Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/427.jpg" pagenum="399"/>
                  ter ſe in ultima proportione Sinuum vel Tangentium angulorum
                    <lb/>
                    <arrow.to.target n="note428"/>
                  contactuum ad radios æquales pertinentium, ubi radii illi in infi­
                    <lb/>
                  nitum diminuuntur. </s>
                  <s>Attractio autem Lunæ in Terram in Syzy­
                    <lb/>
                  giis eſt exceſſus gravitatis ipſius in Terram ſupra vim Solarem
                    <lb/>
                  2
                    <emph type="italics"/>
                  PK
                    <emph.end type="italics"/>
                  (Vide
                    <emph type="italics"/>
                  Figur. </s>
                  <s>pag.
                    <emph.end type="italics"/>
                  394) qua gravitas acceleratrix Lunæ in
                    <lb/>
                  Solem ſuperat gravitatem acceleratricem Terræ in Solem. </s>
                  <s>In Qua­
                    <lb/>
                  draturis autem attractio illa eſt ſumma gravitatis Lunæ in Terram
                    <lb/>
                  & vis Solaris
                    <emph type="italics"/>
                  KT,
                    <emph.end type="italics"/>
                  qua Luna in Terram trahitur. </s>
                  <s>Et hæ attra­
                    <lb/>
                  ctiones, ſi (
                    <emph type="italics"/>
                  AT+CT
                    <emph.end type="italics"/>
                  /2) dicatur N, ſunt ut (178725/
                    <emph type="italics"/>
                  ATq
                    <emph.end type="italics"/>
                  )-(2000/
                    <emph type="italics"/>
                  CTXN
                    <emph.end type="italics"/>
                  ) &
                    <lb/>
                  (178725/
                    <emph type="italics"/>
                  CIq
                    <emph.end type="italics"/>
                  )+(1000/
                    <emph type="italics"/>
                  ATXN
                    <emph.end type="italics"/>
                  ) quam proxime; ſeu ut 178725NX
                    <emph type="italics"/>
                  CTq
                    <emph.end type="italics"/>
                    <lb/>
                  -2000
                    <emph type="italics"/>
                  ATqXCT
                    <emph.end type="italics"/>
                  & 178725 NX
                    <emph type="italics"/>
                  ATq
                    <emph.end type="italics"/>
                  +1000
                    <emph type="italics"/>
                  CTqXAT.
                    <emph.end type="italics"/>
                  Nam
                    <lb/>
                  ſi gravitas acceleratrix Lunæ in Terram exponatur per numerum
                    <lb/>
                  178725, vis mediocris
                    <emph type="italics"/>
                  ML,
                    <emph.end type="italics"/>
                  quæ in Quadraturis eſt
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  vel
                    <lb/>
                    <emph type="italics"/>
                  TK
                    <emph.end type="italics"/>
                  & Lunam trahit in Ter­
                    <lb/>
                    <figure id="id.039.01.427.1.jpg" xlink:href="039/01/427/1.jpg" number="208"/>
                    <lb/>
                  ram, erit 1000, & vis me­
                    <lb/>
                  diocris
                    <emph type="italics"/>
                  TM
                    <emph.end type="italics"/>
                  in Syzygiis erit
                    <lb/>
                  3000; de qua, ſi vis medio­
                    <lb/>
                  cris
                    <emph type="italics"/>
                  ML
                    <emph.end type="italics"/>
                  ſubducatur, mane­
                    <lb/>
                  bit vis 2000 qua Luna in
                    <lb/>
                  Syzygiis diſtrahitur a Terra,
                    <lb/>
                  quamque jam ante nominavi
                    <lb/>
                  2
                    <emph type="italics"/>
                  PK.
                    <emph.end type="italics"/>
                  Velocitas autem Lu­
                    <lb/>
                  næ in Syzygiis
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  eſt ad
                    <lb/>
                  ipſius velocitatem in Qua­
                    <lb/>
                  draturis
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  CT
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  AT
                    <emph.end type="italics"/>
                  & momentum areæ quam
                    <lb/>
                  Luna radio ad Terram du­
                    <lb/>
                  cto deſcribit in Syzygiis ad
                    <lb/>
                  momentum ejuſdem areæ in
                    <lb/>
                  Quadraturis conjunctim; i.e. </s>
                  <s>
                    <lb/>
                  ut 11073
                    <emph type="italics"/>
                  CT
                    <emph.end type="italics"/>
                  ad 10973
                    <emph type="italics"/>
                  AT.
                    <emph.end type="italics"/>
                    <lb/>
                  Sumatur hæc ratio bis in­
                    <lb/>
                  verſe & ratio prior ſemel directe, & fiet curvatura Orbis Lu­
                    <lb/>
                  naris in Syzygiis ad ejuſdem curvaturam in Quadraturis ut
                    <lb/>
                  120406729X178725
                    <emph type="italics"/>
                  ATqXCTq
                    <emph.end type="italics"/>
                  XN-120406729X2000
                    <emph type="italics"/>
                  ATqq
                    <lb/>
                  XCT
                    <emph.end type="italics"/>
                  ad 122611329X178725
                    <emph type="italics"/>
                  ATqXCTq
                    <emph.end type="italics"/>
                  XN+122611329X
                    <lb/>
                  1000
                    <emph type="italics"/>
                  CTqqXAT, i.e.
                    <emph.end type="italics"/>
                  ut 2151969
                    <emph type="italics"/>
                  ATXCT
                    <emph.end type="italics"/>
                  XN-24081
                    <emph type="italics"/>
                  AT cub.
                    <emph.end type="italics"/>
                    <lb/>
                  ad 2191371
                    <emph type="italics"/>
                  ATXCT
                    <emph.end type="italics"/>
                  XN+12261
                    <emph type="italics"/>
                  CT cub.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
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