Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
281
281 		282
282
283
283 		284
284
285
285 		286
286
287
287 		288
288
289
289 		290
290
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/283.jpg" pagenum="255"/>
                  duplicata ratione ipſius
                    <emph type="italics"/>
                  SQ
                    <emph.end type="italics"/>
                  reciproce. </s>
                  <s>Sunt autem arcus illi
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                    <lb/>
                    <arrow.to.target n="note231"/>
                  &
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  ut velocitates deſcriptrices ad invicem, id eſt, in ſubdupli­
                    <lb/>
                  cata ratione
                    <emph type="italics"/>
                  SQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SP,
                    <emph.end type="italics"/>
                  ſive ut
                    <emph type="italics"/>
                  SQ
                    <emph.end type="italics"/>
                  ad √
                    <emph type="italics"/>
                  SPXSQ
                    <emph.end type="italics"/>
                  ; & ob æqua­
                    <lb/>
                  les angulos
                    <emph type="italics"/>
                  SPQ, SQr
                    <emph.end type="italics"/>
                  & æquales areas
                    <emph type="italics"/>
                  PSQ, QSr,
                    <emph.end type="italics"/>
                  eſt ar­
                    <lb/>
                  cus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad arcum
                    <emph type="italics"/>
                  Qr
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  SQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  Sumantur proportionalium
                    <lb/>
                  conſequentium differentiæ, & fiet arcus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad arcum
                    <emph type="italics"/>
                  Rr
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  SQ
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  SP-√SPXSQ,
                    <emph.end type="italics"/>
                  ſeu 1/2
                    <emph type="italics"/>
                  VQ
                    <emph.end type="italics"/>
                  ; nam punctis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  coeunti­
                    <lb/>
                  bus, ratio ultima
                    <emph type="italics"/>
                  SP-√SPXSQ
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  VQ
                    <emph.end type="italics"/>
                  ſit æqualitatis. </s>
                  <s>
                    <lb/>
                  Quoniam decrementum arcus
                    <emph type="italics"/>
                  PQ,
                    <emph.end type="italics"/>
                  ex reſiſtentia oriundum, ſive
                    <lb/>
                  hujus duplum
                    <emph type="italics"/>
                  Rr,
                    <emph.end type="italics"/>
                  eſt ut reſiſtentia & quadratum temporis con­
                    <lb/>
                  junctim; erit reſiſtentia ut (
                    <emph type="italics"/>
                  Rr/PQqXSP
                    <emph.end type="italics"/>
                  ). Erat autem
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Rr,
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  SQ
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  VQ,
                    <emph.end type="italics"/>
                  & inde (
                    <emph type="italics"/>
                  Rr/PQqXSP
                    <emph.end type="italics"/>
                  ) fit ut (1/2
                    <emph type="italics"/>
                  VQ/PQXSPXSQ
                    <emph.end type="italics"/>
                  ) ſive
                    <lb/>
                  ut (1/2
                    <emph type="italics"/>
                  OS/OPXSPq
                    <emph.end type="italics"/>
                  ). Namque punctis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  coeuntibus,
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SQ
                    <emph.end type="italics"/>
                    <lb/>
                  coincidunt, & angulus
                    <emph type="italics"/>
                  PVQ
                    <emph.end type="italics"/>
                  fit rectus; & ob ſimilia triangula
                    <lb/>
                    <emph type="italics"/>
                  PVQ, PSO,
                    <emph.end type="italics"/>
                  fit
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  VQ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  OP
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  OS.
                    <emph.end type="italics"/>
                  Eſt igitur
                    <lb/>
                  (
                    <emph type="italics"/>
                  OS/OPXSPq
                    <emph.end type="italics"/>
                  ) ut reſiſtentia, id eſt, in ratione denſitatis Medii in
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                    <lb/>
                  & ratione duplicata velocitatis conjunctim. </s>
                  <s>Auferatur duplicata
                    <lb/>
                  ratio velocitatis, nempe ratio (1/
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  ), & manebit Medii denſitas in
                    <lb/>
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ut (
                    <emph type="italics"/>
                  OS/OPXSP
                    <emph.end type="italics"/>
                  ). Detur Spiralis, & ob datam rationem
                    <emph type="italics"/>
                  OS
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  OP,
                    <emph.end type="italics"/>
                  denſitas Medii in
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  erit ut (1/
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  ). In Medio igitur cujus
                    <lb/>
                  denſitas eſt reciproce ut diſtantia a centro
                    <emph type="italics"/>
                  SP,
                    <emph.end type="italics"/>
                  corpus gyrari po­
                    <lb/>
                  teſt in hac Spirali.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note231"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Velocitas in loco quovis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ea ſemper eſt quacum cor­
                    <lb/>
                  pus in Medio non reſiſtente gyrari poteſt in Circulo, ad eandem a
                    <lb/>
                  centro diſtantiam
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Medii denſitas, ſi datur diſtantia
                    <emph type="italics"/>
                  SP,
                    <emph.end type="italics"/>
                  eſt ut (
                    <emph type="italics"/>
                  OS/OP
                    <emph.end type="italics"/>
                  ), ſin
                    <lb/>
                  diſtantia illa non datur, ut (
                    <emph type="italics"/>
                  OS/OPXSP
                    <emph.end type="italics"/>
                  ). Et inde Spiralis ad quam­
                    <lb/>
                  libet Medii denſitatem aptari poteſt. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Vis reſiſtentiæ in loco quovis
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  eſt ad vim centripe-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum