Clavius, Christoph, Geometria practica

Page concordance

< >
Scan Original
391 363
392 364
393 365
394 366
395 367
396 368
397 369
398 370
399 371
400 372
401 373
402 374
403 375
404 376
405 377
406 378
407 379
408 380
409 381
410 382
411 383
412 384
413 385
414 386
415 387
416 388
417 389
418 390
419 391
420 392
< >
page |< < (350) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1003" type="section" level="1" n="358">
          <pb o="350" file="378" n="378" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s16332" xml:space="preserve">
              <emph style="sc">Sit</emph>
            datus exceſſus FE, diametri ſupra latus minus, & </s>
            <s xml:id="echoid-s16333" xml:space="preserve">C E, ſupra maius, ita
              <lb/>
            vt differentia exceſſuum ſit F C. </s>
            <s xml:id="echoid-s16334" xml:space="preserve">Ex C, educatur ad FE, perpendicularis CL, ca-
              <lb/>
            piantur que CH, HI, EK, minori exceſſui CE, æquales, ita vt totæ CI, CK, æqua-
              <lb/>
            les ſint, vt pote ipſius CE, duplæ, perficiaturque parallelogrammum FI. </s>
            <s xml:id="echoid-s16335" xml:space="preserve">Diuiſa
              <lb/>
            deinde FK, bifariam in N, deſcribatur ex N, per F, & </s>
            <s xml:id="echoid-s16336" xml:space="preserve">K, ſemicirculus FLK, ſecans
              <lb/>
            CL; </s>
            <s xml:id="echoid-s16337" xml:space="preserve">in L. </s>
            <s xml:id="echoid-s16338" xml:space="preserve">Ducta denique HE, ſumatur illi æqualis CM, iungaturque recta LM.
              <lb/>
            </s>
            <s xml:id="echoid-s16339" xml:space="preserve">Dico L M, differentiam eſſe inter minus latus quæſitum, & </s>
            <s xml:id="echoid-s16340" xml:space="preserve">minorem exceſſum
              <lb/>
            datum CE, ita vt CE, addita ad LM, efficiat minus latus; </s>
            <s xml:id="echoid-s16341" xml:space="preserve">cui ſi addatur F C, dif-
              <lb/>
            ferentia datorum exceſſum, fiat maius la-
              <lb/>
              <figure xlink:label="fig-378-01" xlink:href="fig-378-01a" number="267">
                <image file="378-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/378-01"/>
              </figure>
            tus. </s>
            <s xml:id="echoid-s16342" xml:space="preserve">(Eſt enim differentia exceſſuum dia-
              <lb/>
            metri ſupra vtrumque latus rectanguli æ-
              <lb/>
            qualis exceſſui maioris lateris ſupra mi-
              <lb/>
            nus: </s>
            <s xml:id="echoid-s16343" xml:space="preserve">vt in figura præcedentis propoſ. </s>
            <s xml:id="echoid-s16344" xml:space="preserve">pa-
              <lb/>
            tet; </s>
            <s xml:id="echoid-s16345" xml:space="preserve">vbidiameter eſt BD, vel BE; </s>
            <s xml:id="echoid-s16346" xml:space="preserve">exceſſus
              <lb/>
            maior F E, quo diameter minus latus B F,
              <lb/>
            ſuperat; </s>
            <s xml:id="echoid-s16347" xml:space="preserve">exceſſus minor CE, quo eadem
              <lb/>
            diameter maius latus B C, ſuperat: </s>
            <s xml:id="echoid-s16348" xml:space="preserve">eſt que
              <lb/>
            FC, differentia exceſſuum, exceſſus, quo
              <lb/>
            maius latus B C, ſuperat minus B F,) Ac
              <lb/>
            tandem maiori lateriinuẽto adijciatur minor exceſſus CE, vt diameter habeatur.
              <lb/>
            </s>
            <s xml:id="echoid-s16349" xml:space="preserve">quæ omnia ita demonſtrabuntur. </s>
            <s xml:id="echoid-s16350" xml:space="preserve">Per præcedentem, rectangulum ſub FC, dif-
              <lb/>
            ferentia exceſſuum, & </s>
            <s xml:id="echoid-s16351" xml:space="preserve">CE, minori exceſſu bis ſumptum, hoc eſt, rectangulum
              <lb/>
            FI, vna cum quadrato rectæ CE, bis etiam ſumpto, hoc eſt, vna cum quadrato
              <lb/>
            rectæ HE, vel CM, æquale eſt quadrato rectæ, qua minus latus quæſitum, mi-
              <lb/>
            norem exceſſum CE, ſuperat. </s>
            <s xml:id="echoid-s16352" xml:space="preserve">Cum ergo quadratum rectæ CL, æquale ſit re-
              <lb/>
            ctangulo FI, vt ex demonſtratione vltimæ propoſ. </s>
            <s xml:id="echoid-s16353" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16354" xml:space="preserve">2. </s>
            <s xml:id="echoid-s16355" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s16356" xml:space="preserve">conſtat; </s>
            <s xml:id="echoid-s16357" xml:space="preserve">erunt
              <lb/>
            quo que quadrata rectarum CL, CM, æqualia quadrato eiuſdem rectæ, qua mi-
              <lb/>
            nuslatus quæſitum ſuperat minorem exceſſum CE, Ac proinde cum
              <note symbol="a" position="left" xlink:label="note-378-01" xlink:href="note-378-01a" xml:space="preserve">47. primi.</note>
            tis rectarum CL, CM, ſit æquale quadratum rectæ LM: </s>
            <s xml:id="echoid-s16358" xml:space="preserve">erit quo que quadratum
              <lb/>
            rectæ LM, æquale quadrato rectæ, qua minus latus quæſitum minorem exceſ-
              <lb/>
            ſum CE, ſuperat. </s>
            <s xml:id="echoid-s16359" xml:space="preserve">Eſt ergo LM, exceſſus minoris lateris quæſiti ſupra minorem
              <lb/>
            exceſſum CE. </s>
            <s xml:id="echoid-s16360" xml:space="preserve">Ideo que recta ex LM, CE, conflata erit minus latus quæſitum:
              <lb/>
            </s>
            <s xml:id="echoid-s16361" xml:space="preserve">cui ſi addatur FC, differentia exceſſuum, fiet maius latus quæſitum: </s>
            <s xml:id="echoid-s16362" xml:space="preserve">cui ſi tan-
              <lb/>
            dem minor exceſſus C E, adijciatur, conflabitur diameter quæſita. </s>
            <s xml:id="echoid-s16363" xml:space="preserve">quæ omnia
              <lb/>
            demonſtranda erant.</s>
            <s xml:id="echoid-s16364" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1005" type="section" level="1" n="359">
          <head xml:id="echoid-head386" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s16365" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            recta LM, cuius quadratum æquale eſt rectangulo FI, ſub FC, dif-
              <lb/>
            ferentia exceſſuum, & </s>
            <s xml:id="echoid-s16366" xml:space="preserve">dupla minoris exceſſus CE, comprehenſo vna cum du-
              <lb/>
            plo quadrati exceſſus minoris CE, addita minori exceſſui CE, efficit minus latus
              <lb/>
            quæſitum, &</s>
            <s xml:id="echoid-s16367" xml:space="preserve">c.</s>
            <s xml:id="echoid-s16368" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16369" xml:space="preserve">
              <emph style="sc">Immo</emph>
            quia quadratum rectæ, CL, rectangulo FI, ſub FC, differentia exceſ-
              <lb/>
            ſuum, & </s>
            <s xml:id="echoid-s16370" xml:space="preserve">C K, duplo minoris exceſſus C E, comprehenſo æquale eſt, vt in de-
              <lb/>
            monſtratione dictum eſt; </s>
            <s xml:id="echoid-s16371" xml:space="preserve">& </s>
            <s xml:id="echoid-s16372" xml:space="preserve">rectangulum CP, duplum eſt quadrati exceſſus mi-
              <lb/>
            noris CE, hoc eſt, quadrato rectæ CM, æquale: </s>
            <s xml:id="echoid-s16373" xml:space="preserve">erit quadratũ rectæ LM, toti re-
              <lb/>
            ctãgulo FP, ſub maiori exceſſu FE, & </s>
            <s xml:id="echoid-s16374" xml:space="preserve">EP, dupla minoris exceſſus CE, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum