Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
481
481 		482
482
483
483 		484
484
485
485 		486
486
487
487 		488
488
489
489 		490
490
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/481.jpg" pagenum="453"/>
                  Et per punctum
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  agatur (per hujus Lem. </s>
                  <s>VII.) recta
                    <emph type="italics"/>
                  AEC,
                    <emph.end type="italics"/>
                    <lb/>
                    <arrow.to.target n="note482"/>
                  cujus partes
                    <emph type="italics"/>
                  AE, EC
                    <emph.end type="italics"/>
                  ad rectas
                    <emph type="italics"/>
                  TA
                    <emph.end type="italics"/>
                  &
                    <foreign lang="grc">τ</foreign>
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  terminatæ, ſint ad
                    <lb/>
                  invicem ut tempora V & W: & erunt
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  loca Cometæ in
                    <lb/>
                  plano Eclipticæ in obſervatione prima ac tertia quamproxime, ſi
                    <lb/>
                  modo
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ſit locus ejus recte aſſumptus in obſervatione ſecunda. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note482"/>
                  LIBER
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>Ad
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  biſectam in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  erige perpendiculum
                    <emph type="italics"/>
                  Ii.
                    <emph.end type="italics"/>
                  Per punctum
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                    <lb/>
                  age occultam
                    <emph type="italics"/>
                  Bi
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  parallelam. </s>
                  <s>Junge occultam
                    <emph type="italics"/>
                  Si
                    <emph.end type="italics"/>
                  ſecan­
                    <lb/>
                  tem
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  in
                    <foreign lang="grc">λ</foreign>
                  , & comple parallelogrammum
                    <emph type="italics"/>
                  iI
                    <emph.end type="italics"/>
                    <foreign lang="grc">λμ. </foreign>
                  </s>
                  <s>Cape
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                    <foreign lang="grc">σ</foreign>
                  æqua­
                    <lb/>
                  lem 3
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                    <foreign lang="grc">λ</foreign>
                  , & per Solem
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  age occultam
                    <foreign lang="grc">σξ</foreign>
                  æqualem 3
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">σ</foreign>
                  +3
                    <emph type="italics"/>
                  i
                    <emph.end type="italics"/>
                    <foreign lang="grc">λ</foreign>
                  ,
                    <lb/>
                  Et deletis jam literis
                    <emph type="italics"/>
                  A, E, C, I,
                    <emph.end type="italics"/>
                  a puncto
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  verſus punctum
                    <foreign lang="grc">ξ</foreign>
                    <lb/>
                  duc occultam novam
                    <emph type="italics"/>
                  BE,
                    <emph.end type="italics"/>
                  quæ ſit ad priorem
                    <emph type="italics"/>
                  BE
                    <emph.end type="italics"/>
                  in duplicata
                    <lb/>
                  ratione diſtantiæ
                    <emph type="italics"/>
                  BS
                    <emph.end type="italics"/>
                  ad quantitatem
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  +1/3
                    <emph type="italics"/>
                  i
                    <emph.end type="italics"/>
                    <foreign lang="grc">λ. </foreign>
                  </s>
                  <s>Et per punctum
                    <lb/>
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  iterum duc rectam
                    <emph type="italics"/>
                  AEC
                    <emph.end type="italics"/>
                  eadem lege ac prius, id eſt, ita ut ejus
                    <lb/>
                  partes
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EC
                    <emph.end type="italics"/>
                  ſint ad invicem, ut tempora inter obſervationes
                    <lb/>
                  V & W. </s>
                  <s>Et erunt
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  loca Cometæ magis accurate. </s>
                </p>
                <p type="main">
                  <s>Ad
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  biſectam in
                    <emph type="italics"/>
                  1
                    <emph.end type="italics"/>
                  erigantur perpendicula
                    <emph type="italics"/>
                  AM, CN, IO,
                    <emph.end type="italics"/>
                    <lb/>
                  quarum
                    <emph type="italics"/>
                  AM
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CN
                    <emph.end type="italics"/>
                  ſint tangentes latitudinum in obſervatione
                    <lb/>
                  prima ac tertia ad radios
                    <emph type="italics"/>
                  TA
                    <emph.end type="italics"/>
                  &
                    <foreign lang="grc">τ</foreign>
                    <emph type="italics"/>
                  C.
                    <emph.end type="italics"/>
                  Jungatur
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  ſecans
                    <emph type="italics"/>
                  IO
                    <emph.end type="italics"/>
                    <lb/>
                  in
                    <emph type="italics"/>
                  O.
                    <emph.end type="italics"/>
                  Conſtituatur rectangulum
                    <emph type="italics"/>
                  iI
                    <emph.end type="italics"/>
                    <foreign lang="grc">λμ</foreign>
                  ut prius. </s>
                  <s>In
                    <emph type="italics"/>
                  IA
                    <emph.end type="italics"/>
                  pro­
                    <lb/>
                  ducta capiatur
                    <emph type="italics"/>
                  ID
                    <emph.end type="italics"/>
                  æqualis
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  +2/3
                    <emph type="italics"/>
                  i
                    <emph.end type="italics"/>
                    <foreign lang="grc">λ</foreign>
                  , & agatur occulta
                    <emph type="italics"/>
                  OD.
                    <emph.end type="italics"/>
                    <lb/>
                  Deinde in
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  N
                    <emph.end type="italics"/>
                  capiatur
                    <emph type="italics"/>
                  MP,
                    <emph.end type="italics"/>
                  quæ ſit ad longitudinem
                    <lb/>
                  ſupra inventam X, in ſubduplicata ratione mediocris diſtantiæ Tel­
                    <lb/>
                  luris a Sole (ſeu ſemidiametri Orbis magni) ad diſtantiam
                    <emph type="italics"/>
                  OD.
                    <emph.end type="italics"/>
                    <lb/>
                  Si punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  incidat in punctum
                    <emph type="italics"/>
                  N
                    <emph.end type="italics"/>
                  ; erunt
                    <emph type="italics"/>
                  A, B, C
                    <emph.end type="italics"/>
                  tria loca Co­
                    <lb/>
                  metæ, per quæ Orbis ejus in plano Eclipticæ deſcribi debet. </s>
                  <s>Sin
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  non incidat in punctum
                    <emph type="italics"/>
                  N
                    <emph.end type="italics"/>
                  ; in recta
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  capiatur
                    <lb/>
                    <emph type="italics"/>
                  CG
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  NP
                    <emph.end type="italics"/>
                  æqualis, ita ut puncta
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ad eaſdem partes
                    <lb/>
                  rectæ
                    <emph type="italics"/>
                  NC
                    <emph.end type="italics"/>
                  jaceant. </s>
                </p>
                <p type="main">
                  <s>Eadem methodo qua puncta
                    <emph type="italics"/>
                  E, A, C, G,
                    <emph.end type="italics"/>
                  ex aſſumpto puncto
                    <lb/>
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  inventa ſunt, inveniantur ex aſſumptis utcunque punctis aliis
                    <lb/>
                    <emph type="italics"/>
                  b
                    <emph.end type="italics"/>
                  &
                    <foreign lang="grc">β</foreign>
                  puncta nova
                    <emph type="italics"/>
                  e, a, c, g,
                    <emph.end type="italics"/>
                  &
                    <foreign lang="grc">ε, α, χ, γ. </foreign>
                  </s>
                  <s>Deinde ſi per
                    <emph type="italics"/>
                  G, g,
                    <emph.end type="italics"/>
                    <foreign lang="grc">γ</foreign>
                    <lb/>
                  ducatur circumferentia circuli
                    <emph type="italics"/>
                  Gg
                    <emph.end type="italics"/>
                    <foreign lang="grc">γ</foreign>
                  , ſecans rectam
                    <foreign lang="grc">τ</foreign>
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  : erit
                    <lb/>
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  locus Cometæ in plano Eclipticæ. </s>
                  <s>Et ſi in
                    <emph type="italics"/>
                  AC, ac,
                    <emph.end type="italics"/>
                    <foreign lang="grc">αχ</foreign>
                  capi­
                    <lb/>
                  antur
                    <emph type="italics"/>
                  AF, af,
                    <emph.end type="italics"/>
                    <foreign lang="grc">αφ</foreign>
                  ipſis
                    <emph type="italics"/>
                  CG, eg,
                    <emph.end type="italics"/>
                    <foreign lang="grc">χγ</foreign>
                  reſpective æquales, & per
                    <lb/>
                  puncta
                    <emph type="italics"/>
                  F, f,
                    <emph.end type="italics"/>
                    <foreign lang="grc">φ</foreign>
                  ducatur circumferentia circuli
                    <emph type="italics"/>
                  Ff
                    <emph.end type="italics"/>
                    <foreign lang="grc">φ</foreign>
                  , ſecans rectam
                    <lb/>
                    <emph type="italics"/>
                  AT
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  X;
                    <emph.end type="italics"/>
                  erit punctum
                    <emph type="italics"/>
                  X
                    <emph.end type="italics"/>
                  alius Cometæ locus in plano Eclipticæ. </s>
                  <s>
                    <lb/>
                  Ad puncta
                    <emph type="italics"/>
                  X
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  erigantur tangentes latitudinum Cometæ ad ra­
                    <lb/>
                  dios
                    <emph type="italics"/>
                  TX
                    <emph.end type="italics"/>
                  &
                    <foreign lang="grc">τ</foreign>
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  ; & habebuntur loca duo Cometæ in Orbe proprio. </s>
                  <s>
                    <lb/>
                  Denique (per Prop. </s>
                  <s>XIX. Lib. </s>
                  <s>I.) umbilico
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  per loca illa duo de­
                    <lb/>
                  ſcribatur Parabola, & hæc erit Trajectoria Cometæ.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum