Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Page concordance

< >
Scan Original
321 309
322 310
323 311
324 312
325 313
326 314
327 315
328 316
329 317
330 318
331 319
332 320
333 321
334 322
335 323
336 324
337 325
338 326
339 327
340 328
341 329
342 330
343 331
344 332
345 333
346 334
347 335
348 336
349 337
350 338
< >
page |< < (314) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div606" type="section" level="3" n="23">
              <div xml:id="echoid-div610" type="letter" level="4" n="2">
                <pb o="314" rhead="IO. BABPT. BENED." n="326" file="0326" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0326"/>
              </div>
              <div xml:id="echoid-div611" type="letter" level="4" n="3">
                <head xml:id="echoid-head473" style="it" xml:space="preserve">Modus inueniendi duo triangula
                  <reg norm="varijs" type="lig">varijs</reg>
                conditionibus
                  <lb/>
                affecta.</head>
                <head xml:id="echoid-head474" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3861" xml:space="preserve">QVod etiam quæris ita ſe habet, duo ſcilicet triangula inuenire, æqualia dua-
                    <lb/>
                  bus ſuperficiebus rectilineis propoſitis, quę quidem triangula ſint eiuſdem
                    <lb/>
                  alritudinis, & quod
                    <reg norm="vnunquodque" type="context">vnũquodque</reg>
                  habeat angulum æqualem angulo pro
                    <unsure/>
                  poſito, &
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  alius angulus vnius, cum alio alterius, æquetur duobus rectis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3862" xml:space="preserve">Sint exempli gratia duæ propoſitæ ſuperflcies
                    <var>.c.y.</var>
                  duo verò anguli dati ſint
                    <var>.r.s.</var>
                    <lb/>
                  cum voluerimus inuenire duo triangula (quæ ſint
                    <var>.a.i.u.</var>
                  et
                    <var>.n.t.x.</var>
                  ) tali conditio-
                    <lb/>
                  ne prædita, quod angulus, a. æqualis ſit angulo
                    <var>.s.</var>
                  & angulus
                    <var>.t.</var>
                  angulo
                    <var>.r.</var>
                  & quod
                    <lb/>
                  angulus
                    <var>.x.</var>
                  ſimul cum angulo
                    <var>.u.</var>
                    <reg norm="æ- quentur" type="context">æ-
                      <lb/>
                    quẽtur</reg>
                  duobus rectis, & quod
                    <reg norm="triam" type="context">triã</reg>
                    <lb/>
                    <figure xlink:label="fig-0326-01" xlink:href="fig-0326-01a" number="349">
                      <image file="0326-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0326-01"/>
                    </figure>
                    <reg norm="gulum" type="context">gulũ</reg>
                    <var>.a.i.u.</var>
                  æquale ſit ſuperficiei
                    <var>.
                      <lb/>
                    c.</var>
                  reliquum verò ſuperficiei
                    <var>.y.</var>
                    <lb/>
                  Ex duabus ſuperficiebus
                    <var>.c.</var>
                  et
                    <var>.y.</var>
                    <lb/>
                  conſtituemus duo quadrata, per vl
                    <lb/>
                  timam ſecundi Eucli. accipiemus,
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3863" xml:space="preserve">deinde duo latera tetragonica ip-
                    <lb/>
                  ſorum quadratorum, & inuenie-
                    <lb/>
                  mus tertiam lineam in continua
                    <lb/>
                  proportionalitate cum illis lateri-
                    <lb/>
                  bus ex .10. ſexti, ſeruabimus po-
                    <lb/>
                  ſtea extremas illarum, quæ ſint
                    <var>.z.</var>
                    <lb/>
                  et
                    <var>.l.</var>
                  quarum proportio,
                    <reg norm="eadem" type="context">eadẽ</reg>
                  erit,
                    <lb/>
                  quæ inter duas propoſitas ſuperfi-
                    <lb/>
                  cies reperitur ex .18. ſexti, accipie
                    <lb/>
                  mus, deinde lineam aliquam cu-
                    <lb/>
                  inſuis longitudinis, quæ ſit
                    <var>.q.g.</var>
                  ſu-
                    <lb/>
                  pra quam conſtituemus in puncto
                    <lb/>
                  q. angulum
                    <var>.m.q.g.</var>
                  ęqualem angu-
                    <lb/>
                  lo
                    <var>.s.</var>
                  & angulum
                    <var>.m.q.K.</var>
                  æqualem
                    <lb/>
                  angulo
                    <var>.r.</var>
                  ex .23. primi, poſtea ve-
                    <lb/>
                  rò à quouis puncto ipſius lineæ
                    <var>.q.
                      <lb/>
                    m.</var>
                  puta
                    <var>.o.</var>
                  ducetur
                    <var>.o.f.</var>
                  vſque ad
                    <var>.q.
                      <lb/>
                    g.</var>
                  quorſum volueris, producendo
                    <lb/>
                  ipſam
                    <reg norm="vſque" type="simple">vſq;</reg>
                  . ad
                    <var>.d.</var>
                  ita quod propor-
                    <lb/>
                  tio
                    <var>f.o.</var>
                  ad
                    <var>.o.d.</var>
                  ſit vt
                    <var>.z.</var>
                  ad
                    <var>.l.</var>
                  ex .10.
                    <lb/>
                  ſexti, ducendo poſtea à puncto
                    <var>.d.</var>
                    <lb/>
                  lineam
                    <var>.d.h.E.</var>
                  parallelam lineæ
                    <var>.q.
                      <lb/>
                    g.</var>
                  & quia ex .2. primi Vitellionis
                    <var>.
                      <lb/>
                    h.E.</var>
                  ſecatur ab
                    <var>.q.K.</var>
                  in puncto
                    <var>.b.</var>
                    <lb/>
                  protrahemus
                    <var>.b.o.p.</var>
                  vnde ex ſimi-
                    <lb/>
                  litudine triangulorum habebimus
                    <lb/>
                  proportionem
                    <var>.p.o.</var>
                  ad
                    <var>.o.b.</var>
                  vt
                    <var>.f.o.</var>
                  </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum