis duorum arcuum inæqualium chordam arcus, quo maior
              <lb/>
            arcus minorem ſuperat, inquiſiuimus. </s>
            <s xml:id="echoid-s6738" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s6739" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div510" type="section" level="1" n="248">
          <head xml:id="echoid-head275" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s6740" xml:space="preserve">ITAQVE datis chordis duorum arcuum inæqualium, ſi maioris chorda multiplice-
              <lb/>
              <note position="left" xlink:label="note-192-01" xlink:href="note-192-01a" xml:space="preserve">Praxis.</note>
            tur in chordam arcus, qui cum minori arcu ſemicirculum conficit, quæ quidem per 3. </s>
            <s xml:id="echoid-s6741" xml:space="preserve">pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s6742" xml:space="preserve">datur; </s>
            <s xml:id="echoid-s6743" xml:space="preserve">& </s>
            <s xml:id="echoid-s6744" xml:space="preserve">ex producto ſubtrahatur numerus procreatus ex minoris arcus chorda in chor
              <lb/>
            dam arcus, qui cum arcu maiori ſemicirculum complet, quæ per eandem propoſ. </s>
            <s xml:id="echoid-s6745" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6746" xml:space="preserve">dat@r;
              <lb/>
            </s>
            <s xml:id="echoid-s6747" xml:space="preserve">reliquus autem numerus per diametrum diuidatur, reddetur chorda illius arcus, quo ma-
              <lb/>
            ior arcus minorem ſuperat, nota: </s>
            <s xml:id="echoid-s6748" xml:space="preserve">vt ex figura & </s>
            <s xml:id="echoid-s6749" xml:space="preserve">demonſtratione huius propoſ, manife-
              <lb/>
            ſtum eſt.</s>
            <s xml:id="echoid-s6750" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div512" type="section" level="1" n="249">
          <head xml:id="echoid-head276" xml:space="preserve">PROBL. 6. PROPOS. 14.</head>
          <note position="left" xml:space="preserve">Qua arte ex
            <lb/>
          datis dua-
            <lb/>
          bus chordis
            <lb/>
          cognoſcaf
            <lb/>
          chorda ar-
            <lb/>
          cus cõpoſiti
            <lb/>
          ex duobus
            <lb/>
          arcubus da
            <lb/>
          tarũ duarũ
            <lb/>
          chordarũ.</note>
          <p>
            <s xml:id="echoid-s6751" xml:space="preserve">EX datis chordis duorum arcuum chordam
              <lb/>
            arcus, qui ex duobus illis arcubus componitur, in-
              <lb/>
            ueſtigare.</s>
            <s xml:id="echoid-s6752" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6753" xml:space="preserve">IN circulo ABCDE, cuius centrum F, datæ ſint duæ chordæ AB, BC:
              <lb/>
            </s>
            <s xml:id="echoid-s6754" xml:space="preserve">oporteatq́; </s>
            <s xml:id="echoid-s6755" xml:space="preserve">inueſtigare chordam AC, arcus ABC, ex duobus arcubus AB,
              <lb/>
            BC, compoſiti. </s>
            <s xml:id="echoid-s6756" xml:space="preserve">Ductis duabus diametris AD, BE, & </s>
            <s xml:id="echoid-s6757" xml:space="preserve">rectis BD, CE, CD,
              <lb/>
            DE; </s>
            <s xml:id="echoid-s6758" xml:space="preserve">quoniam data eſt chorda AB, dabitur quoq; </s>
            <s xml:id="echoid-s6759" xml:space="preserve">chorda BD, arcus BCD,
              <lb/>
              <note position="left" xlink:label="note-192-03" xlink:href="note-192-03a" xml:space="preserve">3.huius.</note>
              <figure xlink:label="fig-192-01" xlink:href="fig-192-01a" number="143">
                <image file="192-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/192-01"/>
              </figure>
            reliqui in ſemicirculo ABD. </s>
            <s xml:id="echoid-s6760" xml:space="preserve">Pariratione, quia
              <lb/>
            data eſt chorda BC, dabitur quoq; </s>
            <s xml:id="echoid-s6761" xml:space="preserve">chorda CE,
              <lb/>
            arcus CDE, reliqui in ſemicirculo BCE. </s>
            <s xml:id="echoid-s6762" xml:space="preserve">Et quia
              <lb/>
            anguli AFB, DFE, æquales ſunt, lateraq́; </s>
