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
301 289
302 290
303 291
304 292
305 293
306 294
307 295
308 296
309 297
310 298
311 299
312 300
313 301
314 302
315 303
316 304
317 305
318 306
319 307
320 308
321 309
322 310
323 311
324 312
325 313
326 314
327 315
328 316
329 317
330 318
< >
page |< < (306) of 445 > >|
IO. BAPT. BENED.
    <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-div591" type="section" level="3" n="22">
              <div xml:id="echoid-div594" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s3775" xml:space="preserve">
                    <pb o="306" rhead="IO. BAPT. BENED." n="318" file="0318" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0318"/>
                  ſcientia. </s>
                  <s xml:id="echoid-s3776" xml:space="preserve">Quare ex .9. quinti, ita erit
                    <var>.s.d.</var>
                  ad dictum
                    <var>.d.u.</var>
                  vt ad quadrilaterum
                    <var>.e.q.u.
                      <lb/>
                    x.</var>
                  hoc eſt vt
                    <var>.A.</var>
                  ad
                    <var>.B.</var>
                  ex .11. eiuſdem.</s>
                </p>
                <div xml:id="echoid-div594" type="float" level="5" n="1">
                  <figure xlink:label="fig-0317-01" xlink:href="fig-0317-01a">
                    <image file="0317-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0317-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s3777" xml:space="preserve">Sed ſi punctum
                    <var>.q.</var>
                  fuerit extra ut in .2. figura videre eſt. </s>
                  <s xml:id="echoid-s3778" xml:space="preserve">tunc manifeſtum erit,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  triangulus
                    <var>.e.x.t.</var>
                  maior erit pa-
                    <lb/>
                  rallelogrammo
                    <var>.d.u.</var>
                  per triangu
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0318-01a" xlink:href="fig-0318-01"/>
                  lum
                    <var>.q.t.u.</var>
                  cum triangulus
                    <var>.q.i.p.</var>
                    <lb/>
                  æqualis triangulo
                    <var>.d.i.e.</var>
                  excedat
                    <lb/>
                  quadrilaterum
                    <var>.i.t.u.p.</var>
                  per trian
                    <lb/>
                  gulum
                    <reg norm="dictum" type="context">dictũ</reg>
                    <var>.q.t.u.</var>
                  quapropter
                    <lb/>
                  cum diuiſus fuerit triangulus
                    <var>.e.
                      <lb/>
                    x.t.</var>
                  mediante linea
                    <var>.o.n.K.</var>
                  ita
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                    <reg norm="quadrilaterum" type="context">quadrilaterũ</reg>
                    <var>.e.n.K.t.</var>
                  ſit æquale
                    <lb/>
                  triangulo
                    <var>.q.t.u.</var>
                  ex doctrina præ
                    <lb/>
                  cedenti, habebimus propoſitum.</s>
                </p>
                <div xml:id="echoid-div595" type="float" level="5" n="2">
                  <figure xlink:label="fig-0318-01" xlink:href="fig-0318-01a">
                    <image file="0318-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0318-01"/>
                  </figure>
                </div>
              </div>
              <div xml:id="echoid-div597" type="letter" level="4" n="3">
                <head xml:id="echoid-head461" style="it" xml:space="preserve">Idem de frusto trianguli.</head>
                <head xml:id="echoid-head462" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3779" xml:space="preserve">SEd ſi quadrilaterum dictum eſſet fruſtum alicuius
                    <reg norm="trianguli" type="context">triãguli</reg>
                  ut in figura
                    <var>.A.</var>
                  hic ſub
                    <lb/>
                  ſcripta videre eſt, ſuppoſita,
                    <var>b.d.</var>
                  parallela ad
                    <var>.u.p.</var>
                  ita faciendum eſſet, ducendo
                    <lb/>
                  ſcilicet parallelam
                    <var>.u.x.</var>
                  ad
                    <var>.b.p.</var>
                  quæ producatur vſque ad concurſum cum
                    <var>.b.d.</var>
                    <lb/>
                  in puncto
                    <var>.x.</var>
                    <reg norm="ſitque" type="simple">ſitq́;</reg>
                  proportio data inter
                    <var>.t.a.</var>
                  et
                    <var>.a.e.</var>
                  quas duas lineas cogitemus inuicem
                    <lb/>
                  directè coniunctas, </s>
                  <s xml:id="echoid-s3780" xml:space="preserve">tunc diuidatur tota
                    <var>.t.e.</var>
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0318-02a" xlink:href="fig-0318-02"/>
                  in puncto
                    <var>.i.</var>
                  ita vt
                    <var>.t.i.</var>
                  ad
                    <var>.i.e.</var>
                  ſit vt quadrilate
                    <lb/>
                  ri
                    <var>.p.d.</var>
                  ad trigonum
                    <var>.u.d.x</var>
                  . </s>
                  <s xml:id="echoid-s3781" xml:space="preserve">deinde diuidatur
                    <lb/>
                    <var>t.i.</var>
                  in puncto r. tali modo vt
                    <var>.t.r.</var>
                  ad
                    <var>.r.i.</var>
                  ſe ha-
                    <lb/>
                  beat vt
                    <var>.t.a.</var>
                  ad
                    <var>.a.e.</var>
                  quo facto ex doctrina
                    <reg norm="prae­ cedenti" type="simple">prę­
                      <lb/>
                    cedenti</reg>
                  diuidatur totum parallelogram--
                    <lb/>
                  mum
                    <var>.p.x.</var>
                  mediante linea
                    <var>.o.q.</var>
                  ſecundum
                    <lb/>
                  quod ſe habet
                    <var>.t.r.</var>
                  ad
                    <var>.r.e</var>
                  . </s>
                  <s xml:id="echoid-s3782" xml:space="preserve">Atque ita ſolu-
                    <lb/>
                  tum erit problema, vt exte ipſo ratiotina-
                    <lb/>
                  ri facile potes.</s>
                </p>
                <div xml:id="echoid-div597" type="float" level="5" n="1">
                  <figure xlink:label="fig-0318-02" xlink:href="fig-0318-02a">
                    <image file="0318-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0318-02"/>
                  </figure>
                </div>
              </div>
              <div xml:id="echoid-div599" type="letter" level="4" n="4">
                <head xml:id="echoid-head463" style="it" xml:space="preserve">Fdem de quadrilatero in genere.</head>
                <head xml:id="echoid-head464" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3783" xml:space="preserve">SEd ſi nullum latus parallelum reliquo erit, ita faciendum erit. </s>
                  <s xml:id="echoid-s3784" xml:space="preserve">ſi ſit tale quadrila
                    <lb/>
                  terum
                    <var>.b.d.u.p.</var>
                  oportet vt ipſum conuertamus in triangulum, producendo duo
                    <lb/>
                  quęuis eius latera oppoſita uſque ad interſectionem ut pote
                    <var>.u.p.</var>
                  et
                    <var>.d.b.</var>
                  in puncto
                    <var>.x.</var>
                    <lb/>
                  quo facto, ſupponemus
                    <var>.o.</var>
                  eſſe punctum datum, proportio verò data ſit
                    <var>.t.r.</var>
                  ad
                    <var>.r.i.</var>
                  ad
                    <lb/>
                  iungatur deinde
                    <var>.i.e.</var>
                  ad
                    <var>.t.i.</var>
                  ad quam
                    <var>.e.i.</var>
                  ipſa
                    <var>.t.i.</var>
                  ſe habeat vt quadrilaterum
                    <var>.b.d.u.p.</var>
                  </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>