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
341 329
342 330
343 331
344 332
345 333
346 334
347 335
348 336
349 337
350 338
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
< >
page |< < (342) 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-div642" type="section" level="3" n="28">
              <div xml:id="echoid-div657" type="letter" level="4" n="5">
                <pb o="342" rhead="IO. BAPT. BENED." n="354" file="0354" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0354"/>
                <p>
                  <s xml:id="echoid-s4152" xml:space="preserve">Alia etiam via poſſumus idem concludere. </s>
                  <s xml:id="echoid-s4153" xml:space="preserve">Imaginemur maiorem axem alicu-
                    <lb/>
                  ius ellipſis tranſire per duo puncta
                    <var>.r.</var>
                  et
                    <var>.b.</var>
                  ſupponendo ipſa puncta, ea eſle, quæ ita
                    <lb/>
                  axem diuidunt, vt ſingula produ-
                    <lb/>
                    <figure xlink:label="fig-0354-01" xlink:href="fig-0354-01a" number="385">
                      <image file="0354-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0354-01"/>
                    </figure>
                  cta fectionum ſint, vt inquit Per-
                    <lb/>
                  geus. </s>
                  <s xml:id="echoid-s4154" xml:space="preserve">imaginemur, etiam
                    <var>.p.h.</var>
                  con
                    <lb/>
                  tiguam eſſe ipſi ellipſi in
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.a.</var>
                    <lb/>
                  vnde ſi protractæ fuerint duæ
                    <var>.r.a.</var>
                    <lb/>
                  et
                    <var>.b.a.</var>
                  habebimus ex .48. tertijip-
                    <lb/>
                  ſius Pergei angulos
                    <var>.b.a.h.</var>
                  et
                    <var>.r.a.
                      <lb/>
                    p.</var>
                  inuicem æquales. </s>
                  <s xml:id="echoid-s4155" xml:space="preserve">Ducendo
                    <lb/>
                  poſtea ad quoduis punctum ipſius
                    <lb/>
                    <var>p.h.</var>
                  duas
                    <var>.b.o.</var>
                  et
                    <var>.r.o.</var>
                  certi erimus,
                    <lb/>
                  quod ſecabuntur à gyro oxygo-
                    <lb/>
                  nio, quarum vna ſecta ſit in pun-
                    <lb/>
                  cto
                    <var>.i.</var>
                  ducta poſtea
                    <var>.i.r.</var>
                  clarum erit ex .52. dicti, quod longitudo
                    <var>.b.i.r.</var>
                  æqualis erit lon
                    <lb/>
                  gitudini
                    <var>.b.a.r.</var>
                  & minor ipſa
                    <var>.b.o.r.</var>
                  ex .21. primi Euclid.</s>
                </p>
              </div>
              <div xml:id="echoid-div660" type="letter" level="4" n="6">
                <head xml:id="echoid-head505" style="it" xml:space="preserve">Deerrore Euclidis circa ſpeculum vstorium.</head>
                <head xml:id="echoid-head506" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4156" xml:space="preserve">VErum ſpeculum vſtorium, illud non eſt, quod ab Euclide traditum fuit, &
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  tu etiam putas, Nam Euclides errat, cum credat radios reflexos à ſuperficie
                    <lb/>
                  ſphærica concaua ſeinuicem in centro ſpeculi interſecare. </s>
                  <s xml:id="echoid-s4157" xml:space="preserve">Nam cum omnes lineę
                    <lb/>
                  recte à centro, & cir cunferentia alicuius ſphæræ terminatæ, ſint eidem circunferen-
                    <lb/>
                  tiæ perpendiculares, ſequeretur ex neceſſitate radios incidentiæ etiam perpendicu
                    <lb/>
                  lares eidem ſuperficiei eſſe, cum anguli incidentiæ ſemper æquales ſint angulis re-
                    <lb/>
                  flexionis, vnde etiam ex neceſſitate ſequeretur punctum corporis lucidi, à quo radij
                    <lb/>
                  luminoſi excunt, in centro ſpeculi reperiri. </s>
                  <s xml:id="echoid-s4158" xml:space="preserve">quod quidem falſiſſimum eſt.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4159" xml:space="preserve">Alia etiam via poſſum hanc oſtendere impoſſibilitatem, & tibi probabo, quod
                    <lb/>
                  in nullo aliquo puncto poſſunt inuicem conuenire ipſi radijrefle xi omnes.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4160" xml:space="preserve">Sit igitur
                    <var>.l.a.c.</var>
                    <reg norm="conis" type="context">cõis</reg>
                  ſectio ſuperficiei reflexionis cum ſpeculo, cuius centrum ſit
                    <var>.o.</var>
                    <lb/>
                  punctum verò lucidum ſit
                    <var>.g.</var>
                    <reg norm="protrahaturque" type="simple">protrahaturq́</reg>
                    <var>.g.o.a</var>
                  . </s>
                  <s xml:id="echoid-s4161" xml:space="preserve">Nunc autem primum dico, quod
                    <lb/>
                  radij reflexi à punctis diuerſarum
                    <reg norm="diſtantiarum" type="context">diſtantiarũ</reg>
                  ab
                    <var>.a.</var>
                  non
                    <reg norm="coincident" type="context">coincidẽt</reg>
                  inuicem in aliquo
                    <lb/>
                  puncto lineę
                    <var>.g.o.a</var>
                  : ſint ergo duo puncta
                    <var>.u.</var>
                  et
                    <var>.r.</var>
                  diuerſarum
                    <reg norm="diſtantiarum" type="context">diſtantiarũ</reg>
                  ab
                    <var>.a.</var>
                  à quibus
                    <lb/>
                  veniant duo radij incidentiæ
                    <var>.g.r.</var>
                  et
                    <var>.g.u.</var>
                  radius verò reflexus ab
                    <var>.r.</var>
                  ſit
                    <var>.r.e.</var>
                  protrahatur
                    <lb/>
                    <var>u.e.</var>
                  quam dico effe non poſſe radium reflexum ab
                    <var>.u.</var>
                  quotieſcunque eius incidens
                    <lb/>
                  deſcendat ab
                    <var>.g</var>
                  . </s>
                  <s xml:id="echoid-s4162" xml:space="preserve">Protrahantur ergo duæ lineæ
                    <var>.o.r.</var>
                  et
                    <var>.o.u.</var>
                  vnde cum dixerit aliquis
                    <lb/>
                    <var>u.e.</var>
                    <reg norm="reflexum" type="context">reflexũ</reg>
                  eſſe ipſius
                    <var>.g.u.</var>
                  igitur anguli
                    <var>.g.u.o.</var>
                  et
                    <var>.o.u.e.</var>
                  erunt inuicem æquales, & ſic
                    <lb/>
                  etiam erunt duo
                    <var>.g.r.o.</var>
                  et
                    <var>.o.r.e.</var>
                  vnde ex tertia ſexti & .11. quinti Eucli. proportio
                    <var>.g.
                      <lb/>
                    u.</var>
                  ad
                    <var>.u.e.</var>
                  æqualis eſſet ei, quæ
                    <var>.g.r.</var>
                  ad
                    <var>.r.e.</var>
                  quod quidem impoſſibile eſſe demonſtra-
                    <lb/>
                  bo, eo quod cum
                    <var>.g.u.</var>
                  maior ſit
                    <var>.g.r.</var>
                  ex .8. tertij, erit ex .8. quinti proportio ipſius
                    <var>.g.u.</var>
                    <lb/>
                  ad
                    <var>.r.e.</var>
                  maior proportione ipſius
                    <var>.g.r.</var>
                  ad
                    <var>.r.e.</var>
                  ſed ex .7. tertij
                    <var>.u.e.</var>
                  minor eſt
                    <var>.r.e.</var>
                  erit igi-
                    <lb/>
                  tur ex dicta .8. quinti maior proportio
                    <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                    <var>.g.u.</var>
                  ad
                    <var>.u.e.</var>
                  quam
                    <var>.g.u.</var>
                  ad
                    <var>.r.e.</var>
                  vnde eo ma­ </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum