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

Table of figures

< >
[Figure 141]
Page: 191
[Figure 142]
Page: 191
[Figure 143]
Page: 192
[Figure 144]
Page: 193
[Figure 145]
Page: 193
[Figure 146]
Page: 195
[Figure 147]
Page: 198
[Figure 148]
Page: 199
[Figure 149]
Page: 202
[Figure 150]
Page: 203
[Figure 151]
Page: 204
[Figure 152]
Page: 205
[Figure 153]
Page: 206
[Figure 154]
Page: 210
[Figure 155]
Page: 211
[Figure 156]
Page: 212
[Figure 157]
Page: 213
[Figure 158]
Page: 309
[Figure 159]
Page: 310
[Figure 160]
Page: 311
[Figure 161]
Page: 312
[Figure 162]
Page: 312
[Figure 163]
Page: 313
[Figure 164]
Page: 314
[Figure 165]
Page: 315
[Figure 166]
Page: 316
[Figure 167]
Page: 317
[Figure 168]
Page: 319
[Figure 169]
Page: 321
[Figure 170]
Page: 322
< >
page |< < (300) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div779" type="section" level="1" n="453">
          <p>
            <s xml:id="echoid-s8788" xml:space="preserve">
              <pb o="300" file="312" n="312" rhead=""/>
            vero latera AB, AC, ſunt inæqualia, ſit AC, maius, ex quo abſcindatur re-
              <lb/>
            cta CE, minori lateri AB, æqualis, & </s>
            <s xml:id="echoid-s8789" xml:space="preserve">ex A, E, ad tertium latus BC, perpen
              <lb/>
              <figure xlink:label="fig-312-01" xlink:href="fig-312-01a" number="161">
                <image file="312-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/312-01"/>
              </figure>
            diculares demittantur AD, EF, quarum vtraq;
              <lb/>
            </s>
            <s xml:id="echoid-s8790" xml:space="preserve">cadet intra triangulum, quando angulus B, ma-
              <lb/>
            iori lateri AC, oppoſitus acutus eſt. </s>
            <s xml:id="echoid-s8791" xml:space="preserve">Erit enim
              <lb/>
            & </s>
            <s xml:id="echoid-s8792" xml:space="preserve">tunc angulus quoq; </s>
            <s xml:id="echoid-s8793" xml:space="preserve">C, acutus, cum minor
              <lb/>
            ſit, quam B. </s>
            <s xml:id="echoid-s8794" xml:space="preserve">Quare perpendicularis AD, intra
              <lb/>
              <note position="left" xlink:label="note-312-01" xlink:href="note-312-01a" xml:space="preserve">18. primi.
                <lb/>
              Schol. 13.
                <lb/>
              ſecundi.
                <lb/>
              Schol. 12.
                <lb/>
              ſecundi.</note>
            triangulum cadet, ac proinde & </s>
            <s xml:id="echoid-s8795" xml:space="preserve">perpendi@ula-
              <lb/>
            ris EF. </s>
            <s xml:id="echoid-s8796" xml:space="preserve">Quando vero angulus B, obtuſus eſt,
              <lb/>
            cadet quidem AD, ſemper extra triangulum,
              <lb/>
            at EF, cadere poteſt vel extra etiam, vel in pun
              <lb/>
            ctum B, vel intra triangulum. </s>
            <s xml:id="echoid-s8797" xml:space="preserve">Quomodocunq;
              <lb/>
            </s>
            <s xml:id="echoid-s8798" xml:space="preserve">autem cadant dictæ perpendiculares, ſemper ea-
              <lb/>
              <note position="left" xlink:label="note-312-02" xlink:href="note-312-02a" xml:space="preserve">18. primi.
                <lb/>
              Coroll. 4.
                <lb/>
              ſexti.</note>
            dem erit demonſtratio. </s>
            <s xml:id="echoid-s8799" xml:space="preserve">Nam cum AD, EF, ſint
              <lb/>
            parallelæ, erunt triangula CEF, CAD, ſimi-
              <lb/>
            lia. </s>
            <s xml:id="echoid-s8800" xml:space="preserve">Quamobrem erit, vt CE, ad EF, ita CA, ad AD. </s>
            <s xml:id="echoid-s8801" xml:space="preserve">Cum ergo ex ijs, quæ
              <lb/>
              <note position="left" xlink:label="note-312-03" xlink:href="note-312-03a" xml:space="preserve">4. ſexti.</note>
            in definitionibus ſinuum tradidimus, poſito ſinu toto CE, recta EF, ſit ſinus
              <lb/>
            anguli C; </s>
            <s xml:id="echoid-s8802" xml:space="preserve">poſito item ſinu toto AB, recta AD, ſit ſinus anguli ABD; </s>
            <s xml:id="echoid-s8803" xml:space="preserve">ſintq;
              <lb/>
            </s>
            <s xml:id="echoid-s8804" xml:space="preserve">ſinus toti CE, AB, reſpectu quorum illi ſunt ſinus, æquales; </s>
            <s xml:id="echoid-s8805" xml:space="preserve">liquet eſſe, vt
              <lb/>
            CE, hoc eſt, latus AB, ad EF, ſinum anguli C, ita latus CA, ad AD, ſinum
              <lb/>
            anguli ABD: </s>
            <s xml:id="echoid-s8806" xml:space="preserve">Et permutando, vt latus AB, ad latus AC, ita EF, ſinum
              <lb/>
            anguli C, ad AD, ſinum anguli ABD, hoc eſt, in poſteriori triangulo, ad
              <lb/>
            ſinum anguli ABC, cum duo anguli ad B, æquales ſint duobus rectis, & </s>
            <s xml:id="echoid-s8807" xml:space="preserve">pro-
              <lb/>
            inde eundem ſinum habeant, vt in definitionibus ſinuum docuimus. </s>
            <s xml:id="echoid-s8808" xml:space="preserve">Ex quo
              <lb/>
            conſtat, ita eſſe minus latus AB, ad maius AC, vt eſt EF, ſinus anguli C, mi-
              <lb/>
            nori lateri oppoſiti ad AD, ſinum anguli ABC, maiori lateri oppoſiti: </s>
            <s xml:id="echoid-s8809" xml:space="preserve">Et
              <lb/>
            conuertendo, ita eſſe maius latus AC, ad minus AB, vt eſt AD, ſinus angu-
              <lb/>
            li ABC, maiori lateri oppoſiti ad EF, ſinum anguli C, minori lateri oppo-
              <lb/>
            ſiti. </s>
            <s xml:id="echoid-s8810" xml:space="preserve">Non aliter oſtendemus eſſe, vt latus AB, ad latus BC, ita ſinum anguli
              <lb/>
            C, ad ſinum anguli A: </s>
            <s xml:id="echoid-s8811" xml:space="preserve">Vel vt latus BC, ad latus AB, ita ſinum anguli A, ad
              <lb/>
            ſinum anguli C. </s>
            <s xml:id="echoid-s8812" xml:space="preserve">&</s>
            <s xml:id="echoid-s8813" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8814" xml:space="preserve">dummodo ex puncto, vbi conueniunt latera aſſumpta
              <lb/>
            inæqualia, (ſi forte æqualia non ſunt) ducas ad latus oppoſitum lineam per-
              <lb/>
            pendicularem, & </s>
            <s xml:id="echoid-s8815" xml:space="preserve">minori lateri ex maiore rectam æqualem abſcindas, initio
              <lb/>
            facto ab altero puncto extremo maioris lateris, vbi cum tertio latere coniun-
              <lb/>
            gitur, vt à nobis factum eſt, &</s>
            <s xml:id="echoid-s8816" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8817" xml:space="preserve"/>
          </p>
          <figure number="162">
            <image file="312-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/312-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s8818" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s8819" xml:space="preserve">Sit rurſus triangulum non
              <lb/>
            rectangulum ABC: </s>
            <s xml:id="echoid-s8820" xml:space="preserve">de rectangulo enim in
              <lb/>
            principio huius demonſtrationis iam eſt de-
              <lb/>
            monſtratum. </s>
            <s xml:id="echoid-s8821" xml:space="preserve">Dico eſſe, vt latus AB, ad latus
              <lb/>
            AC, ita ſinum anguli C, ad ſinum anguli B:
              <lb/>
            </s>
            <s xml:id="echoid-s8822" xml:space="preserve">Vel vt latus AC, ad latus AB, ita ſinum an-
              <lb/>
            guli B, ad ſinum anguli C, &</s>
            <s xml:id="echoid-s8823" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8824" xml:space="preserve">Ducta enim ex
              <lb/>
            A, vbi duo late-
              <lb/>
              <note position="right" xlink:label="note-312-04" xlink:href="note-312-04a" xml:space="preserve">
                <lb/>
              latus AB. # ſin. ang. C.
                <lb/>
              latus AD. # ſin. ang. D.
                <lb/>
              latus AC. # ſin. ang. B.
                <lb/>
              </note>
            ra aſſumpta co-
              <lb/>
            eunt, ad tertiũ
              <lb/>
            latus BC, per-
              <lb/>
            pẽdiculari AD,
              <lb/>
            quæ vel i@tra triangulum cadet, vel extra, prout anguli B, & </s>
            <s xml:id="echoid-s8825" xml:space="preserve">C, acuti </s>
          </p>
        </div>
      </text>
    </echo>
Impressum