Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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      <text>
        <body>
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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/507.jpg" pagenum="476"/>
                    <arrow.to.target n="note505"/>
                  prædictis tribus Cometæ locis obſervatis, inveniantur in hoc novo
                    <lb/>
                  plano loca tria vera (at ſupra:) deinde etiam Orbis per loca
                    <lb/>
                  illa tranſiens, & ejuſdem areæ duæ inter obſervationes deſcriptæ,
                    <lb/>
                  quæ ſint
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  e,
                    <emph.end type="italics"/>
                  nec non tempus totum
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  quo area tota
                    <emph type="italics"/>
                  d+e
                    <emph.end type="italics"/>
                  de­
                    <lb/>
                  ſcribi debeat. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note505"/>
                  DE MUNDI
                    <lb/>
                  SYSTEMATE</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Oper.
                    <emph.end type="italics"/>
                  3. Servetur Longitudo Nodorum in operatione prima, &
                    <lb/>
                  augeatur inclinatio Plani Trajectoriæ ad planum Eclipticæ, addi­
                    <lb/>
                  tis ad inclinationem illam 20′ vel 30′, quæ dicantur
                    <expan abbr="q.">que</expan>
                  Deinde
                    <lb/>
                  ex obſervatis prædictis tribus Cometæ locis apparentibus, inve­
                    <lb/>
                  niantur in hoc novo Plano loca tria vera, Orbiſque per loca
                    <lb/>
                  illa tranſiens, ut & ejuſdem areæ duæ inter obſervationes de­
                    <lb/>
                  ſcriptæ, quæ ſint
                    <foreign lang="grc">δ</foreign>
                  &
                    <foreign lang="grc">ε</foreign>
                  , & tempus totum
                    <foreign lang="grc">τ</foreign>
                  quo area tota
                    <foreign lang="grc">δ</foreign>
                  +
                    <foreign lang="grc">ε</foreign>
                    <lb/>
                  deſcribi debeat. </s>
                </p>
                <p type="main">
                  <s>Jam ſit C ad I ut A ad B, & G ad 1 ut D ad E, &
                    <emph type="italics"/>
                  g
                    <emph.end type="italics"/>
                  ad 1 ut
                    <lb/>
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  e,
                    <emph.end type="italics"/>
                  &
                    <foreign lang="grc">γ</foreign>
                  ad 1 ut
                    <foreign lang="grc">δ</foreign>
                  ad
                    <foreign lang="grc">ε</foreign>
                  ; ſitque S tempus verum inter obſerva­
                    <lb/>
                  tionem primam ac tertiam; & ſignis + & -probe obſervatis
                    <lb/>
                  quærantur numeri
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  n,
                    <emph.end type="italics"/>
                  ea lege, ut ſit 2G-2C=
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  G-
                    <emph type="italics"/>
                  mg+
                    <lb/>
                  n
                    <emph.end type="italics"/>
                  G-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <foreign lang="grc">γ</foreign>
                  , & 2T-2S æquale
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  T-
                    <emph type="italics"/>
                  mt+n
                    <emph.end type="italics"/>
                  T-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <foreign lang="grc">τ. </foreign>
                  </s>
                  <s>Et ſi, in
                    <lb/>
                  operatione prima, I deſignet inclinationem plani Trajectoriæ ad
                    <lb/>
                  planum Eclipticæ, & K longitudinem Nodi alterutrius, erit
                    <lb/>
                  I+
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  Q vera inclinatio Plani Trajectoriæ ad Planum Eclipticæ, &
                    <lb/>
                  K+
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  P vera longitudo Nodi. </s>
                  <s>Ac denique ſi in operatione
                    <lb/>
                  prima, ſecunda ac tertia, quantitates R,
                    <emph type="italics"/>
                  r
                    <emph.end type="italics"/>
                  &
                    <foreign lang="grc">ρ</foreign>
                  deſignent Latera
                    <lb/>
                  recta Trajectoriæ, & quantitates 1/L, 1/
                    <emph type="italics"/>
                  l,
                    <emph.end type="italics"/>
                  1/
                    <foreign lang="grc">λ</foreign>
                  ejuſdem Latera tranſ­
                    <lb/>
                  verſa reſpective: erit R+
                    <emph type="italics"/>
                  mr-m
                    <emph.end type="italics"/>
                  R+
                    <emph type="italics"/>
                  n
                    <foreign lang="grc">ρ</foreign>
                  -n
                    <emph.end type="italics"/>
                  R verum Latus re­
                    <lb/>
                  ctum, & (1/L+
                    <emph type="italics"/>
                  ml-m
                    <emph.end type="italics"/>
                  L+
                    <emph type="italics"/>
                  n
                    <foreign lang="grc">λ</foreign>
                  -n
                    <emph.end type="italics"/>
                  L) verum Latus tranſverſum Tra­
                    <lb/>
                  jectoriæ quam Cometa deſcribit. </s>
                  <s>Dato autem Latere tranſverſo
                    <lb/>
                  datur etiam tempus periodicum Cometæ.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Cæterum Cometarum revolventium tempora periodica, & Or­
                    <lb/>
                  bium latera tranſverſa, haud ſatis accurate determinabuntur, niſi
                    <lb/>
                  per collationem Cometarum inter ſe, qui diverſis temporibus ap­
                    <lb/>
                  parent. </s>
                  <s>Si plures Cometæ, poſt æqualia temporum intervalla,
                    <lb/>
                  eundem Orbem deſcripſiſſe reperiantur, concludendum erit hos
                    <lb/>
                  omnes eſſe unum & eundem Cometam, in eodem Orbe revolven­
                    <lb/>
                  tem. </s>
                  <s>Et tum demum ex revolutionum temporibus, dabuntur Or­
                    <lb/>
                  bium latera tranſverſa, & ex his lateribus determinabuntur Or­
                    <lb/>
                  bes Elliptici. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
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    </archimedes>
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