Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/274.jpg" pagenum="246"/>
                    <arrow.to.target n="note222"/>
                  velocitas, altera ut quadratum velocitatis: & ipſius (1/
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  ) decremen­
                    <lb/>
                  tum eſt ut ſumma quantitatum (1/
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  ) & (
                    <emph type="italics"/>
                  CG/GDq
                    <emph.end type="italics"/>
                  ), quarum prior eſt
                    <lb/>
                  ipſa (1/
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  ), & poſterior (
                    <emph type="italics"/>
                  CG/GDq
                    <emph.end type="italics"/>
                  ) eſt ut (1/
                    <emph type="italics"/>
                  GDq
                    <emph.end type="italics"/>
                  ). Proinde (1/
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  ), ob an­
                    <lb/>
                  alogum decrementum, eſt ut velocitas. </s>
                  <s>Et ſi quantitas
                    <emph type="italics"/>
                  GD,
                    <emph.end type="italics"/>
                  ipſi (1/
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  reciproce proportionalis, quantitate data
                    <emph type="italics"/>
                  CG
                    <emph.end type="italics"/>
                  augeatur; ſumma
                    <emph type="italics"/>
                  CD,
                    <emph.end type="italics"/>
                    <lb/>
                  tempore
                    <emph type="italics"/>
                  ABED
                    <emph.end type="italics"/>
                  uniformiter creſcente, creſcet in progreſſione
                    <lb/>
                  Geometrica.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note222"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Igitur. </s>
                  <s>ſi, datis punctis
                    <emph type="italics"/>
                  A, G,
                    <emph.end type="italics"/>
                  exponatur tempus per
                    <lb/>
                  aream Hyperbolicam
                    <emph type="italics"/>
                  ABED,
                    <emph.end type="italics"/>
                  exponi poteſt velocitas per ipſius
                    <lb/>
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  reciprocam (1/
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  ). </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Sumendo autem
                    <emph type="italics"/>
                  GA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  GD
                    <emph.end type="italics"/>
                  ut velocitatis reciproca ſub
                    <lb/>
                  initio, ad velocitatis reciprocam in fine temporis cujuſvis
                    <emph type="italics"/>
                  ABED,
                    <emph.end type="italics"/>
                    <lb/>
                  invenietur punctum
                    <emph type="italics"/>
                  G.
                    <emph.end type="italics"/>
                  Eo autem invento, velocitas ex dato quo­
                    <lb/>
                  vis alio tempore inveniri poteſt. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XII. THEOREMA IX.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Iiſdem poſitis, dico quod ſi ſpatia deſcripta ſumantur in progreſſio­
                    <lb/>
                  ne Arithmetica, velocitates data quadam quantitate auctæ e­
                    <lb/>
                  runt in progreſſione Geometrica.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>In Aſymptoto
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  detur pun­
                    <lb/>
                    <figure id="id.039.01.274.1.jpg" xlink:href="039/01/274/1.jpg" number="161"/>
                    <lb/>
                  ctum
                    <emph type="italics"/>
                  R,
                    <emph.end type="italics"/>
                  & erecto perpendiculo
                    <emph type="italics"/>
                  RS,
                    <emph.end type="italics"/>
                    <lb/>
                  quod occurrat Hyperbolæ in
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  ex­
                    <lb/>
                  ponatur deſcriptum ſpatium per a­
                    <lb/>
                  ream Hyperbolicam
                    <emph type="italics"/>
                  RSED
                    <emph.end type="italics"/>
                  ; &
                    <lb/>
                  velocitas erit ut longitudo
                    <emph type="italics"/>
                  GD,
                    <emph.end type="italics"/>
                    <lb/>
                  quæ cum data
                    <emph type="italics"/>
                  CG
                    <emph.end type="italics"/>
                  componit longi­
                    <lb/>
                  tudinem
                    <emph type="italics"/>
                  CD,
                    <emph.end type="italics"/>
                  in progreſſione Geo­
                    <lb/>
                  metrica decreſcentem, interea dum
                    <lb/>
                  ſpatium
                    <emph type="italics"/>
                  RSED
                    <emph.end type="italics"/>
                  augetur in Arith­
                    <lb/>
                  metica. </s>
                </p>
                <p type="main">
                  <s>Etenim ob datum ſpatii incrementum
                    <emph type="italics"/>
                  EDde,
                    <emph.end type="italics"/>
                  lineola
                    <emph type="italics"/>
                  Dd,
                    <emph.end type="italics"/>
                  quæ </s>
                </p>
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