Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
251
251 		252
252
253
253 		254
254
255
255 		256
256
257
257 		258
258
259
259 		260
260
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/259.jpg" pagenum="231"/>
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  generantur, ut ſumma particularum ſectoris
                    <emph type="italics"/>
                  ATD,
                    <emph.end type="italics"/>
                  id eſt, </s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note207"/>
                  tempus totum ut ſector totus.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note207"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  æquetur quartæ parti ipſius
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  ſpatium
                    <lb/>
                  quod corpus tempore quovis cadendo deſcribit, erit ad ſpatium
                    <lb/>
                  quod corpus velocitate maxima
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  eodem tempore uniformiter
                    <lb/>
                  progrediendo deſcribere poteſt, ut area
                    <emph type="italics"/>
                  ABNK,
                    <emph.end type="italics"/>
                  qua ſpatium
                    <lb/>
                  cadendo deſcriptum exponitur, ad aream
                    <emph type="italics"/>
                  ATD
                    <emph.end type="italics"/>
                  qua tempus ex­
                    <lb/>
                  ponitur. </s>
                  <s>Nam cum ſit
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AK,
                    <emph.end type="italics"/>
                  erit (per
                    <lb/>
                  Corol. </s>
                  <s>1, Lem. </s>
                  <s>11 hujus)
                    <emph type="italics"/>
                  LK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ut 2
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AP,
                    <emph.end type="italics"/>
                  hoc eſt,
                    <lb/>
                  ut 2
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  & inde
                    <emph type="italics"/>
                  LK
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  ad (1/4
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  vel)
                    <lb/>
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ; eſt &
                    <emph type="italics"/>
                  KN
                    <emph.end type="italics"/>
                  ad (
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  vel)
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  ; itaque ex
                    <lb/>
                  æquo
                    <emph type="italics"/>
                  LKN
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DPQ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CK.
                    <emph.end type="italics"/>
                  Sed erat
                    <emph type="italics"/>
                  DPQ
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  DTV
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC.
                    <emph.end type="italics"/>
                  Ergo rurſus ex æquo
                    <emph type="italics"/>
                  LKN
                    <emph.end type="italics"/>
                  eſt ad
                    <emph type="italics"/>
                  DTV
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ; hoc eſt, ut velocitas corporis cadentis ad veloci­
                    <lb/>
                  tatem maximam quam corpus cadendo poteſt acquirere. </s>
                  <s>Cum
                    <lb/>
                  igitur arearum
                    <emph type="italics"/>
                  ABNK
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ATD
                    <emph.end type="italics"/>
                  momenta
                    <emph type="italics"/>
                  LKN
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DTV
                    <emph.end type="italics"/>
                    <lb/>
                  ſunt ut velocitates, erunt arearum illarum partes omnes ſimul
                    <lb/>
                  genitæ ut ſpatia ſimul deſcripta, ideoque areæ totæ ab initio
                    <lb/>
                  genitæ
                    <emph type="italics"/>
                  ABNK
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ATD
                    <emph.end type="italics"/>
                  ut ſpatia tota ab initio deſcenſus de­
                    <lb/>
                  ſcripta.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Idem conſequitur etiam de ſpatio quod in aſcenſu de­
                    <lb/>
                  ſcribitur. </s>
                  <s>Nimirum quod ſpatium illud omne ſit ad ſpatium, uNI­
                    <lb/>
                  formi cum velocitate
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  eodem tempore deſcriptum, ut eſt area
                    <lb/>
                    <emph type="italics"/>
                  ABnk
                    <emph.end type="italics"/>
                  ad ſectorem
                    <emph type="italics"/>
                  ADt.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Velocitas corporis tempore
                    <emph type="italics"/>
                  ATD
                    <emph.end type="italics"/>
                  cadentis eſt ad ve­
                    <lb/>
                  locitatem, quam eodem tempore in ſpatio non reſiſtente acquire­
                    <lb/>
                  ret, ut triangulum
                    <emph type="italics"/>
                  APD
                    <emph.end type="italics"/>
                  ad ſectorem Hyperbolicum
                    <emph type="italics"/>
                  ATD.
                    <emph.end type="italics"/>
                    <lb/>
                  Nam velocitas in Medio non reſiſtente foret ut tempus
                    <emph type="italics"/>
                  ATD,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  in Medio reſiſtente eſt ut
                    <emph type="italics"/>
                  AP,
                    <emph.end type="italics"/>
                  id eſt, ut triangulum
                    <emph type="italics"/>
                  APD.
                    <emph.end type="italics"/>
                  Et
                    <lb/>
                  velocitates illæ initio deſcenſus æquantur inter ſe, perinde ut areæ
                    <lb/>
                  illæ
                    <emph type="italics"/>
                  ATD, APD.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Eodem argumento velocitas in aſcenſu eſt ad velocita­
                    <lb/>
                  tem, qua corpus eodem tempore in ſpatio non reſiſtente omnem
                    <lb/>
                  ſuum aſcendendi motum amittere poſſet, ut triangulum
                    <emph type="italics"/>
                  ApD
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  ſectorem Circularem
                    <emph type="italics"/>
                  AtD
                    <emph.end type="italics"/>
                  ; ſive ut recta
                    <emph type="italics"/>
                  Ap
                    <emph.end type="italics"/>
                  ad arcum
                    <emph type="italics"/>
                  At.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Eſt igitur tempus quo corpus in Medio reſiſtente caden­
                    <lb/>
                  do velocitatem
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  acquirit, ad tempus quo velocitatem maximam
                    <lb/>
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  in ſpatio non reſiſtente cadendo acquirere poſſet, ut ſector
                    <lb/>
                    <emph type="italics"/>
                  ADT
                    <emph.end type="italics"/>
                  ad triangulum
                    <emph type="italics"/>
                  ADC
                    <emph.end type="italics"/>
                  : & tempus, quo velocitatem
                    <emph type="italics"/>
                  Ap
                    <emph.end type="italics"/>
                  in </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum