Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                    <pb xlink:href="039/01/242.jpg" pagenum="214"/>
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                  tatis ſubducantur reſiſtentiæ, & manebunt
                    <emph type="italics"/>
                  ABHC, KkHC, LlHC,
                    <lb/>
                  NnHC,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ut vires abſolutæ quibus corpus in principio ſingu­
                    <lb/>
                  lorum temporum urgetur, atque adeo (per motus Legem 11) ut
                    <lb/>
                  incrementa velocitatum, id eſt, ut rectangula
                    <emph type="italics"/>
                  Ak, Kl, Lm, Mn,
                    <emph.end type="italics"/>
                  &c;
                    <lb/>
                  & propterea (per Lem. </s>
                  <s>I. Lib. </s>
                  <s>II) in progreſſione Geometrica. </s>
                  <s>Qua­
                    <lb/>
                  re ſi rectæ
                    <emph type="italics"/>
                  Kk, Ll, Mm, Nn,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>productæ occurrant Hyperbolæ
                    <lb/>
                  in
                    <emph type="italics"/>
                  q, r, s, t,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>erunt areæ
                    <emph type="italics"/>
                  ABqK, KqrL, LrsM, MstN,
                    <emph.end type="italics"/>
                  &c.
                    <lb/>
                  </s>
                  <s>æquales, adeoque tum temporibus tum viribus gravitatis ſemper
                    <lb/>
                  æqualibus analogæ. </s>
                  <s>Eſt autem area
                    <emph type="italics"/>
                  ABqK
                    <emph.end type="italics"/>
                  (per Corol. </s>
                  <s>3. Lem. </s>
                  <s>VII,
                    <lb/>
                  & Lem. </s>
                  <s>VIII, Lib. </s>
                  <s>I) ad aream
                    <emph type="italics"/>
                  Bkq
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  Kq
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  kq
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  AK,
                    <emph.end type="italics"/>
                    <lb/>
                  hoc eſt, ut vis gravitatis ad reſiſtentiam in medio temporis primi. </s>
                  <s>
                    <lb/>
                  Et ſimili argumento areæ
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                    <figure id="id.039.01.242.1.jpg" xlink:href="039/01/242/1.jpg" number="144"/>
                    <lb/>
                    <emph type="italics"/>
                  qKLr, rLMs, sMNt,
                    <emph.end type="italics"/>
                  &c.
                    <lb/>
                  </s>
                  <s>ſunt ad areas
                    <emph type="italics"/>
                  qklr, rlms,
                    <lb/>
                  smnt,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ut vires gravi­
                    <lb/>
                  tatis ad reſiſtentias in me­
                    <lb/>
                  dio temporis ſecundi, ter­
                    <lb/>
                  tii, quarti, &c. </s>
                  <s>Proinde cum
                    <lb/>
                  areæ æquales
                    <emph type="italics"/>
                  BAKq, qKLr,
                    <lb/>
                  rLMs, sMNt,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ſint vi­
                    <lb/>
                  ribus gravitatis analogæ, e­
                    <lb/>
                  runt areæ
                    <emph type="italics"/>
                  Bkq, qklr, rlms,
                    <lb/>
                  smnt,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>reſiſtentiis in mediis ſingulorum temporum, hoc eſt (per
                    <lb/>
                  Hypotheſin) velocitatibus, atque adeo deſcriptis ſpatiis analogæ. </s>
                  <s>
                    <lb/>
                  Sumantur analogarum ſummæ, & erunt areæ
                    <emph type="italics"/>
                  Bkq, Blr, Bms, Bnt,
                    <emph.end type="italics"/>
                    <lb/>
                  &c. </s>
                  <s>ſpatiis totis deſcriptis analogæ; necnon areæ
                    <emph type="italics"/>
                  ABqK, ABrL,
                    <lb/>
                  ABsM, ABtN,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>temporibus. </s>
                  <s>Corpus igitur inter deſcenden­
                    <lb/>
                  dum, tempore quovis
                    <emph type="italics"/>
                  ABrL,
                    <emph.end type="italics"/>
                  deſcribit ſpatium
                    <emph type="italics"/>
                  Blr,
                    <emph.end type="italics"/>
                  & tempore
                    <lb/>
                    <emph type="italics"/>
                  LrtN
                    <emph.end type="italics"/>
                  ſpatium
                    <emph type="italics"/>
                  rlnt. </s>
                  <s>Q.E.D.
                    <emph.end type="italics"/>
                  Et ſimilis eſt demonſtratio motus
                    <lb/>
                  expoſiti in aſcenſu.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note190"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Igitur velocitas maxima, quam corpus cadendo poteſt
                    <lb/>
                  acquirere, eſt ad velocitatem dato quovis tempore acquiſitam, ut
                    <lb/>
                  vis data gravitatis qua perpetuo urgetur, ad vim reſiſtentiæ qua in
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                  fine temporis illius impeditur. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Tempore autem aucto in progreſſione Arithmetica, ſumma
                    <lb/>
                  velocitatis illius maximæ ac velocitatis in aſcenſu (atque etiam earun
                    <lb/>
                  dem differentia in deſcenſu) decreſcit in progreſſione Geometrica. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Sed & differentiæ ſpatiorum, quæ in æqualibus tempo
                    <lb/>
                  rum differentiis deſcribuntur, decreſcunt in eadem progreſſion
                    <lb/>
                  Geometrica. </s>
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