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# Title: Lectures De Potentia Restitutiva, Or Of Spring (shelfmarks Leibn. Marg. 105, Stück 1; Leibn. Marg. 105)
# Folio 20, page id 859264114:0026
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Etie porvers, that is, as the RoOE ot the porvers im.
prested, and theporers imprest being asthe Praperi-
um or he excels ot the Triangle or (quare OE the
Wrhole space to be pastabore the lquare oF the space
vetunpalled; it uxon the Center A, and (paCC AC
(C beins che point trom wrhich the Springis suppoled
let 90) a Cirole be describedas C OG F, and ordinates
drarrn From any point ot C A thc space to DC Past,
a5 From B, B, tothe said Circle, as BG, BC, chele Lines
BC, B C, Will represent the Velocity ot the Spring re-
turnins EromC tOB, B, ec. the Paid ordinates being
alivars in the lame proportion ith thc Roots ot the
LFAPCZILIS CDE B, CD EB FOr putinS AC =
t0 a, and a B = b, B G rill alvays bc equal to
L a2 =bb, the square oF che ordinate being alrays
equal to the Rectansle oF theintercepted parts oF the
Diameter.
Hlarins thus Found theVelocities, tO Wit; BO, BO.
AF, to lnd thetimes correspondins, on the Diame-
ter A C dram a Parabola C HIF Whole Vertex is C, and
irtrich passeth chrough the point P. The Oordinates
oF ehis Parabola BII, BII, AP, arc in the lame prO-
vorcion with thc ROOtSOFthe spaceS C B, C B, C A,
then makino OB to HIB as IIB to IB, andchrouoh
thc points C IIF draming thC CUrVC CTTTE, thC
respectire ordinates oF this curre BaII represent the
Proportionate time thac che Sprivs spends in re-
curnins che spaceS C B, C B, C A.
TE the porvers or Stiftnels oF the Spring be greater
than wrhat I betore suppoled, and theretore must bc
expressed by che Priangle C dc A. then che V elocities
ils be cheOrdinates in an E Iliple aS C7 y N, oreater
thon ehe Circle, a5 it will allo if the porver bc the
Came, and the bulkmored by the Spring belels. Then
villthe S. like Line oF times meet ith che Live A. F
et a point as X within chepoint F. But if the porversot
the Spring beeakerthan Isuppoled, thenwill C scc
A seprelenE the POrerS, and C y yO the FIipHS OF
relocus.