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
351 339
352 340
353 341
354 342
355 343
356 344
357 345
358 346
359 347
360 348
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
< >
page |< < (374) 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-div726" type="section" level="3" n="40">
              <div xml:id="echoid-div726" type="letter" level="4" n="1">
                <pb o="374" rhead="IO. BAPT. BENED." n="386" file="0386" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0386"/>
                <p>
                  <s xml:id="echoid-s4426" xml:space="preserve">At poterit aliquis mihi obijcere quod cum
                    <var>.i.o.</var>
                  fuiſſet longior
                    <var>.i.e.</var>
                  per decem vi-
                    <lb/>
                  ces tantummodo, exiſtente oculo in
                    <var>.e.</var>
                  uel
                    <var>.c.</var>
                  per gradus .90. ab
                    <var>.a</var>
                  . </s>
                  <s xml:id="echoid-s4427" xml:space="preserve">tunc punctus
                    <var>.u.</var>
                  vel
                    <lb/>
                  n. ab ipſo oculo non videretur ob terræ globoſitatem. </s>
                  <s xml:id="echoid-s4428" xml:space="preserve">Imaginemur igitur à puncto
                    <lb/>
                  u. recta
                    <var>.u.b.</var>
                  tangens quartam
                    <var>.a.e.</var>
                  in puncto
                    <var>.b.</var>
                  vt in ſecunda figura videre eſt, in qua
                    <lb/>
                  ducantur
                    <var>.c.b</var>
                  :
                    <var>i.b</var>
                  : et
                    <var>.i.u.</var>
                  quæ
                    <var>.i.u.</var>
                  ſecabit arcum
                    <var>.c.</var>
                    <lb/>
                    <figure xlink:label="fig-0386-01" xlink:href="fig-0386-01a" number="427">
                      <image file="0386-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0386-01"/>
                    </figure>
                  b. in puncto
                    <var>.p.</var>
                  per æqualia et
                    <var>.c.b.</var>
                  ſimiliter in pun-
                    <lb/>
                  cto
                    <var>.y.</var>
                  quod nulli dubium eſt, cum
                    <var>.c.u.</var>
                  æqualis ſit
                    <var>.
                      <lb/>
                    u.b.</var>
                  ex .35. tertij Euclidis, </s>
                  <s xml:id="echoid-s4429" xml:space="preserve">unde ex octaua primi an-
                    <lb/>
                  gulus
                    <var>.c.i.u.</var>
                  æqualis erit angulo
                    <var>.u.i.b.</var>
                  & ideo arcus
                    <var>.
                      <lb/>
                    c.p.</var>
                  æquabitur arcui
                    <var>.p.b.</var>
                  ſed ex .4. primi
                    <var>.c.y.</var>
                  æqua
                    <lb/>
                  lis erit ipſi
                    <var>.y.b</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4430" xml:space="preserve">Nunc ſuppoſita
                    <var>.c.i.</var>
                  decima parte ipſius
                    <var>.c.u.</var>
                  nemi
                    <lb/>
                  ni dubium erit quod cum
                    <var>.u.i.</var>
                  ſubtendatur angulo
                    <lb/>
                  recto
                    <var>.u.c.i.</var>
                  (iam ſupra diximus angulum
                    <var>.c.</var>
                  ſenſibi-
                    <lb/>
                  liter minime differre à recto) ipſa vt ſinus totus erit
                    <lb/>
                  partium .100000. cuius quadratum cum diuiſum
                    <lb/>
                  fuerit in partes æquales centum &
                    <reg norm="vnam" type="context">vnã</reg>
                  , illarum vna
                    <lb/>
                  æqualis erit quadrto
                    <var>.c.i.</var>
                  reliquę vero quadrato ip-
                    <lb/>
                  ſius
                    <var>.u.c.</var>
                  ex proportione duplicata quadratorum ad
                    <lb/>
                  eam quam continent eorum latera. </s>
                  <s xml:id="echoid-s4431" xml:space="preserve">Sed quadra-
                    <lb/>
                  tum ipſius
                    <var>.u.i.</var>
                  eſt partium .10000000000. </s>
                  <s xml:id="echoid-s4432" xml:space="preserve">quare
                    <lb/>
                  quadratum
                    <var>.c.i.</var>
                  erit .99009900. cuius radix
                    <var>.c.i.</var>
                    <lb/>
                  erit partium .9950. vnde quadratum ipſius
                    <var>.c.u.</var>
                  erit
                    <lb/>
                  partium .9900990100. cuius radix
                    <var>.u.c.</var>
                  erit
                    <reg norm="partium" type="context">partiũ</reg>
                    <lb/>
                  99500. vnde angulus
                    <var>.c.i.u.</var>
                  erit graduum .84. & mi
                    <lb/>
                  nu .17. & angulus
                    <var>.c.u.i.</var>
                  qui reſpondet ſinui
                    <var>.c.i.</var>
                  erit
                    <lb/>
                  gra .5. & min .43. cuius duplum, hoc eſt angulus
                    <var>.c.
                      <lb/>
                    u.b.</var>
                  erit grad .11. min .26. æqualis ferè angulo iam
                    <lb/>
                  ſupradicto. </s>
                  <s xml:id="echoid-s4433" xml:space="preserve">ſed
                    <var>.c.y.</var>
                  ſinus anguli
                    <var>.c.i.y.</var>
                  erit ſimiliter
                    <lb/>
                  partium .99500. talium vt
                    <var>.c.i.</var>
                  ſunt .100000. ſed vt
                    <lb/>
                    <var>c.i.</var>
                  eſt partium .9950. </s>
                  <s xml:id="echoid-s4434" xml:space="preserve">tunc
                    <var>.c.y.</var>
                  erit partium .9900
                    <lb/>
                  hoc eſt quaſi decima pars ipſius
                    <var>.c.u.</var>
                  </s>
                  <s xml:id="echoid-s4435" xml:space="preserve">quare ſi ocu-
                    <lb/>
                  lus in
                    <var>.e.</var>
                  non videbit punctum
                    <var>.u.</var>
                  hoc punctum be-
                    <lb/>
                  ne videbitur ab oculo in
                    <var>.b.</var>
                  abſque ſenſibili dimi-
                    <lb/>
                  nutione anguli in puncto
                    <var>.u.</var>
                  vt probauimus.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div730" type="section" level="3" n="41">
              <div xml:id="echoid-div730" type="letter" level="4" n="1">
                <head xml:id="echoid-head554" xml:space="preserve">DE MAGNITVDINIBVS FIGVRARVM
                  <lb/>
                iſoperimetrarum.</head>
                <head xml:id="echoid-head555" style="it" xml:space="preserve">Domino Ioanni Mariæ Agatio.</head>
                <p>
                  <s xml:id="echoid-s4436" xml:space="preserve">
                    <emph style="sc">QVamvis</emph>
                  à Theone ſupra Ptolomei Almageſtum ſufficienter traditum
                    <lb/>
                  ſit de magnitudinibus figurarum iſopetimetrarum, nihilominus vt tibi
                    <lb/>
                  morem geram, ea nunc ſcribo, quæ mihi in mentem venerunt contra
                    <lb/>
                    <reg norm="Alexandrum" type="context">Alexãdrum</reg>
                  Piccolhomineum,
                    <reg norm="antequam" type="context">antequã</reg>
                  aliquid ipſius Theonis vidiſſem </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>