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
361 349
362 350
363 351
364 352
365 353
366 354
367 355
368 356
369 357
370 358
371 359
372 360
373 361
374 362
375 363
376 364
377 365
378 366
379 367
380 368
381 369
382 370
383 371
384 372
385 373
386 374
387 375
388 376
389 377
390 378
< >
page |< < (358) 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-div690" type="section" level="3" n="32">
              <div xml:id="echoid-div690" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4293" xml:space="preserve">
                    <pb o="358" rhead="IO. BAPT. BENED." n="370" file="0370" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0370"/>
                  ſecunda definitione eiuſdem libr
                    <var>.a.m.l.</var>
                  efficiet angulos rectos cum duabus
                    <var>.b.c.</var>
                  et
                    <var>.K.
                      <lb/>
                    i.</var>
                  in punctis
                    <var>.m.</var>
                  et
                    <var>.l.</var>
                  et
                    <var>.k.i.</var>
                  parallela erit ipſi
                    <var>.b.c.</var>
                  ex .28. primi, quod etiam poteſt con
                    <lb/>
                  cludi mediante .16. vndecimi, cum
                    <var>.k.i.</var>
                  et
                    <var>.b.c.</var>
                  ſint communes ſectiones duorum pla
                    <lb/>
                  norum cum triangulari. </s>
                  <s xml:id="echoid-s4294" xml:space="preserve">Deinde ex .29. primi anguli
                    <var>.a.i.m.</var>
                  et
                    <var>.a.c.l.</var>
                  erunt inuicem
                    <lb/>
                  æquales, idem etiam dico de angulis
                    <var>.a.k.i.</var>
                  et
                    <var>.a.b.c.</var>
                  anguli poſtea ad
                    <var>.a.</var>
                  communes
                    <lb/>
                  ſunt triangulis
                    <var>.l.a.c.</var>
                  et
                    <var>.m.a.i.</var>
                  vt triangulis
                    <var>.l.a.b.</var>
                  et
                    <var>.m.a.k</var>
                  . </s>
                  <s xml:id="echoid-s4295" xml:space="preserve">Vnde ex .4. ſexti, eadem
                    <lb/>
                  proportio erit ipſius
                    <var>.m.i.</var>
                  ad
                    <var>.l.c.</var>
                  & ipſius
                    <var>.m.k.</var>
                  ad
                    <var>.l.b.</var>
                  vt ipſius
                    <var>.a.m.</var>
                  ad
                    <var>.a.l</var>
                  . </s>
                  <s xml:id="echoid-s4296" xml:space="preserve">Quare ex
                    <lb/>
                  vndecima quinti, ita erit ipſius
                    <var>.m.k.</var>
                  ad
                    <var>.l.b.</var>
                  vt ipſius
                    <var>.m.i.</var>
                  ad
                    <var>.l.c.</var>
                  & ex .13. eiuſdem, ita
                    <lb/>
                  erit ipſius
                    <var>.k.i.</var>
                  ad
                    <var>.b.c.</var>
                  vt
                    <var>.m.i.</var>
                  ad
                    <var>.l.c.</var>
                  ſed ipſius
                    <var>.m.i.</var>
                  ad
                    <var>.l.c.</var>
                  eſt vt ipſius
                    <var>.a.m.</var>
                  ad
                    <var>.a.l.</var>
                  quod
                    <lb/>
                  iam dictum eſt, vnde ex .11. dicta, ita erit ipſius
                    <var>.k.i.</var>
                  ad
                    <var>.b.c.</var>
                  vt ipſius
                    <var>.a.m.</var>
                  ad
                    <var>.a.l.</var>
                  & ex
                    <lb/>
                  16. dicti ita erit ipſius
                    <var>.a.m.</var>
                  ad
                    <var>.k.i.</var>
                  vt ipſius
                    <var>.a.l.</var>
                  ad
                    <var>.b.c</var>
                  . </s>
                  <s xml:id="echoid-s4297" xml:space="preserve">Quare ex definitione ab Eu-
                    <lb/>
                  cli. poſita in .11, lib. pars coni ſuperior ſimilis erit cono totali.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4298" xml:space="preserve">Deinde ſciendum eſt illud quod Euclid. ſcribit in .10. duodecimi lib. hoc eſt,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  proportio duarum pyramidum inuicem
                    <lb/>
                  ſimilium, triplicata eſt ei diametrorum
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0370-01a" xlink:href="fig-0370-01"/>
                  ſuarum baſium, hoc eſt, quod proportio
                    <var>.
                      <lb/>
                    b.c.</var>
                  ad
                    <var>.k.i.</var>
                  tertia pars erit proportionis to
                    <lb/>
                  tius pyramidis
                    <var>.a.b.c.</var>
                  partiali pyramidi
                    <var>.a.
                      <lb/>
                    k.i.</var>
                  ſed ita eſt ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.i.</var>
                  vt ipſius
                    <var>.b.
                      <lb/>
                    c.</var>
                  ad
                    <var>.k.i.</var>
                  ex .4. ſexti cum trianguli
                    <var>.a.b.c.</var>
                    <lb/>
                  et
                    <var>.a.k.i.</var>
                  ſint æquianguli, quod ex ijs, quę
                    <lb/>
                  ſuperius diximus facile compręhenditur.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4299" xml:space="preserve">Quare
                    <reg norm="proportio" type="simple">ꝓportio</reg>
                    <var>.a.c.</var>
                  ad
                    <var>.a.i.</var>
                  tertia pars erit
                    <lb/>
                  proportionis totius coni
                    <var>.a.b.c.</var>
                  ad eius par
                    <lb/>
                  tem abſciſſam
                    <var>.a.k.i.</var>
                  ſed eadem proportio
                    <lb/>
                  ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.i.</var>
                  erat etiam tertia pars pro
                    <lb/>
                  portionis ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.d</var>
                  . </s>
                  <s xml:id="echoid-s4300" xml:space="preserve">Quare ex com
                    <lb/>
                  muni conceptu, proportio totius pyramidis, ad partem abſciſſam, æqualis erit pro-
                    <lb/>
                  portioni ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.d</var>
                  .</s>
                </p>
                <div xml:id="echoid-div691" type="float" level="5" n="2">
                  <figure xlink:label="fig-0370-01" xlink:href="fig-0370-01a">
                    <image file="0370-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0370-01"/>
                  </figure>
                </div>
              </div>
              <div xml:id="echoid-div693" type="letter" level="4" n="2">
                <head xml:id="echoid-head526" style="it" xml:space="preserve">De differentia caloris Solis propter vaporum
                  <unsure/>
                  <lb/>
                altitudinem.</head>
                <head xml:id="echoid-head527" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4301" xml:space="preserve">NOlo, mihi credas, ſed ex rationibus, quas tibi ſcribo conſidera, quod quo
                    <lb/>
                    <reg norm="tieſcunque" type="simple">tieſcunq;</reg>
                  craſſities vel
                    <reg norm="denſitas" type="context">dẽſitas</reg>
                    <reg norm="vaporum" type="context">vaporũ</reg>
                  , ſeu altitudo, maior eſſet ea, quę nunc re-
                    <lb/>
                  peritur, </s>
                  <s xml:id="echoid-s4302" xml:space="preserve">tunc minor differentia eſſet inter maiorem
                    <reg norm="minoremque" type="simple">minoremq́;</reg>
                  calorem Solis, quam
                    <lb/>
                  nunc ſentiamus. </s>
                  <s xml:id="echoid-s4303" xml:space="preserve">Pro cuius rei euidentia, imaginemur in hac ſubſcripta figura, li-
                    <lb/>
                  neam
                    <var>.o.a.</var>
                  pro ſemidiametro terræ, et
                    <var>.a.c.</var>
                  pro craſſitie vaporum, vt nunc ſe
                    <lb/>
                  habet, et
                    <var>.a.d.</var>
                  pro maiori craſſitie, imaginemurq́ue lineam
                    <var>.a.b.</var>
                  quaſi perpen-
                    <lb/>
                  dicularem ad
                    <var>.o.a.</var>
                  quæ abſciſſa ſit in puncto u. à circunferentia
                    <var>.c.u.</var>
                  inferiori prio-
                    <lb/>
                  rum vaporum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4304" xml:space="preserve">Tunc dico minorem eſſe proportionem ipſius
                    <var>.a.b.</var>
                  ad
                    <var>.a.d.</var>
                  quam ipſius
                    <var>.a.u.</var>
                  ad
                    <var>.a.
                      <lb/>
                    c.</var>
                  cogitemus ergo protractas eſſe lineas
                    <var>.o.b</var>
                  :
                    <var>d.b</var>
                  :
                    <var>c.u.</var>
                  et
                    <var>.c.n.</var>
                  quæ
                    <var>.c.n.</var>
                  ſecabit
                    <var>.a.u.</var>
                  in </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>