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 figures

< >
[331. Figure]
[332. Figure]
[333. Figure]
[334. Figure]
[335. Figure]
[336. Figure]
[337. Figure]
[338. Figure]
[339. Figure]
[340. Figure]
[341. Figure]
[342. Figure]
[343. Figure]
[344. Figure]
[345. Figure]
[346. Figure]
[347. Figure]
[348. Figure]
[349. Figure]
[350. Figure]
[351. Figure]
[352. Figure]
[353. Figure]
[354. Figure]
[355. Figure]
[356. Figure]
[357. Figure]
[358. Figure]
[359. Figure]
[360. Figure]
< >
page |< < (296) of 445 > >|
IO. BAPT. BENED.
    <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-div564" type="section" level="3" n="17">
              <div xml:id="echoid-div571" type="letter" level="4" n="4">
                <pb o="296" rhead="IO. BAPT. BENED." n="308" file="0308" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0308"/>
                <p>
                  <s xml:id="echoid-s3659" xml:space="preserve">Sed etiam alio vniuerſaliori modo potes probare, quod ita ſit
                    <var>.u.x.</var>
                  ad
                    <var>.x.y.</var>
                  vt
                    <var>.c.e.</var>
                    <lb/>
                  ad
                    <var>.e.a.</var>
                  cogitando in linea
                    <var>.c.a.</var>
                  punctum quoddam quod vocabimus ſimiliter
                    <var>.y.</var>
                  in
                    <lb/>
                  tali ſitu locatum, quod diuidat
                    <var>.c.a.</var>
                  eadem proportione qua
                    <var>.y.</var>
                  diuidit
                    <var>.u.s.</var>
                  vnde cum
                    <lb/>
                    <var>e.s.</var>
                  diuiſa eodem modo etiam ſit à puncto
                    <var>.s.</var>
                  ex ſupradicta quinta lib. de quadratura
                    <lb/>
                  parabolæ, erit igitur proportio
                    <var>.a.y.</var>
                  ad
                    <var>.y.c.</var>
                  vt
                    <var>.e.s.</var>
                  ad
                    <var>.s.c.</var>
                  per .11. quinti Eucli. </s>
                  <s xml:id="echoid-s3660" xml:space="preserve">& com
                    <lb/>
                  ponendo ita erit
                    <reg norm="totius" type="simple">totiꝰ</reg>
                    <var>.a.c.</var>
                  ad totum
                    <var>.y.c.</var>
                  vt abſcisſi
                    <var>.s.c.</var>
                  ad abſciſsum
                    <var>.s.c.</var>
                  </s>
                  <s xml:id="echoid-s3661" xml:space="preserve">quare reſidui
                    <lb/>
                    <var>a.e.</var>
                  ad reſiduum
                    <var>.y.s.</var>
                  erit vt totius
                    <var>.a.c.</var>
                  ad totum
                    <var>.y.c.</var>
                  & permutando, ita erit
                    <var>.a.c.</var>
                  ad
                    <var>.a.
                      <lb/>
                    e.</var>
                  vt
                    <var>.y.c.</var>
                  ad
                    <var>.y.s.</var>
                  & diuidendo, ita erit
                    <var>.
                      <lb/>
                    c.e.</var>
                  ad
                    <var>.e.a.</var>
                  ut
                    <var>.c.s.</var>
                  ad
                    <var>.s.y.</var>
                  & quia pun-
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0308-01a" xlink:href="fig-0308-01"/>
                  ctum
                    <var>.s.</var>
                  diuidit
                    <var>.c.a.</var>
                  eodem modo, quo
                    <lb/>
                  x. diuidit
                    <var>.u.s.</var>
                  per ſupradictam
                    <reg norm="quintam" type="context">quintã</reg>
                  ,
                    <lb/>
                  ergo ita erit
                    <var>.c.s.</var>
                  ad
                    <var>.s.y.</var>
                  in linea
                    <var>.c.a.</var>
                  vt
                    <lb/>
                    <var>u.x.</var>
                  ad
                    <var>.x.y.</var>
                  </s>
                  <s xml:id="echoid-s3662" xml:space="preserve">vnde ex .11. quinti
                    <var>.c.e.</var>
                  ad
                    <lb/>
                    <var>e.a.</var>
                  erit, vt
                    <var>.u.x.</var>
                  ad
                    <var>.x,y</var>
                  . </s>
                  <s xml:id="echoid-s3663" xml:space="preserve">quare ſequitur,
                    <lb/>
                  primum, ſecundum, tertium, & quartum lemma ſuperflua eſſe.</s>
                </p>
                <div xml:id="echoid-div571" type="float" level="5" n="1">
                  <figure xlink:label="fig-0308-01" xlink:href="fig-0308-01a">
                    <image file="0308-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0308-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s3664" xml:space="preserve">Quod deinde ponit pro corellario in fine .6. lemmatis, aliter quam per .6. lemma
                    <lb/>
                  poteſt demonſtrari, hoc mode. </s>
                  <s xml:id="echoid-s3665" xml:space="preserve">Nam ſuperius demonſtrauimus eandem propor-
                    <lb/>
                  tionem eſſe
                    <var>.l.b.</var>
                  ad
                    <var>.b.m.</var>
                  quæ
                    <var>.c.e.</var>
                  ad
                    <var>.e.a.</var>
                    <reg norm="idem" type="context">idẽ</reg>
                  dico de proportione
                    <var>.u.x.</var>
                  ad
                    <var>.x.y.</var>
                  & om-
                    <lb/>
                  nium æquidiſtantium ad
                    <var>.h.e.</var>
                  quibus rationibus mediantibus codem modo ſcies,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                    <var>u.y.</var>
                  ad
                    <var>.y.r.</var>
                  erit, vt
                    <var>.c.d.</var>
                  ad
                    <var>.d.c.</var>
                  & ita dico de omnibus
                    <reg norm="æquidiſtantibus" type="context">æquidiſtãtibus</reg>
                  . ad
                    <var>.h.e.</var>
                  </s>
                  <s xml:id="echoid-s3666" xml:space="preserve">vnde
                    <var>.l.b.</var>
                    <lb/>
                  ad
                    <var>.b.m.</var>
                  erit vt
                    <var>.u.x.</var>
                  ad
                    <var>.x.y.</var>
                  et
                    <var>.l.m.</var>
                  ad
                    <var>.m.d.</var>
                  vt
                    <var>.u.y.</var>
                  ad
                    <var>.y.r.</var>
                  per .11. quinti, ſed cum ſit
                    <var>.l.
                      <lb/>
                    b.</var>
                  ad
                    <var>.b.m.</var>
                  vt
                    <var>.u.x.</var>
                  ad
                    <var>.x.y.</var>
                  componendo erit
                    <var>.l.m.</var>
                  ad
                    <var>.b.m.</var>
                  vt
                    <var>.u.x.</var>
                  ad
                    <var>.x.y.</var>
                  & euerſim
                    <var>.b.
                      <lb/>
                    m.</var>
                  ad
                    <var>.m.b.</var>
                  erit, vt
                    <var>.x.y.</var>
                  ad
                    <var>.y.u.</var>
                  & per æquam proportionalitatem erit
                    <var>.b.m.</var>
                  ad
                    <var>.m.d.</var>
                  vt
                    <unsure/>
                    <lb/>
                    <var>x.y.</var>
                  ad
                    <var>.y.r.</var>
                  quod eſt propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3667" xml:space="preserve">Non video etiam, quare ipſe ducat lineam
                    <var>.s.r.</var>
                  cum in ipſo contextu nihil ſaciac
                    <lb/>
                  de dicta
                    <var>.s.r</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3668" xml:space="preserve">Comentum poſtea contextus
                    <var>.P.</var>
                  pulchrius eſſet, ſi diceret, quod cum ita ſit totius,
                    <lb/>
                    <var>l.a.</var>
                  ad totum
                    <var>.a.d.</var>
                  ſic ſe habebit abſciſſum
                    <var>.a.i.</var>
                  ad abſciſſum
                    <var>.a.z.</var>
                  eo quod ita eſt, vt ſcis,
                    <lb/>
                  hoc eſt in proportione dupla, ergo reſidui
                    <var>.i.l.</var>
                  ad reſiduum
                    <var>.d.z.</var>
                  erit vt totius
                    <var>.a.l.</var>
                  ad
                    <lb/>
                  totum
                    <var>.a.d.</var>
                  hoc eſt in proportione dupla.</s>
                </p>
              </div>
              <div xml:id="echoid-div573" type="letter" level="4" n="5">
                <head xml:id="echoid-head438" style="it" xml:space="preserve">De Viſu.</head>
                <head xml:id="echoid-head439" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3669" xml:space="preserve">RAtio vnde ſiat, vt videamus diſtinctè omnes eolores, cum in qualibet aeris par
                    <lb/>
                  te, quo lumina reſlexa poſſunt peruenire mixta ſint, & non diſtincta, oritur à
                    <lb/>
                  paruitate ipſius pupillæ oculorum, & à magna expanſione virtutis viſiuæ in ſuperſi-
                    <lb/>
                  cie concaua orbis continentis humores diaphanos oculorum per ramuſculos nerui
                    <lb/>
                  optici remotè ab ipſa pupilla. </s>
                  <s xml:id="echoid-s3670" xml:space="preserve">& quamuis radii luminoſi frangantur ab vnoquoque
                    <lb/>
                  humore diuerſimodè, hoc nihilominus maximè iuuat ad diſtinctionem radiorum,
                    <lb/>
                  ſed & ſi directè procederent, idem ferè eueniret, non tamen ſuis locis, cogita exem-
                    <lb/>
                  pli gratia lineam
                    <var>.a.u.e.</var>
                  vt communis ſectio cuiuſdam plani ſecantis ſphæram oculi,
                    <lb/>
                  per centrum ipſius, & pupillæ, et
                    <var>.o.</var>
                  punctum ſit proximum centro ipſius pupillæ,
                    <lb/>
                  ſed interius aliquantulum, extra
                    <reg norm="autem" type="context">autẽ</reg>
                    <reg norm="oculum" type="context">oculũ</reg>
                  , ſint varij colores, vt
                    <var>.c.n.t.</var>
                  in dicto plano.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3671" xml:space="preserve">Iam nulli dubium eſt quod lumina quæ producuntur ab
                    <var>.c.n.t.</var>
                  ad
                    <var>.o.</var>
                  in ipſo
                    <var>.o.</var>
                  mi- </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>