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 |< < (390) 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-div737" type="section" level="3" n="42">
              <div xml:id="echoid-div737" type="letter" level="4" n="1">
                <p>
                  <pb o="390" rhead="IO. BAPT. BENED." n="402" file="0402" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0402"/>
                  <s xml:id="echoid-s4626" xml:space="preserve">Vbiautem ſcriptum eſt
                    <lb/>
                    <q open="" close="">ad vtrunque ſimul
                      <var>.b.d</var>
                    :
                      <var>d.a.</var>
                    cum dupla
                      <var>.b.c.</var>
                    </q>
                    <lb/>
                  dicendum eſt ita,
                    <lb/>
                  ad vtranque ſimul
                    <var>.b.d.b.a.</var>
                  cum dupla
                    <var>.b.c</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4627" xml:space="preserve">Inquit deinde Archi. quod ſicut ſe haber
                    <var>.e.a.</var>
                  ad
                    <var>.d.a.</var>
                  ita ſe habebit duplum
                    <var>.M.N.</var>
                    <lb/>
                  ad duplum
                    <var>.N</var>
                  . </s>
                  <s xml:id="echoid-s4628" xml:space="preserve">Quod quidem verum eſt ex .13. quinti, huiuſmodi verò antecedons
                    <lb/>
                  & conſequens, Archi. manifeſtat ex ſuis partibus, ſumendo duplum
                    <var>.e.b.</var>
                  cum duplo
                    <lb/>
                    <var>b.d.</var>
                  pro duplo
                    <var>.M.</var>
                  & duplum
                    <var>.b.d.</var>
                  cum duplo
                    <var>.a.b.</var>
                  cum quadruplo
                    <var>.b.c.</var>
                  pro duplo
                    <var>.N.</var>
                    <lb/>
                  quę ſimul iuncta æquantur duplo
                    <var>.e.b.</var>
                  cum duplo
                    <var>.a.b.</var>
                  cum quadruplo
                    <var>.b.d.</var>
                  cum qua-
                    <lb/>
                  druplo
                    <var>.b.c.</var>
                  ex quo æquabuntur
                    <var>.A.</var>
                  vocentur igitur hæc omnia
                    <var>.A.</var>
                  potius quàm du-
                    <lb/>
                  plum ipſius
                    <var>.M.N</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4629" xml:space="preserve">Verum etiam ſcribit, vbi dicit, quod proportio
                    <var>.e.a.</var>
                  ad tres quintas ipſius
                    <var>.a.d.</var>
                  erit
                    <lb/>
                  vt
                    <var>.A.</var>
                  ad tres quintas dupli
                    <var>.N.</var>
                  ex .22. quinti. </s>
                  <s xml:id="echoid-s4630" xml:space="preserve">Sed cum ex ſuppoſito ita ſe habeat
                    <var>.f.
                      <lb/>
                    g.</var>
                  ad tres quintas ipſius
                    <var>.a.d.</var>
                  quemadmodum
                    <var>.b.e.</var>
                  ad
                    <var>.e.a.</var>
                  erit ex .16. quinti verum
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  dicit Archimed. </s>
                  <s xml:id="echoid-s4631" xml:space="preserve">hoc eſt, ita ſe habere
                    <var>.b.e.</var>
                  ad
                    <var>.f.g.</var>
                  vt
                    <var>.e.a.</var>
                  ad tres quintas ipſius
                    <var>.a.d</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4632" xml:space="preserve">Et per .11. eiuſdem verum etiam erit quod ſicut ſe habet
                    <var>.e.b.</var>
                  ad
                    <var>.f.g.</var>
                  ita ſe habe-
                    <lb/>
                  bit
                    <var>.A.</var>
                  ad tres quintas dupli
                    <var>.N.</var>
                  quod quidem duplum
                    <var>.N.</var>
                  ſignificetur per
                    <var>.Q</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4633" xml:space="preserve">Sed ſuperius iam demonſtratum fuit (vbi
                    <var>.X.</var>
                  ) quod
                    <var>.o.b.</var>
                  ad
                    <var>.b.e.</var>
                  ita ſe habebat vt
                    <lb/>
                    <var>H.A.</var>
                  ad
                    <var>.A.</var>
                  &
                    <reg norm="nunc" type="context">nũc</reg>
                  demum probatum fuit ita eſſe
                    <var>.A.</var>
                  ad tres quintas ipſius
                    <var>.Q.</var>
                  vt
                    <var>.e.b.</var>
                    <lb/>
                  ad
                    <var>.f.g</var>
                  . </s>
                  <s xml:id="echoid-s4634" xml:space="preserve">Quare ex .22. quinti ita erit
                    <var>.H.A.</var>
                  ad tres quintas ipſius
                    <var>.Q.</var>
                  vt
                    <var>.o.b.</var>
                  ad
                    <var>.f.g.</var>
                  vt
                    <lb/>
                    <note xlink:label="note-0402-01" xlink:href="note-0402-01a" position="left" xml:space="preserve">Y</note>
                  idem inquit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4635" xml:space="preserve">Sed
                    <var>.H.A.</var>
                  ad
                    <var>.Q.</var>
                  (vt ex ſuis partibus videre eſt) ita ſe habet vt tres ad duo ex .13.
                    <lb/>
                  quinti, vt inquit Archimedes.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4636" xml:space="preserve">Ipſe etiam dicit proportionem
                    <var>.H.A.</var>
                  ad tres quintas ipſius
                    <var>.Q.</var>
                  eſſe vt quinque
                    <lb/>
                  ad duo. </s>
                  <s xml:id="echoid-s4637" xml:space="preserve">Pro cuius rei euidentia imaginemur tam
                    <var>.H.A.</var>
                  quam
                    <var>.Q.</var>
                  diuiſa per
                    <reg norm="quinque" type="simple">quinq;</reg>
                    <lb/>
                  partes æquales, vnde ex .16. quinti habebimus quamlibet quintam
                    <reg norm="partem" type="context">partẽ</reg>
                  ipſius
                    <var>.Q.</var>
                    <lb/>
                    <reg norm="æqualem" type="context">æqualẽ</reg>
                  eſſe duabus tertijs vniuſcuiuſque quintæ partis
                    <var>.H.A.</var>
                  vnde tres quintæ ipſius
                    <lb/>
                  Q. erunt, ex communi conceptu, ſex tertiæ vnius quintæ ipſius
                    <var>.H.A.</var>
                  hoc eſt duæ
                    <lb/>
                  quintæ. ipſius
                    <var>.H.A</var>
                  . </s>
                  <s xml:id="echoid-s4638" xml:space="preserve">Quare
                    <var>.o.b.</var>
                  ita ſe habebit ad
                    <var>.f.g.</var>
                  vt quinque ad duo ex commu
                    <lb/>
                  ni
                    <reg norm="conceptu" type="context">cõceptu</reg>
                  , cum
                    <var>.o.b.</var>
                  ad
                    <var>.f.g.</var>
                  probatum fuerit ſe habere vt
                    <var>.H.A.</var>
                  ad tres quintas ipſius
                    <lb/>
                  Q. (vbi
                    <var>.Y.</var>
                  ) ſed iam probatum fuit (vbi. ω) quod
                    <var>.o.a.</var>
                  ad
                    <var>.h.g.</var>
                  erat etiam vt
                    <lb/>
                  quinque ad duo, hoc eſt quod
                    <var>.f.h.</var>
                  erit duæ quintę ipſius
                    <var>.a.b</var>
                  . </s>
                  <s xml:id="echoid-s4639" xml:space="preserve">Quod eſt propoſitum.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>