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]

Table of Notes

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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="336" rhead="IO. BAPT. BENED." n="348" file="0348" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0348"/>
                <p>
                  <s xml:id="echoid-s4079" xml:space="preserve">Animal igitur, ſecundum diſtantiam obiecti, oculum accommodat ad recipien-
                    <lb/>
                  dum quam exactiſſimè ſpeciem ipſius obiecti, & hoc voluendo ambos oculos, vnum
                    <lb/>
                  verſus alium, ita quod interſectio axium ſit in ſitu ſeu loco dicti obiecti, nam tunc vi
                    <lb/>
                  dent ambo vel aliquis eorum ſolus, in tali diſtantia exactè obiectum videbit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4080" xml:space="preserve">Vnde ſequitur obiectum viſibile, compræhenſibile non eſſe ab vno tantummodo
                    <lb/>
                  oculo in quolibet ſitu axis ipſius oculi, ſed in eo, vbi alius axis interſecatur à dicto.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4081" xml:space="preserve">Quæ quidem interſectio poteſt fieri propinqua, vel remota à viſu, ad certos tamen
                    <lb/>
                  terminos vſque.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4082" xml:space="preserve">De huiuſmodi axium viſualium interſectione ſcribit Alhazem in .2. et .15. propo
                    <lb/>
                  ſitione tertij lib. Vitellio verò in .32. et .45. eiuſdem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4083" xml:space="preserve">Quod igitur dico, verum eſt, ideſt, quod ſi vno tantummodo oculo aſpiciemus
                    <lb/>
                  obiectum aliquod, ipſum nunquam perfectè proſpicietur, niſi cum oculus ita ſitus
                    <lb/>
                  fuerit, vt eius axis cum axe alterius in loco obiecti ſe inuicem ſecent, quamuis alter
                    <lb/>
                  oculus nihil videat,
                    <reg norm="cum" type="context">cũ</reg>
                    <reg norm="autem" type="wordlist">aũt</reg>
                  duobus oculis in tali ſitu
                    <reg norm="conſtitutis" type="context">cõſtitutis</reg>
                    <reg norm="obiectum" type="context">obiectũ</reg>
                  videmus, vnum
                    <lb/>
                  tantummodo nobis cernere videbimur, & ſi extra talem punctum interſectionis ip-
                    <lb/>
                  ſum obiectum poſitum fuerit, tunc duo talia, obiecta nobis apparebunt, ſed huiuſ
                    <lb/>
                  modi rei cauſam alias tibi manifeſtabo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4084" xml:space="preserve">His igitur cognitis, ponamus aliquam
                    <lb/>
                    <figure xlink:label="fig-0348-01" xlink:href="fig-0348-01a" number="375">
                      <image file="0348-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0348-01"/>
                    </figure>
                  ſpeculi ſuperficiem eſſe
                    <var>.g.h.</var>
                  in figura
                    <var>.B.</var>
                    <lb/>
                  obiectum autem viſibile
                    <var>.b.</var>
                  oculos vero
                    <var>.a.</var>
                    <lb/>
                  et
                    <var>.u.</var>
                  punctum autem
                    <var>.n.</var>
                  in ſuperficie ſpecu
                    <lb/>
                  li, à quo imago ipſius
                    <var>.b.</var>
                  reflectit ad
                    <var>.a.</var>
                  &
                    <lb/>
                  punctum
                    <var>.t.</var>
                  à quo reflectitur ad
                    <var>.u.</var>
                  et
                    <var>.c.e.</var>
                    <lb/>
                  ſit
                    <reg norm="communis" type="context">cõmunis</reg>
                  ſectio ſuperficiei reflexionis
                    <lb/>
                  radiorum
                    <var>.b.n.a.</var>
                  et
                    <var>.c.f.</var>
                  ſit communis ſectio
                    <lb/>
                  ſuperficiei reflexionis radiorum
                    <var>.b.t.u.</var>
                  qua
                    <lb/>
                  rum
                    <reg norm="vnaquæque" type="simple">vnaquæq;</reg>
                  ſuperficies reflexionis, ere-
                    <lb/>
                  cta eſt ad ſuperficiem ſpeculi
                    <var>.g.h.</var>
                  vt ſupra
                    <lb/>
                  diximus. </s>
                  <s xml:id="echoid-s4085" xml:space="preserve">Nunc ex .19. vndecimi Eucl. ſequitur communem ſectionem harum dua-
                    <lb/>
                  rum ſuperficierum. (b.c.d. ſcilicet) ad rectos etiam eſſe ſupra ſuperficiem ſpeculi
                    <var>.g.
                      <lb/>
                    h.</var>
                  cum qua
                    <var>.b.c.</var>
                  quælibet linearum
                    <var>.a.n.</var>
                  vel
                    <var>.u.t.</var>
                  reflexarum ( productę cum fuerint )
                    <lb/>
                  ſeinuicem interſecabunt eo quod duo anguli
                    <var>.d.c.n.</var>
                  et
                    <var>.d.n.c.</var>
                  ſimul collecti minores
                    <lb/>
                  ſunt duobus rectis, & ita
                    <var>.d.c.t.</var>
                  cum
                    <var>.d.t.c.</var>
                  cum anguli
                    <var>.a.n.e.</var>
                  et
                    <var>.u.t.f.</var>
                  reflexi, ipſis con-
                    <lb/>
                  trapoſiti, æquales ſint angulis
                    <var>.b.n.c.</var>
                  et
                    <var>.b.t.c.</var>
                  incidentiæ, quorum
                    <reg norm="vnuſquiſque" type="simple">vnuſquiſq;</reg>
                  ex .32.
                    <lb/>
                  primi, minor eſt recto.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4086" xml:space="preserve">Dico etiam quod in eodem puncto huiuſmodi catheti
                    <var>.b.c.d.</var>
                  in quo interſecabi-
                    <lb/>
                  tur à linea
                    <var>.a.n.</var>
                  in eodem ſecabitur à linea
                    <var>.u.t.</var>
                  & quod punctum dicti concurſus, tan-
                    <lb/>
                  tum depreſſum erit ſub ſuperficie ſpeculi
                    <var>.g.h.</var>
                  quantum
                    <var>.b.</var>
                  ſupra ipſam reperietur.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4087" xml:space="preserve">Nam anguli
                    <var>.b.n.c.</var>
                  et
                    <var>.d.n.c.</var>
                  ſunt inuicem æquales,
                    <reg norm="angulique" type="simple">anguliq́;</reg>
                    <var>.b.c.n.</var>
                  et
                    <var>.d.c.n.</var>
                  recti
                    <var>.c.n.</var>
                    <lb/>
                  verò communis ambobus triangulis
                    <var>.b.c.n.</var>
                  et
                    <var>.d.c.n.</var>
                  vnde ex .26. primi Eucli. latus
                    <var>.d.
                      <lb/>
                    c.</var>
                  commune, vt trianguli
                    <var>.d.c.n.</var>
                  æquale erit lateri communi
                    <var>.b.c.</var>
                  vt trianguli
                    <var>.b.c.n.</var>
                    <lb/>
                  Idem etiam dico de latere
                    <var>.d.c.</var>
                  vt ipſius trianguli
                    <var>.d.c.t.</var>
                  quod æquatur lateri
                    <var>.b.c.</var>
                  vt
                    <lb/>
                  trianguli
                    <var>.b.c.t</var>
                  . </s>
                  <s xml:id="echoid-s4088" xml:space="preserve">Vnde cum
                    <var>.b.c.</var>
                  vnum, & idem ſit: </s>
                  <s xml:id="echoid-s4089" xml:space="preserve">d.c. igitur etiam erit, & ipſum
                    <reg norm="vnum" type="context">vnũ</reg>
                    <lb/>
                  & idem, quod erit propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4090" xml:space="preserve">Nunc autem cum hi duo radij ſeinuicem ſecent in puncto
                    <var>.d.</var>
                  ergo in ipſo puncto
                    <var>.
                      <lb/>
                    d.</var>
                  videbimur nobis videre
                    <reg norm="imaginem" type="context">imaginẽ</reg>
                  obiecti .b:
                    <reg norm="cum" type="context">cũ</reg>
                  ope
                    <reg norm="duorum" type="context">duorũ</reg>
                    <reg norm="iſtorum" type="context">iſtorũ</reg>
                    <reg norm="radiorum" type="context">radiorũ</reg>
                    <var>.n.a.</var>
                  et
                    <var>.t.
                      <lb/>
                    u.</var>
                  ita inuicem
                    <reg norm="ſitorum" type="context">ſitorũ</reg>
                  , videamur nobis
                    <reg norm="imaginem" type="context">imaginẽ</reg>
                  proſpicere. </s>
                  <s xml:id="echoid-s4091" xml:space="preserve">Vnde ſi in tali caſu, vnus </s>
                </p>
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