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="039/01/270.jpg" pagenum="242"/>
                    <arrow.to.target n="note218"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note218"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Reg.
                    <emph.end type="italics"/>
                  4. Quoniam denſitas Medii prope verticem Hyperbolæ
                    <lb/>
                  major eſt quam in loco
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ut habeatur denſitas mediocris, debet
                    <lb/>
                  ratio minimæ tangentium
                    <emph type="italics"/>
                  GT
                    <emph.end type="italics"/>
                  ad tangentem
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  inveniri, &
                    <lb/>
                  denſitas in
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  angeri in ratione paudo majore quam ſemiſummæ
                    <lb/>
                  harum tangentium ad minimam tangentium
                    <emph type="italics"/>
                  GT.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Reg.
                    <emph.end type="italics"/>
                  5. Si dantur longitudines
                    <emph type="italics"/>
                  AH, AI,
                    <emph.end type="italics"/>
                  & deſcribenda ſit Figu­
                    <lb/>
                  ra
                    <emph type="italics"/>
                  AGK:
                    <emph.end type="italics"/>
                  produc
                    <emph type="italics"/>
                  HN
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  X,
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  HX
                    <emph.end type="italics"/>
                  æqualis facto ſub
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  +1 &
                    <lb/>
                    <emph type="italics"/>
                  AI
                    <emph.end type="italics"/>
                  ; centroque
                    <emph type="italics"/>
                  X
                    <emph.end type="italics"/>
                  & Aſymptotis
                    <emph type="italics"/>
                  MX, NX
                    <emph.end type="italics"/>
                  per punctum
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  deſcriba­
                    <lb/>
                  tur Hyperbola, ea lege, ut ſit
                    <emph type="italics"/>
                  AI
                    <emph.end type="italics"/>
                  ad quamvis
                    <emph type="italics"/>
                  VG
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  XV
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  XI
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                  .
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Reg.
                    <emph.end type="italics"/>
                  6. Quo major eſt numerus
                    <emph type="italics"/>
                  n,
                    <emph.end type="italics"/>
                  eo magis accuratæ ſunt hæ
                    <lb/>
                  Hyperbolæ in aſcenſu corporis ab
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  & minus accuratæ in ejus de­
                    <lb/>
                  ſcenſu ad
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  ; & contra. </s>
                  <s>Hyperbola Conica mediocrem rationem
                    <lb/>
                  tenet, eſt que cæteris ſimplicior. </s>
                  <s>Igitur ſi Hyperbola ſit hujus generis,
                    <lb/>
                  & punctum
                    <emph type="italics"/>
                  K,
                    <emph.end type="italics"/>
                  ubi corpus projectum incidet in rectam quamvis
                    <emph type="italics"/>
                  AN
                    <emph.end type="italics"/>
                    <lb/>
                  per punctum
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  tranſeuntem, quæratur: occurrat producta
                    <emph type="italics"/>
                  AN
                    <emph.end type="italics"/>
                    <lb/>
                  Aſymptotis
                    <emph type="italics"/>
                  MX, NX
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  N,
                    <emph.end type="italics"/>
                  & ſumatur
                    <emph type="italics"/>
                  NK
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  AM
                    <emph.end type="italics"/>
                  æqualis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Reg.
                    <emph.end type="italics"/>
                  7. Et hinc liquet methodus expedita determinandi hanc
                    <lb/>
                  Hyperbolam ex Phænomenis. </s>
                  <s>Projiciantur corpora duo ſimilia &
                    <lb/>
                  æqualia, eadem velocitate, in angulis diverſis
                    <emph type="italics"/>
                  HAK, hAk,
                    <emph.end type="italics"/>
                  inci­
                    <lb/>
                  dantQ.E.I. planum Horizontis in
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  k
                    <emph.end type="italics"/>
                  ; & notetur proportio
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  Ak.
                    <emph.end type="italics"/>
                  Sit ea
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  e.
                    <emph.end type="italics"/>
                  Tum erecto cujuſvis longitudinis perpen­
                    <lb/>
                  diculo
                    <emph type="italics"/>
                  AI,
                    <emph.end type="italics"/>
                  aſſume utcunque longitudinem
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  Ah,
                    <emph.end type="italics"/>
                  & inde
                    <lb/>
                  collige graphice longitudines
                    <emph type="italics"/>
                  AK, Ak,
                    <emph.end type="italics"/>
                  per Reg. </s>
                  <s>6. Si ratio
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  Ak
                    <emph.end type="italics"/>
                  ſit eadem cum ratione
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  e,
                    <emph.end type="italics"/>
                  longitudo
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  recte aſſump­
                    <lb/>
                  ta fuit. </s>
                  <s>Sin minus cape in recta infinita
                    <emph type="italics"/>
                  SM
                    <emph.end type="italics"/>
                  longitudinem
                    <emph type="italics"/>
                  SM
                    <emph.end type="italics"/>
                    <lb/>
                  æqualem aſſumptæ
                    <emph type="italics"/>
                  AH,
                    <emph.end type="italics"/>
                  & erige perpendiculum
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  æquale ra­
                    <lb/>
                  tionum differentiæ
                    <emph type="italics"/>
                  (AK/Ak)-d/e
                    <emph.end type="italics"/>
                  ductæ in rectam quamvis datam. </s>
                  <s>Si­
                    <lb/>
                  mili methodo ex aſſumptis pluribus longitudinibus
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  invenien­
                    <lb/>
                  da ſunt plura puncta
                    <emph type="italics"/>
                  N,
                    <emph.end type="italics"/>
                  & per omnia a­
                    <lb/>
                    <figure id="id.039.01.270.1.jpg" xlink:href="039/01/270/1.jpg" number="157"/>
                    <lb/>
                  genda Curva linea regularis
                    <emph type="italics"/>
                  NNXN,
                    <emph.end type="italics"/>
                  ſe­
                    <lb/>
                  cans rectam
                    <emph type="italics"/>
                  SMMM
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  X.
                    <emph.end type="italics"/>
                  Aſſumatur
                    <lb/>
                  demum
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  æqualie abſciſſæ
                    <emph type="italics"/>
                  SX
                    <emph.end type="italics"/>
                  & inde
                    <lb/>
                  denuo inveniatur longitudo
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  ; & lon­
                    <lb/>
                  gitudines, quæ ſint ad aſſumptam longitu­
                    <lb/>
                  dinem
                    <emph type="italics"/>
                  AI
                    <emph.end type="italics"/>
                  & hanc ultimam
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  ut longitudo
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  per experi­
                    <lb/>
                  mentum cognita ad ultimo inventam longitudinem
                    <emph type="italics"/>
                  AK,
                    <emph.end type="italics"/>
                  erunt veræ
                    <lb/>
                  illæ longitudines
                    <emph type="italics"/>
                  AI
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  AH,
                    <emph.end type="italics"/>
                  quas invenire oportuit. </s>
                  <s>Hiſce vero
                    <lb/>
                  datis dabitur & reſiſtentia Medii in loco
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  quippe quæ ſit ad vim
                    <lb/>
                  gravitatis ut
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  ad 2
                    <emph type="italics"/>
                  AI.
                    <emph.end type="italics"/>
                  Augenda eſt autem denſitas. </s>
                  <s>Medii per
                    <lb/>
                  Reg. </s>
                  <s>4; & reſiſtentia modo inventa, ſi in eadem ratione augeatur, fiet
                    <lb/>
                  accuratior. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum