Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
261
261 		262
262
263
263 		264
264
265
265 		266
266
267
267 		268
268
269
269 		270
270
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/267.jpg" pagenum="239"/>
                  Aſymptoton ejus in
                    <emph type="italics"/>
                  V,
                    <emph.end type="italics"/>
                  fuerit
                    <emph type="italics"/>
                  VG
                    <emph.end type="italics"/>
                  reciproce ut ipſius
                    <emph type="italics"/>
                  ZX
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                    <lb/>
                    <arrow.to.target n="note215"/>
                  dignitas aliqua
                    <emph type="italics"/>
                  DN
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                  ,
                    <emph.end type="italics"/>
                  cujus index eſt numerus
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  : & quæratur
                    <lb/>
                  Medii denſitas, qua Projectile progrediatur in hac curva. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note215"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>Pro
                    <emph type="italics"/>
                  BN, BD, NX
                    <emph.end type="italics"/>
                  ſcribantur A, O, C reſpective, ſitque
                    <emph type="italics"/>
                  VZ
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  XZ
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  e,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  VG
                    <emph.end type="italics"/>
                  æqualis (
                    <emph type="italics"/>
                  bb/DN
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  ), & erit
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  æqua­
                    <lb/>
                  lis A-O,
                    <emph type="italics"/>
                  VG
                    <emph.end type="italics"/>
                  =(
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  /—
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  A-O),
                    <emph type="italics"/>
                  VZ
                    <emph.end type="italics"/>
                  =
                    <emph type="italics"/>
                  d/e
                    <emph.end type="italics"/>
                  —A-O, &
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  NX-VZ
                    <lb/>
                  -VG
                    <emph.end type="italics"/>
                  æqualis C-
                    <emph type="italics"/>
                  d/e
                    <emph.end type="italics"/>
                  A+
                    <emph type="italics"/>
                  d/e
                    <emph.end type="italics"/>
                  O-(
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  /—
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  A-O). Reſolvatur terminus ille
                    <lb/>
                  (
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  /—
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  A-O) in ſeriem infinitam (
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  /A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  )+(
                    <emph type="italics"/>
                  nbb
                    <emph.end type="italics"/>
                  /A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +1
                    <emph.end type="sup"/>
                  )O+(
                    <emph type="italics"/>
                  nn+n
                    <emph.end type="italics"/>
                  /2A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +2
                    <emph.end type="sup"/>
                  )
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  O
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  +
                    <lb/>
                  (
                    <emph type="italics"/>
                  n
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  +3nn+2n
                    <emph.end type="italics"/>
                  /6A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +3
                    <emph.end type="sup"/>
                  )
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  O
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  &c. </s>
                  <s>ac fiet
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  æqualis C-
                    <emph type="italics"/>
                  d/e
                    <emph.end type="italics"/>
                  A-(
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  /A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  )+
                    <lb/>
                    <emph type="italics"/>
                  d/e
                    <emph.end type="italics"/>
                  O-(
                    <emph type="italics"/>
                  nbb
                    <emph.end type="italics"/>
                  /A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +1
                    <emph.end type="sup"/>
                  )O-(
                    <emph type="italics"/>
                  +nn+n
                    <emph.end type="italics"/>
                  /2A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +2
                    <emph.end type="sup"/>
                  )
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  O
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  -(
                    <emph type="italics"/>
                  +n
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  +3nn+2n
                    <emph.end type="italics"/>
                  /6A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +3
                    <emph.end type="sup"/>
                  )
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  O
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  &c. </s>
                  <s>Hu­
                    <lb/>
                  jus ſeriei terminus ſecundus
                    <emph type="italics"/>
                  d/e
                    <emph.end type="italics"/>
                  O-(
                    <emph type="italics"/>
                  nbb
                    <emph.end type="italics"/>
                  /A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +1
                    <emph.end type="sup"/>
                  )O uſurpandus eſt pro Q
                    <emph type="italics"/>
                  o,
                    <emph.end type="italics"/>
                    <lb/>
                  tertius (
                    <emph type="italics"/>
                  nn+n
                    <emph.end type="italics"/>
                  /2A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +2
                    <emph.end type="sup"/>
                  )
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  O
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  pro R
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  , quartus (
                    <emph type="italics"/>
                  n
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  +3nn+2n
                    <emph.end type="italics"/>
                  /6A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +3
                    <emph.end type="sup"/>
                  )
                    <emph type="italics"/>
                  bb
                    <emph.end type="italics"/>
                  O
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  pro
                    <lb/>
                  S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  . </s>
                  <s>Et inde Medii denſitas (S/R√1+QQ), in loco quovis
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  fit
                    <lb/>
                  (
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +2/3√A
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  +(
                    <emph type="italics"/>
                  dd/ee
                    <emph.end type="italics"/>
                  )A
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  -(
                    <emph type="italics"/>
                  2dnbb/e
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  )A+(
                    <emph type="italics"/>
                  nnb
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  4
                    <emph.end type="sup"/>
                  /A
                    <emph type="sup"/>
                  2
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  )), adeoque ſi in
                    <emph type="italics"/>
                  VZ
                    <emph.end type="italics"/>
                  capiatur
                    <emph type="italics"/>
                  VY
                    <emph.end type="italics"/>
                    <lb/>
                  æqualis
                    <emph type="italics"/>
                  nXVG,
                    <emph.end type="italics"/>
                  denſitas illa eſt reciproce ut
                    <emph type="italics"/>
                  XY.
                    <emph.end type="italics"/>
                  Sunt enim A
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                    <lb/>
                  & (
                    <emph type="italics"/>
                  dd/ee
                    <emph.end type="italics"/>
                  )A
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  -(2
                    <emph type="italics"/>
                  dnbb/e
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  )A+(
                    <emph type="italics"/>
                  nnb
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  4
                    <emph.end type="sup"/>
                  /A
                    <emph type="sup"/>
                  2
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ) ipſarum
                    <emph type="italics"/>
                  XZ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ZY
                    <emph.end type="italics"/>
                  quadrata. </s>
                  <s>Reſiſten­
                    <lb/>
                  tia autem in eodem loco
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  fit ad gravitatem ut 3S in (
                    <emph type="italics"/>
                  XY
                    <emph.end type="italics"/>
                  /A) ad 4RR,
                    <lb/>
                  id eſt,
                    <emph type="italics"/>
                  XY
                    <emph.end type="italics"/>
                  ad (
                    <emph type="italics"/>
                  2nn+2n/n+2)VG.
                    <emph.end type="italics"/>
                  Et velocitas ibidem ea ipſa eſt qua­
                    <lb/>
                  cum corpus projectum in Parabola pergeret, verticem
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  diametrum
                    <lb/>
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  & latus rectum (1+QQ/R) ſeu (2
                    <emph type="italics"/>
                  XYquad./—nn+n
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  VG
                    <emph.end type="italics"/>
                  ) habente.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum