Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Centro
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S,
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Aſymptotis
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SA, Sx,
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deſcribatur Hyperbola quæ
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vis, quæ ſecet perpendicula
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AH, BI, CK,
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&c. </
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>in
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a, b, c,
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>ut &
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perpendicula ad Aſymptoton
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Sx
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demiſſa
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Ht, Iu, Kw
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in
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h, i, k
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;
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& denſitatum differentiæ
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tu, uw,
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>erunt üt
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(AH/SA), (BI/SB),
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>Et
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rectangula
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tuXth, uwXui,
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&c. </
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>ſeu
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tp, uq,
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&c. </
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>ut
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(AHXtb/SA),
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(BIXui/SB),
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&c. </
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>id eſt, ut
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Aa, Bb,
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>Eſt enim, ex natura Hyperbolæ,
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SA
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ad
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AH
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vel
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St,
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ut
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th
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ad
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Aa,
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adeoque (
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AHXth/SA
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) æquale
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Aa
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Et ſimili argumento eſt (
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BIXui/SB
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) æquale
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Bb,
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&c. </
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<
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>Sunt autem
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Aa,
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Bb, Cc,
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>continue proportionales, & propterea differentiis ſu
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is
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Aa-Bb, Bb-Cc,
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>proportionales; ideoQ.E.D.fferentiis
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hiſce proportionalia ſunt rectangula
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tp, uq,
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&c. </
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>ut & ſummis diffe
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rentiarum
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Aa-Cc
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vel
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Aa-Dd
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ſummæ rectangulorum
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tp+uq
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vel
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tp+uq+wr.
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Sunto ejuſmodi termini quam plurimi, & ſum
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ma omnium differentiarum, puta
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Aa-Ff,
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erit ſummæ omnium
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rectangulorum, puta
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zthn,
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proportionalis. </
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>Augeatur numerus
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terminorum & minuantur diſtantiæ punctorum
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A, B, C,
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&c. </
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<
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>in in
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nitum, & rectangula illa evadent æqualia areæ Hyperbolicæ
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zthn,
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adeoque huic areæ proportionalis eſt differentia
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Aa-Ff.
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Suman-</
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