Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                    <pb xlink:href="039/01/167.jpg" pagenum="139"/>
                  dio) ut
                    <emph type="italics"/>
                  BW
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BV,
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  AO+OR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AO,
                    <emph.end type="italics"/>
                  id eſt (cum ſint
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                    <lb/>
                    <arrow.to.target n="note115"/>
                  ad
                    <emph type="italics"/>
                  CO, CO
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CR
                    <emph.end type="italics"/>
                  & diviſim
                    <emph type="italics"/>
                  AO
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OR
                    <emph.end type="italics"/>
                  proportionales,) ut
                    <lb/>
                    <emph type="italics"/>
                  CA+CO
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  vel, ſi biſecetur
                    <emph type="italics"/>
                  BV
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  E,
                    <emph.end type="italics"/>
                  ut 2
                    <emph type="italics"/>
                  CE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CB.
                    <emph.end type="italics"/>
                    <lb/>
                  Proinde, per Corol. </s>
                  <s>1. Prop. </s>
                  <s>XLIX, longitudo partis rectæ Fili
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                    <lb/>
                  æquatur ſemper Cycloidis arcui
                    <emph type="italics"/>
                  PS,
                    <emph.end type="italics"/>
                  & Filum totum
                    <emph type="italics"/>
                  APT
                    <emph.end type="italics"/>
                  æquatur
                    <lb/>
                  ſemper Cycloidis arcui dimidio
                    <emph type="italics"/>
                  APS,
                    <emph.end type="italics"/>
                  hoc eſt (per Corol. </s>
                  <s>2. Prop. </s>
                  <s>
                    <lb/>
                  XLIX) longitudini
                    <emph type="italics"/>
                  AR.
                    <emph.end type="italics"/>
                  Et propterea viciſſim ſi Filum manet ſem­
                    <lb/>
                  per æquale longitudini
                    <emph type="italics"/>
                  AR
                    <emph.end type="italics"/>
                  movebitur punctum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  in Cycloide
                    <lb/>
                  data
                    <emph type="italics"/>
                  QRS.
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note115"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Filum
                    <emph type="italics"/>
                  AR
                    <emph.end type="italics"/>
                  æquatur Semicycloidi
                    <emph type="italics"/>
                  AS,
                    <emph.end type="italics"/>
                  adeoque ad ſemi­
                    <lb/>
                  diametrum
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  eandem habet rationem quam ſimilis illi Semicy­
                    <lb/>
                  clois
                    <emph type="italics"/>
                  SR
                    <emph.end type="italics"/>
                  habet ad ſemidiametrum
                    <emph type="italics"/>
                  CO.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LI. THEOREMA XVIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Vis centripeta tendens undique ad Globi centrum
                    <emph.end type="italics"/>
                  C
                    <emph type="italics"/>
                  ſit in locis
                    <lb/>
                  ſingulis ut diſtantia loci cujuſque a centro, & hac ſola Vi a­
                    <lb/>
                  gente corpus
                    <emph.end type="italics"/>
                  T
                    <emph type="italics"/>
                  oſcilletur (modo jam deſcripto) in perimetro Cy­
                    <lb/>
                  cloidis
                    <emph.end type="italics"/>
                  QRS:
                    <emph type="italics"/>
                  dico quod oſcillationum utcunQ.E.I.æqualium
                    <lb/>
                  æqualia erunt Tempora.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam in Cycloidis tangentem
                    <emph type="italics"/>
                  TW
                    <emph.end type="italics"/>
                  infinite productam cadat per­
                    <lb/>
                  pendiculum
                    <emph type="italics"/>
                  CX
                    <emph.end type="italics"/>
                  & jungatur
                    <emph type="italics"/>
                  CT.
                    <emph.end type="italics"/>
                  Quoniam vis centripeta qua cor­
                    <lb/>
                  pus
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  impellitur verſus
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  eſt ut diſtantia
                    <emph type="italics"/>
                  CT,
                    <emph.end type="italics"/>
                  atque hæc (per Legum
                    <lb/>
                  Corol. </s>
                  <s>2.) reſolvitur in partes
                    <emph type="italics"/>
                  CX, TX,
                    <emph.end type="italics"/>
                  quarum
                    <emph type="italics"/>
                  CX
                    <emph.end type="italics"/>
                  impellen­
                    <lb/>
                  do corpus directe a
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  diſtendit filum
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  & per ejus reſiſtentiam
                    <lb/>
                  tota ceſſat, nullum alium edens effectum; pars autem altera
                    <emph type="italics"/>
                  TX,
                    <emph.end type="italics"/>
                    <lb/>
                  urgendo corpus tranſverſim ſeu verſus
                    <emph type="italics"/>
                  X,
                    <emph.end type="italics"/>
                  directe accelerat motum
                    <lb/>
                  ejus in Cycloide; manifeſtum eſt quod corporis acceleratio, huic
                    <lb/>
                  vi acceleratrici proportionalis, ſit ſingulis momentis ut longitudo
                    <lb/>
                    <emph type="italics"/>
                  TX,
                    <emph.end type="italics"/>
                  id eſt, (ob datas
                    <emph type="italics"/>
                  CV, WV
                    <emph.end type="italics"/>
                  iiſque proportionales
                    <emph type="italics"/>
                  TX, TW,
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  ut longitudo
                    <emph type="italics"/>
                  TW,
                    <emph.end type="italics"/>
                  hoc eſt (per Corol. </s>
                  <s>1. Prop. </s>
                  <s>XLIX,) ut longitudo
                    <lb/>
                  arcus Cycloidis
                    <emph type="italics"/>
                  TR.
                    <emph.end type="italics"/>
                  Pendulis igitur duobus
                    <emph type="italics"/>
                  APT, Apt
                    <emph.end type="italics"/>
                  de per­
                    <lb/>
                  pendiculo
                    <emph type="italics"/>
                  AR
                    <emph.end type="italics"/>
                  inæqualiter deductis & ſimul dimiſſis, acceleratio­
                    <lb/>
                  nes eorum ſemper erunt ut arcus deſcribendi
                    <emph type="italics"/>
                  TR, tR.
                    <emph.end type="italics"/>
                  Sunt au­
                    <lb/>
                  tem partes ſub initio deſcriptæ ut accelerationes, hoc eſt, ut totæ
                    <lb/>
                  ſub initio deſcribendæ, & propterea partes quæ manent deſcriben-</s>
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