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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIPIA MATLIEMaCLO
penduli quam habet resictentia ad gravicatem, erie DL exponens
L. YV P 1
relittentixe. Cenero C et incervallo C A vel C B construatur demi. Secb
circulus BF C A. Deseribat autem corpus tempore quam minimo
spatium D d ec crectis perpendiculis D F, de circumtereneia Oc
currentibus in F. ex es crune haec ur relocitates quas corpus in va-
cuo, descendendo a puncto B, acquireret in locis D ec d. Patet
hoc Der PrOD. LTT. Lib. T. Exponantur itaque lx velocitates per
Derpendicula illa DF, des Sicque D F velocitas quam acquirie
in D cadendo de B in Medio relictente. EE AI CCNETO C et inter-
vallo CF delcribatur Circulus ffM Occurrens rectis de de AB in
S ec M, eric M locus ad quem deinceps absque ulteriore ressten-
eia alcenderet, et df relociras quam acquireret in d.
Onde etiam
si Fe designet relocitatis momentum quod corpus D, describendo
spacium quam minimum D d, ex resiltencia Medii amittie; et su
matur C NV aequalis C8: exic N locus ad quem corpus deinccps
ab (que ulteriore resistentia a(cenderet, e M NV crit decrementum
alcensus ex velocitatis illius amistione oriundum. Ad af demieta-
cur perpendiculum m, e velocitatis D S decrementum PG a
relistentia D K genitum, erit ad velocitatis ejusdem incremencum
Fm 2 vi CD genitum, uc vis generans D K ad vim generantem
CD. Sed ex ob similia
criangula Pmf, FBC,
EDC, eAt fm ad Fm
Ceu D d, uE C D ad
DE; _c Cx aequo F8 2d
D a uE DR ad DF
lcem Rh ad fis ut DF
2d C fi; d ex xquo
percurbate, Ph (eu MIN
ad D a UE DR ad C Fi
Ccu C M; ideoque summa omnium M NV X C M aequalis crit lumMX
omnium D aZ D R. Ad punctum mobile M erisi semper incelli-
sacur ordinata rectangula aequalis indeterminatae C. M, qua motu
continuo ducatur in totam lonsitudinem Aa; et craperium ex illo
motu descriptum sire huic aequale rectangulum Aa X Z a B aequabitur
lummae omnium M N Z C. M, adeoque summx omnium D d X DR.
id CA, arCX BK KV T a.
Q. E. D.
C0ro. ne en legeTentientia ae arcuum C. a. C. B ditterentia Lan
collisi porest provorrio relistentix ad gravicatem quam proxime.
Nam
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