Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                    <pb xlink:href="039/01/296.jpg" pagenum="268"/>
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                  Centro
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  Aſymptotis
                    <emph type="italics"/>
                  SA, Sx,
                    <emph.end type="italics"/>
                  deſcribatur Hyperbola quæ­
                    <lb/>
                  vis, quæ ſecet perpendicula
                    <emph type="italics"/>
                  AH, BI, CK,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>in
                    <emph type="italics"/>
                  a, b, c,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ut &
                    <lb/>
                  perpendicula ad Aſymptoton
                    <emph type="italics"/>
                  Sx
                    <emph.end type="italics"/>
                  demiſſa
                    <emph type="italics"/>
                  Ht, Iu, Kw
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  h, i, k
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  & denſitatum differentiæ
                    <emph type="italics"/>
                  tu, uw,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>erunt üt
                    <emph type="italics"/>
                  (AH/SA), (BI/SB),
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Et
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                  rectangula
                    <emph type="italics"/>
                  tuXth, uwXui,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ſeu
                    <emph type="italics"/>
                  tp, uq,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ut
                    <emph type="italics"/>
                  (AHXtb/SA),
                    <lb/>
                  (BIXui/SB),
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>id eſt, ut
                    <emph type="italics"/>
                  Aa, Bb,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Eſt enim, ex natura Hyperbolæ,
                    <lb/>
                    <emph type="italics"/>
                  SA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  St,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  th
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Aa,
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                  adeoque (
                    <emph type="italics"/>
                  AHXth/SA
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                  ) æquale
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.296.1.jpg" xlink:href="039/01/296/1.jpg" number="173"/>
                    <lb/>
                  Et ſimili argumento eſt (
                    <emph type="italics"/>
                  BIXui/SB
                    <emph.end type="italics"/>
                  ) æquale
                    <emph type="italics"/>
                  Bb,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Sunt autem
                    <emph type="italics"/>
                  Aa,
                    <lb/>
                  Bb, Cc,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>continue proportionales, & propterea differentiis ſu­
                    <lb/>
                  is
                    <emph type="italics"/>
                  Aa-Bb, Bb-Cc,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>proportionales; ideoQ.E.D.fferentiis
                    <lb/>
                  hiſce proportionalia ſunt rectangula
                    <emph type="italics"/>
                  tp, uq,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ut & ſummis diffe­
                    <lb/>
                  rentiarum
                    <emph type="italics"/>
                  Aa-Cc
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  Aa-Dd
                    <emph.end type="italics"/>
                  ſummæ rectangulorum
                    <emph type="italics"/>
                  tp+uq
                    <emph.end type="italics"/>
                    <lb/>
                  vel
                    <emph type="italics"/>
                  tp+uq+wr.
                    <emph.end type="italics"/>
                  Sunto ejuſmodi termini quam plurimi, & ſum­
                    <lb/>
                  ma omnium differentiarum, puta
                    <emph type="italics"/>
                  Aa-Ff,
                    <emph.end type="italics"/>
                  erit ſummæ omnium
                    <lb/>
                  rectangulorum, puta
                    <emph type="italics"/>
                  zthn,
                    <emph.end type="italics"/>
                  proportionalis. </s>
                  <s>Augeatur numerus
                    <lb/>
                  terminorum & minuantur diſtantiæ punctorum
                    <emph type="italics"/>
                  A, B, C,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>in in­
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                  nitum, & rectangula illa evadent æqualia areæ Hyperbolicæ
                    <emph type="italics"/>
                  zthn,
                    <emph.end type="italics"/>
                    <lb/>
                  adeoque huic areæ proportionalis eſt differentia
                    <emph type="italics"/>
                  Aa-Ff.
                    <emph.end type="italics"/>
                  Suman-</s>
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