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# Title: Lectures De Potentia Restitutiva, Or Of Spring (shelfmarks Leibn. Marg. 105, Stück 1; Leibn. Marg. 105)
# Folio 17, page id 859264114:0023
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Thave here already Thewed then that the porrerot
all Sprinssisproportionare tothe deprec ot Aexure,
2iz. One deoree ot Aexure, or onc space bended hath
onc porer, tro hath tro, and chrechrach threc, and
(0 Formard. And erery point ot the space of Aexure
hatha peculiar porver, and consequentlr chere being
intinite poines of the space, there mult be infinite de-
grees oF porer.
And consequently all thole pomers beginning From
noushe, and endins at the lalt degree ot tention or
bendine, added together into one lum, or apgrerate,
Will be in duplicate proportion co che spacc bended or
degree oF Aexure; that is, the aggresate oF the
porvers oF the Sprins cended trom its quielcent po-
Aure by all the intermediate points to one space
(Beit Wrhat lenoth vou pleale) is equal, or in the
Tame proportion to the square ol one (suppotins
the Caid space infinitely divisible into the Fractions ot
OnC;) totmo, isequal, or in che lame proportion to
the (quare ot trro, thatistour; to chrec is equalor
in thelame proportionto the (quare ot chree, thatis
nine, and (0 Formard; and consequently che agore.
sate oF the Crstspace willbeone, oF the second space
will bethree, of the third space will be sive, oF rhe
tourth wils beseren, and so onmards in an Rrichme-
cical proportion, beins the degrees or excesses by
Whichthele aggregates exceed onc another.
TheSprins cheretore in returnine from any degree
oF Aexure, tortich ic hach been bent by any porrer
receiveth at crery point of the space returned an
impulse equal to the porver oF the Spring in that
point ot Tention, and in recurnins the irhole it re-
ceireth the wrtiole aegregate ot alltheforces belono-
instothe oreatest degrecot that Tension trom Which
it returned; (0 a Sprins bent tro spaces in its return
reccivech Four degrees oF impulle, chat is, three in
the trst space returnino, and onc in the second; 10
Bentchree spaces it receireth in its Wrhole return nine
deorees