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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 268, page id 1041163592:0302
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268
PHILOSOPMISE NATDRALIS
DEMoTD CEnErO S, ACymptotIS SA, Sa, describatur Hyperbola que
Conronon vis, quae secet perpendicula A, BL, CK, _C. in a, b, 6, etc. UC de
perpendicula ad alympeoton S’x demissa I+, Tu, R W in B, I, K3
ec densitatum differencixe +U H W, _C. CrunE u  I
d
FodcC. LC
rectangula FW Z FB, it  Z W in _C. (CU F p, ug, dec. u = XFB
BTX VI
SB
ec. id est, uE A a, Bb, ecc. F A enim, ex natura Fyperboloe,
5A 2d AH vel SF ut +B ad Aa, adeoque
IHIXtL
Ec Smili argumento est=
L. XUE
P sequale BB, _C. Sunt autem Aa3
Bb, CC, aC. continue proportionales, ec propterca disterentiis su-
is Aa = Bb; Bb = CC. ecc. proportionales; ideogue diAerCMLIS
portionalia lune rectangula +p, ug. ec. uc de summis diste-
rentiarum Aa =CC vel Aa = D d Cummxe rectansulorum +p F uq
vel Ip L ug F 2Or. Sunco ejusmodi termini quam plurimi, sc sum-
ma omnium diferenciarum, pura Aa - ff, erie lummx omnium
rectangulorum, puta zthn proporcionalis. AUGCAEUT numeruS
cerminorum de minuantur distantiae punctorum A, B, C, ecc. in in-
nitum, ec rectangula illa cradent aequalia arex Flyperbolica ZYBn
adeoque huic areae proporcionalis est differentia Aa -Ff. Suman-
X
tisce pre