Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  <s>
                    <pb xlink:href="039/01/294.jpg" pagenum="266"/>
                    <arrow.to.target n="note242"/>
                  tatem
                    <emph type="italics"/>
                  BI
                    <emph.end type="italics"/>
                  ut ſumma omnium
                    <emph type="italics"/>
                  AH+BI+CK+DL,
                    <emph.end type="italics"/>
                  in infiNI­
                    <lb/>
                  tum, ad ſummam omnium
                    <emph type="italics"/>
                  BI+CK+DL,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Et
                    <emph type="italics"/>
                  BI
                    <emph.end type="italics"/>
                  den­
                    <lb/>
                  ſitas ſecundæ
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  eſt ad
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  denſitatem tertiæ
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  ut ſumma om­
                    <lb/>
                  nium
                    <emph type="italics"/>
                  BI+CK+DL,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ad ſummam omnium
                    <emph type="italics"/>
                  CK+DL,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>
                    <lb/>
                  Sunt igitur ſummæ illæ differentiis ſuis
                    <emph type="italics"/>
                  AH, BI, CK,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>pro­
                    <lb/>
                  portionales, atque adeo continue proportionales, per hujus Lem. </s>
                  <s>I.
                    <lb/>
                  proindeQ.E.D.fferentiæ
                    <emph type="italics"/>
                  AH, BI, CK,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ſummis proportionales,
                    <lb/>
                  ſunt etiam continue proportionales. </s>
                  <s>Quare cum denſitates in locis
                    <emph type="italics"/>
                  A,
                    <lb/>
                  B, C,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ſint ut
                    <emph type="italics"/>
                  AH, BI, CK,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>erunt etiam hæ continue propor­
                    <lb/>
                  tionales. </s>
                  <s>Pergatur per ſaltum, & (ex æquo) in diſtantiis
                    <emph type="italics"/>
                  SA, SC,
                    <lb/>
                  SE
                    <emph.end type="italics"/>
                  continue proportionalibus, erunt denſitates
                    <emph type="italics"/>
                  AH, CK, EM
                    <emph.end type="italics"/>
                    <lb/>
                  continue proportionales. </s>
                  <s>Et eodem argumento, in diſtantiis qui­
                    <lb/>
                  buſvis continue proportionalibus
                    <emph type="italics"/>
                  SA, SD, SG,
                    <emph.end type="italics"/>
                  denſitates
                    <emph type="italics"/>
                  AH, DL,
                    <lb/>
                  GO
                    <emph.end type="italics"/>
                  erunt continue proportionales. </s>
                  <s>Coeant jam puncta
                    <emph type="italics"/>
                  A, B, C,
                    <lb/>
                  D, E,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>eo ut progreſſio gravitatum ſpecificarum a fundo
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  ſummitatem Fluidi continua reddatur, & in diſtantiis quibuſvis con­
                    <lb/>
                  tinue proportionalibus
                    <emph type="italics"/>
                  SA, SD, SG,
                    <emph.end type="italics"/>
                  denſitates
                    <emph type="italics"/>
                  AH, DL, GO,
                    <emph.end type="italics"/>
                    <lb/>
                  ſemper exiſtentes continue proportionales, manebunt etiamnum
                    <lb/>
                  continue proportionales.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note242"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Hinc ſi detur denſitas Fluidi in duobus locis, puta
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  E,
                    <emph.end type="italics"/>
                  colligi poteſt ejus denſitas
                    <lb/>
                    <figure id="id.039.01.294.1.jpg" xlink:href="039/01/294/1.jpg" number="171"/>
                    <lb/>
                  in alio quovis loco
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                    <emph.end type="italics"/>
                  Centro
                    <lb/>
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  Aſymptotis rectangulis
                    <emph type="italics"/>
                  SQ,
                    <lb/>
                  SX,
                    <emph.end type="italics"/>
                  deſcribatur Hyperbola ſe­
                    <lb/>
                  cans perpendicula
                    <emph type="italics"/>
                  AH, EM,
                    <lb/>
                  QT
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  a, e, q,
                    <emph.end type="italics"/>
                  ut & perpendicu­
                    <lb/>
                  la
                    <emph type="italics"/>
                  HX, MY, TZ,
                    <emph.end type="italics"/>
                  ad Aſymp­
                    <lb/>
                  toton
                    <emph type="italics"/>
                  SX
                    <emph.end type="italics"/>
                  demiſſa, in
                    <emph type="italics"/>
                  h, m
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  t.
                    <emph.end type="italics"/>
                    <lb/>
                  Fiat area
                    <emph type="italics"/>
                  ZYmtZ
                    <emph.end type="italics"/>
                  ad aream da­
                    <lb/>
                  tam
                    <emph type="italics"/>
                  YmhX
                    <emph.end type="italics"/>
                  ut area data
                    <emph type="italics"/>
                  EeqQ
                    <emph.end type="italics"/>
                    <lb/>
                  ad aream datam
                    <emph type="italics"/>
                  EeaA
                    <emph.end type="italics"/>
                  ; & li­
                    <lb/>
                  nea
                    <emph type="italics"/>
                  Zt
                    <emph.end type="italics"/>
                  producta abſcindet li­
                    <lb/>
                  neam
                    <emph type="italics"/>
                  QT
                    <emph.end type="italics"/>
                  denſitati proportio­
                    <lb/>
                  nalem. </s>
                  <s>Namque ſi lineæ
                    <emph type="italics"/>
                  SA, SE, SQ
                    <emph.end type="italics"/>
                  ſunt continue proportiona­
                    <lb/>
                  les, erunt areæ
                    <emph type="italics"/>
                  EeqQ, EeaA
                    <emph.end type="italics"/>
                  æquales, & inde areæ his propor­
                    <lb/>
                  tionales
                    <emph type="italics"/>
                  YmtZ, XhmY
                    <emph.end type="italics"/>
                  etiam æquales, & lineæ
                    <emph type="italics"/>
                  SX, SY, SZ,
                    <emph.end type="italics"/>
                  id eſt
                    <lb/>
                    <emph type="italics"/>
                  AH, EM, QT
                    <emph.end type="italics"/>
                  continue proportionales, ut oportet. </s>
                  <s>Et ſi lineæ
                    <lb/>
                    <emph type="italics"/>
                  SA, SE, SQ
                    <emph.end type="italics"/>
                  obtinent alium quemvis ordinem in ſerie continue
                    <lb/>
                  proportionalium, lineæ
                    <emph type="italics"/>
                  AH, EM, QT,
                    <emph.end type="italics"/>
                  ob proportionales areas
                    <lb/>
                  Hyperbolicas, obtinebunt eundem ordinem in alia ſerie quantita­
                    <lb/>
                  tum continue proportionalium. </s>
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