            <s xml:id="echoid-s6763" xml:space="preserve">FA,
              <lb/>
              <note position="left" xlink:label="note-192-04" xlink:href="note-192-04a" xml:space="preserve">15. primi.</note>
            FB, lateribus FD, FE, æqualia, æquales quoque
              <lb/>
            erunt baſes AB, DE; </s>
            <s xml:id="echoid-s6764" xml:space="preserve">ac proinde cum AB, data
              <lb/>
              <note position="left" xlink:label="note-192-05" xlink:href="note-192-05a" xml:space="preserve">4.primi.</note>
            ſit, data quoq; </s>
            <s xml:id="echoid-s6765" xml:space="preserve">erit DE. </s>
            <s xml:id="echoid-s6766" xml:space="preserve">Quoniam igitur rectan-
              <lb/>
            gulum ſub datis rectis BD, CE, æquale eſt rectan
              <lb/>
              <note position="left" xlink:label="note-192-06" xlink:href="note-192-06a" xml:space="preserve">11.huius.</note>
            gulis ſub datis rectis BC, DE, & </s>
            <s xml:id="echoid-s6767" xml:space="preserve">ſub diametro
              <lb/>
            BE, ac recta CD: </s>
            <s xml:id="echoid-s6768" xml:space="preserve">ſi rectangulum ſub BC, DE,
              <lb/>
            datum auferatur ex rectangulo dato ſub BD, CE; </s>
            <s xml:id="echoid-s6769" xml:space="preserve">notum relinquetur rectan
              <lb/>
            gulum ſub BE, CD. </s>
            <s xml:id="echoid-s6770" xml:space="preserve">quo diuiſo per diametrum notam BE, nota fiet chor-
              <lb/>
            da CD; </s>
            <s xml:id="echoid-s6771" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s6772" xml:space="preserve">chorda AC, reliqui arcus ABC, in ſemicirculo ACD,
              <lb/>
              <note position="left" xlink:label="note-192-07" xlink:href="note-192-07a" xml:space="preserve">3. huius.</note>
            nota erit.</s>
            <s xml:id="echoid-s6773" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6774" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s6775" xml:space="preserve">Quoniam data eſt chorda AB, dabitur etiam BD, reliqui ar-
              <lb/>
              <note position="left" xlink:label="note-192-08" xlink:href="note-192-08a" xml:space="preserve">3.huius.</note>
            cus BCD, in ſemicirculo ABD: </s>
            <s xml:id="echoid-s6776" xml:space="preserve">Data eſt autem & </s>
            <s xml:id="echoid-s6777" xml:space="preserve">BC. </s>
            <s xml:id="echoid-s6778" xml:space="preserve">Igitur cum chordæ
              <lb/>
            BD, BC, datæ ſint, dabitur quoq; </s>
            <s xml:id="echoid-s6779" xml:space="preserve">chorda CD, arcus CD, quo maior arcus
              <lb/>
              <note position="left" xlink:label="note-192-09" xlink:href="note-192-09a" xml:space="preserve">13. huius.</note>
            BD, minorem arcum BC, ſuperat; </s>
            <s xml:id="echoid-s6780" xml:space="preserve">ac proinde rurſus chorda AC, reliqui
              <lb/>
              <note position="left" xlink:label="note-192-10" xlink:href="note-192-10a" xml:space="preserve">3.huius.</note>
            arcus ABC, in ſemicirculo ACD, dabitur. </s>
            <s xml:id="echoid-s6781" xml:space="preserve">Ex datis ergo chordis duorum ar
              <lb/>
            cuum chordam arcus, qui ex duobus illis arcubus componitur, inueſtigaui-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s6782" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s6783" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div515" type="section" level="1" n="250">
          <head xml:id="echoid-head277" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s6784" xml:space="preserve">ITAQVE datis chordis duorum arcuum, ſi chordæ arcuum duorum, qui cum illis ſe-
              <lb/>
              <note position="left" xlink:label="note-192-11" xlink:href="note-192-11a" xml:space="preserve">Praxis.</note>
            micirculos complent, quæ quidem per propoſ. </s>
            <s xml:id="echoid-s6785" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6786" xml:space="preserve">dantur, inter ſe multiplicentur; </s>
            <s xml:id="echoid-s6787" xml:space="preserve">& </s>
            <s xml:id="echoid-s6788" xml:space="preserve">ex </s>
          </p>
        </div>
      </text>
    </echo>
Impressum