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]

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          <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>
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