Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
191
191 		192
192
193
193 		194
194
195
195 		196
196
197
197 		198
198
199
199 		200
200
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/194.jpg" pagenum="166"/>
                    <arrow.to.target n="note142"/>
                  revolutionis quam proxime. </s>
                  <s>Conjungantur hæ rationes cum ratio­
                    <lb/>
                  nibus Corollarii 14, & in quolibet corporum
                    <emph type="italics"/>
                  T, P, S
                    <emph.end type="italics"/>
                  Syſtemate,
                    <lb/>
                  ubi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  circum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ſibi propinquum, &
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  circum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  longinquum re­
                    <lb/>
                  volvitur, errores angulares corporis
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  de centro
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  apparentes,
                    <lb/>
                  erunt, in ſingulis revolutionibus corporis illius
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ut quadratum
                    <lb/>
                  temporis periodici corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  directe & quadratum temporis pe­
                    <lb/>
                  riodici corporis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  inverſe. </s>
                  <s>Et inde motus medius Augis erit in da­
                    <lb/>
                  ta ratione ad motum medium Nodorum; & motus uterque erit ut tempus periodicum corporis &c. </s>
                  <s>
                    <lb/>
                  quadratum temporis periodici corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  directe & quadratum
                    <lb/>
                  temporis periodici corporis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  inverſe. </s>
                  <s>Augendo vel minuendo
                    <lb/>
                  Excentricitatem & Inclinationem Orbis
                    <emph type="italics"/>
                  PAB
                    <emph.end type="italics"/>
                  non mutantur mo­
                    <lb/>
                  tus Augis & Nodorum ſenſibiliter, niſi ubi eædem ſunt nimis
                    <lb/>
                  magnæ. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note142"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  17. Cum autem linea
                    <emph type="italics"/>
                  LM
                    <emph.end type="italics"/>
                  nunc major ſit nunc minor
                    <lb/>
                  quam radius
                    <emph type="italics"/>
                  PT,
                    <emph.end type="italics"/>
                  exponatur vis mediocris
                    <emph type="italics"/>
                  LM
                    <emph.end type="italics"/>
                  per radium il­
                    <lb/>
                  lum
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ; & erit hæc ad
                    <lb/>
                    <figure id="id.039.01.194.1.jpg" xlink:href="039/01/194/1.jpg" number="112"/>
                    <lb/>
                  vim mediocrem
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                    <lb/>
                  vel
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  (quam expo­
                    <lb/>
                  nere licet per
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  ) ut
                    <lb/>
                  longitudo
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ad lon­
                    <lb/>
                  gitudinem
                    <emph type="italics"/>
                  ST.
                    <emph.end type="italics"/>
                  Eſt au­
                    <lb/>
                  tem vis mediocris
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                    <lb/>
                  vel
                    <emph type="italics"/>
                  ST,
                    <emph.end type="italics"/>
                  qua corpus
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                    <lb/>
                  retinetur in Orbe ſuo
                    <lb/>
                  circum
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  ad vim qua
                    <lb/>
                  corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  retinetur in Orbe ſuo circum
                    <emph type="italics"/>
                  T,
                    <emph.end type="italics"/>
                  in ratione compoſita ex
                    <lb/>
                  ratione radii
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  ad radium
                    <emph type="italics"/>
                  PT,
                    <emph.end type="italics"/>
                  & ratione duplicata temporis pe­
                    <lb/>
                  riodici corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  circum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ad tempus periodicum corporis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                    <lb/>
                  circum
                    <emph type="italics"/>
                  S.
                    <emph.end type="italics"/>
                  Et ex æquo, vis mediocris
                    <emph type="italics"/>
                  LM,
                    <emph.end type="italics"/>
                  ad vim qua corpus
                    <lb/>
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  retinetur in Orbe ſuo circum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  (quave corpus idem
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  eo­
                    <lb/>
                  dem tempore periodico, circum punctum quodvis immobile
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  diſtantiam
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  revolvi poſſet) eſt in ratione illa duplicata periodi­
                    <lb/>
                  eorum temporum. </s>
                  <s>Datis igitur temporibus periodicis una cum di­
                    <lb/>
                  ſtantia
                    <emph type="italics"/>
                  PT,
                    <emph.end type="italics"/>
                  datur vis mediocris
                    <emph type="italics"/>
                  LM
                    <emph.end type="italics"/>
                  ; & ea data, datur etiam vis
                    <lb/>
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  quamproxime per analogiam linearum
                    <emph type="italics"/>
                  PT, MN.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  18. Iiſdem legibus quibus corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  circum corpus
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  re­
                    <lb/>
                  volvitur, fingamus corpora plura fluida circum idem
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ad æqua­
                    <lb/>
                  les ab ipſo diſtantias moveri; deinde ex his contiguis factis confla­
                    <lb/>
                  ri Annulum fluidum, rotundum ac corpori
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  concentricum; &
                    <lb/>
                  ſingulæ Annuli partes, motus ſuos omnes ad legem corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  per-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum