Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/169.jpg" pagenum="141"/>
                  oſcillationis unius, ut arcus
                    <emph type="italics"/>
                  HI
                    <emph.end type="italics"/>
                  (tempus quo corpus
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  perveniet
                    <lb/>
                    <arrow.to.target n="note117"/>
                  ad
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  ) ad ſemiperipheriam
                    <emph type="italics"/>
                  HKM
                    <emph.end type="italics"/>
                  (tempus quo corpus
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  per­
                    <lb/>
                  veniet ad
                    <emph type="italics"/>
                  M.
                    <emph.end type="italics"/>
                  ) Et velocitas corporis penduli in loco
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  eſt ad ve­
                    <lb/>
                  locitatem ipſius in loco infimo
                    <emph type="italics"/>
                  R,
                    <emph.end type="italics"/>
                  (hoc eſt, velocitas corporis
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  in
                    <lb/>
                  loco
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  ad velocitatem ejus in loco
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  ſeu incrementum momenta­
                    <lb/>
                  neum lineæ
                    <emph type="italics"/>
                  HL
                    <emph.end type="italics"/>
                  ad incrementum momentaneum lineæ
                    <emph type="italics"/>
                  HG,
                    <emph.end type="italics"/>
                  arcu­
                    <lb/>
                  bus
                    <emph type="italics"/>
                  HI, HK
                    <emph.end type="italics"/>
                  æquabili fluxu creſcentibus) ut ordinatim applicata
                    <lb/>
                    <emph type="italics"/>
                  LI
                    <emph.end type="italics"/>
                  ad radium
                    <emph type="italics"/>
                  GK,
                    <emph.end type="italics"/>
                  ſive ut √
                    <emph type="italics"/>
                    <expan abbr="SRq.-TRq.">SRq.-TRque</expan>
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SR.
                    <emph.end type="italics"/>
                  Unde cum,
                    <lb/>
                  in oſcillationibus inæqualibus, deſcribantur æqualibus temporibus
                    <lb/>
                  arcus totis oſcillationum arcubus proportionales; habentur, ex da­
                    <lb/>
                  tis temporibus, & velocitates & arcus deſcripti in oſcillationibus
                    <lb/>
                  univerſis. </s>
                  <s>Quæ erant primo invenienda. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note117"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>Oſcillentur jam Funipendula
                    <lb/>
                    <figure id="id.039.01.169.1.jpg" xlink:href="039/01/169/1.jpg" number="100"/>
                    <lb/>
                  corpora in Cycloidibus diverſis
                    <lb/>
                  intra Globos diverſos, quorum
                    <lb/>
                  diverſæ ſunt etiam Vires abſolu­
                    <lb/>
                  tæ, deſcriptis: &, ſi Vis abſolu­
                    <lb/>
                  ta Globi cujuſvis
                    <emph type="italics"/>
                  QOS
                    <emph.end type="italics"/>
                  dicatur V,
                    <lb/>
                  Vis acceleratrix qua
                    <expan abbr="Pendulũ">Pendulum</expan>
                  urge­
                    <lb/>
                  tur in circumferentia hujus Globi,
                    <lb/>
                  ubi incipit directe verſus centrum
                    <lb/>
                  ejus moveri, erit ut diſtantia Cor­
                    <lb/>
                  poris penduli a centro illo & Vis abſoluta Globi conjunctim, hoc
                    <lb/>
                  eſt, ut
                    <emph type="italics"/>
                  CO
                    <emph.end type="italics"/>
                  XV. </s>
                  <s>Itaque lineola
                    <emph type="italics"/>
                  HY,
                    <emph.end type="italics"/>
                  quæ ſit ut hæc Vis accelera­
                    <lb/>
                  trix
                    <emph type="italics"/>
                  CO
                    <emph.end type="italics"/>
                  XV, deſcribetur dato tempore; &, ſi erigatur normalis
                    <emph type="italics"/>
                  YZ
                    <emph.end type="italics"/>
                    <lb/>
                  circumferentiæ occurrens in
                    <emph type="italics"/>
                  Z,
                    <emph.end type="italics"/>
                  arcus naſcens
                    <emph type="italics"/>
                  HZ
                    <emph.end type="italics"/>
                  denotabit datum
                    <lb/>
                  illud tempus. </s>
                  <s>Eſt autem arcus hic naſcens
                    <emph type="italics"/>
                  HZ
                    <emph.end type="italics"/>
                  in ſubduplicata ra­
                    <lb/>
                  tione rectanguli
                    <emph type="italics"/>
                  GHY,
                    <emph.end type="italics"/>
                  adeoque ut √
                    <emph type="italics"/>
                  GHXCO
                    <emph.end type="italics"/>
                  XV. </s>
                  <s>Unde Tem­
                    <lb/>
                  pus oſcillationis integræ in Cycloide
                    <emph type="italics"/>
                  QRS
                    <emph.end type="italics"/>
                  (cum ſit ut ſemiperi­
                    <lb/>
                  pheria
                    <emph type="italics"/>
                  HKM,
                    <emph.end type="italics"/>
                  quæ oſcillationem illam integram denotat, directe,
                    <lb/>
                  utque arcus
                    <emph type="italics"/>
                  HZ,
                    <emph.end type="italics"/>
                  qui datum tempus ſimiliter denotat, inverſe) fiet
                    <lb/>
                  ut
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  directe & √
                    <emph type="italics"/>
                  GHXCO
                    <emph.end type="italics"/>
                  XV inverſe, hoc eſt, ob æquales
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  SR,
                    <emph.end type="italics"/>
                  ut √(
                    <emph type="italics"/>
                  SR/CO
                    <emph.end type="italics"/>
                  XV), ſive (per Corol. </s>
                  <s>Prop. </s>
                  <s>L) ut √(
                    <emph type="italics"/>
                  AR/AC
                    <emph.end type="italics"/>
                  XV).
                    <lb/>
                  Itaque Oſcillationes in Globis & Cycloidibus omnibus, quibuſ­
                    <lb/>
                  cunque cum Viribus abſolutis factæ, ſunt in ratione quæ compo­
                    <lb/>
                  nitur ex ſubduplicata ratione longitudinis Fili directe, & ſubdu­
                    <lb/>
                  plicata ratione diſtantiæ inter punctum ſuſpenſionis & centrum </s>
                </p>
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