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
321 309
322 310
323 311
324 312
325 313
326 314
327 315
328 316
329 317
330 318
331 319
332 320
333 321
334 322
335 323
336 324
337 325
338 326
339 327
340 328
341 329
342 330
343 331
344 332
345 333
346 334
347 335
348 336
349 337
350 338
< >
page |< < (335) 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-div650" type="letter" level="4" n="3">
                <pb o="335" rhead="EPISTOLAE." n="347" file="0347" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0347"/>
                <p>
                  <s xml:id="echoid-s4064" xml:space="preserve">Nam circa æqualitatem angulorum reflexionis & incidentiæ, iam tibi probaui
                    <lb/>
                  illud non vniuerſaliter euenire à breuitate aggregati radiorum incidentiæ reflexio-
                    <lb/>
                    <reg norm="nisque" type="simple">nisq́;</reg>
                  . </s>
                  <s xml:id="echoid-s4065" xml:space="preserve">Sed hoc naſcitur potius ab eo, quod cum radius incidentiæ non poſſit ſuper
                    <lb/>
                  ficiem corporis opaci penetrare, reflectit, vt citra ipſam
                    <reg norm="cum" type="context">cũ</reg>
                  angulo æquali ei, quem
                    <lb/>
                  faceret cum eadem ſuperficie vltra ipſam ſi tranſiuiſſet.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4066" xml:space="preserve">Exempli gratia ſit
                    <var>.a.</var>
                  obiectum
                    <var>.b.</var>
                    <reg norm="autem" type="context">autẽ</reg>
                  oculus in figura
                    <var>.A.</var>
                  et
                    <var>.c.e.</var>
                  ſuperficies ipſius
                    <lb/>
                  ſpeculi
                    <var>.d.</var>
                  verò ſit punctum ipſius ſuperficiei, à quo ad oculum reflectitur imago ip-
                    <lb/>
                    <figure xlink:label="fig-0347-01" xlink:href="fig-0347-01a" number="374">
                      <image file="0347-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0347-01"/>
                    </figure>
                  ſius
                    <var>.a</var>
                  . </s>
                  <s xml:id="echoid-s4067" xml:space="preserve">Nunc ſi radius
                    <var>.a.d.</var>
                  incidentiæ, recta
                    <lb/>
                  incederet ſub
                    <var>.c.e.</var>
                  efficeret angulum
                    <var>.e.d.h.</var>
                    <lb/>
                  æqualem angulo
                    <var>.c.d.a.</var>
                  eius contrapoſito,
                    <lb/>
                  ſed quia impeditur ipſæ radius ab opacitate
                    <lb/>
                  ipſius ſpeculi
                    <var>.c.e.</var>
                  ne vlterius incedat, propte
                    <lb/>
                  rea reflectitur ab ipſa ſuperficie ſpeculi, con-
                    <lb/>
                  ſtituens cum ipſa angulum
                    <var>.e.d.b.</var>
                  æqualem
                    <lb/>
                  angulo
                    <var>.e.d.h.</var>
                  ſed quia angulus
                    <var>.c.d.a.</var>
                  eſt
                    <reg norm="etiam" type="context">etiã</reg>
                    <lb/>
                  ęqualis ipſi angulo
                    <var>.e.d.h.</var>
                  propterea angulus
                    <var>.e.d.b.</var>
                  ęqualis exiſtit angulo
                    <var>.c.d.</var>
                  a; </s>
                  <s xml:id="echoid-s4068" xml:space="preserve">per
                    <lb/>
                  accidens igitur ſequitur
                    <var>.a.d.</var>
                  et
                    <var>.d.b.</var>
                  ſimul ſumptas, breuiorem facere longiludinem
                    <lb/>
                  omni alia, quæ ab ipſa ſuperficie
                    <var>.c.e.</var>
                  ad eadem puncta
                    <var>.a.b.</var>
                  ducta eſſet, </s>
                  <s xml:id="echoid-s4069" xml:space="preserve">quare natu-
                    <lb/>
                  ræintentio eſt efficere angulum
                    <var>.e.d.b.</var>
                  æqualem angulo
                    <var>.e.d.h.</var>
                  vnde ex accidenti po
                    <lb/>
                  ſtea ſequitur, ipſum æqualem eſſe angulo
                    <var>.c.d.a.</var>
                  & deinde
                    <reg norm="quod" type="wordlist">qđ</reg>
                  lineæ
                    <var>.a.d.</var>
                  et
                    <var>.d.b.</var>
                  con-
                    <lb/>
                  ſtituant longitudinem breuiorem. </s>
                  <s xml:id="echoid-s4070" xml:space="preserve">Quare illud quod omnes putabant eſſe primum
                    <lb/>
                  & perſe, vltimum eſt, & exaccidenti.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4071" xml:space="preserve">Quare vero ſuperficies, quæ vocatur reflexionis, in qua ſunt duæ lineę, hoc eſt
                    <lb/>
                  incidentię,
                    <reg norm="reflexionisque" type="simple">reflexionisq́;</reg>
                  , ſemper ſit perpendicularis ſuperficiei ipſius ſpeculi: </s>
                  <s xml:id="echoid-s4072" xml:space="preserve">Hæc
                    <lb/>
                  eſt ratio, quia cum quilibet radius incidentiæ, perpendicularis ipſi ſuperficiei ſpe-
                    <lb/>
                  culi, in ſeipſo reflectit, ex ijſdem dictis rationibus, hoc eſt, quia cum tali angulo vult
                    <lb/>
                  reflecti, cum quali tranſiret, ita etiam purandum eſt, quodradius incidens obliquus,
                    <lb/>
                  cum in ſeipſum non poſſit redire, quia non eſt perpendicularis ſuperficiei ſpeculi,
                    <lb/>
                  reflectitur tamen per planum erectum ipſi ſuperficiei ſpeculi, vt in eo, cui magis re-
                    <lb/>
                  ſiſtit ſuperficies corporis opaci, quàm alicui alij plano ipſius infiniti inclinatorum
                    <lb/>
                  planorum, ab vtraque parte ipſius plani perpendicularis, quod vnum etiam tan-
                    <lb/>
                  tummodo eſt, & in quo, radius maiorem vim obtinet reflectendi, ſeu in eo, in quo
                    <lb/>
                  radius ipſe cum maiori reſiſtentia repercutitur à ſuperficie corporis opaci.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4073" xml:space="preserve">Poſtremo
                    <reg norm="ſciendum" type="context context">ſciẽdũ</reg>
                  vnde oriatur,
                    <reg norm="quod" type="simple">ꝙ</reg>
                  rei viſibilis imago, à ſpeculo plano reflexa, ſem
                    <lb/>
                  per in catheto incidentiæ videatur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4074" xml:space="preserve">Pro cuius rei ratione cognoſcendum primò eſt, quo modo fit perfecta
                    <reg norm="ſimplexque" type="simple">ſimplexq́;</reg>
                    <lb/>
                  viſio, & non reflexa, deinde proſequemur ad reliqua huius tertiæ propoſitionis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4075" xml:space="preserve">Animaduertendum igitur eſt, quod
                    <reg norm="quotieſcunque" type="simple">quotieſcunq;</reg>
                  obiectum aliquod viſibile aſpi
                    <lb/>
                  cimus, nos nunquam perfectè illud comprehendere poſſumus, niſi in puncto con-
                    <lb/>
                  curſus, ſeu interſectionis axium viſualium, ſeu radialium ( vt ita loquar )
                    <reg norm="quam" type="context">quã</reg>
                    <reg norm="inter- ſectionem" type="context">inter-
                      <lb/>
                    ſectionẽ</reg>
                  , nos efficimus ope reuolutionis oculorum
                    <reg norm="adinuicem" type="context">adinuicẽ</reg>
                  , hoc eſt voluendo vnum
                    <lb/>
                  verſus alium, ita vt in ſitu ipſius obiecti, ſeinuicem ſecent axes iam dicti, </s>
                  <s xml:id="echoid-s4076" xml:space="preserve">tunc enim
                    <lb/>
                  vtroque oculo mediante, exacte rem perſpicimus, cęteris .8. circunſtantijs non ob-
                    <lb/>
                  ſtantibus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4077" xml:space="preserve">Vnde ſtantibus oculis in tali ſitu, altero reſpectu alterius, ſi eorum alter tectus;
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4078" xml:space="preserve">ſeu velatus fuerit, tune alio tantummodo oculo mediante, videbimus obiectum,
                    <lb/>
                  in ea diſtantia, exactius, quam in quauis alia propinquiori, & remotiori.</s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>