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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0281
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and B will bC
Flence, il the Body B be at rest, the POInES D
nc, asls e Cale Ot che Elule
LLB.C B: ana doublins ine, COmlequenE TeFMIS O
the Proportion B - ] A. 2 A :: AB, 2CB. Lhac
is in words, As the Asgresare or Sum of the Bodies
srst Lines in che. Figure. And becaule B. A: 3
A C. C B: cheretore by compotiion B-) A. A:
25 to the double os the movine or strikine Boc)S
u Beelocitys of the strikins Body be before the
Shock. be 1o the Velocity of the Duiescent Body after it.
C OR. 2.
WVheresore, is rhe Bodies A, B are esjual, ete
Sum or Aggresate oF them must DC2. A. Wtience
the Velocier ot the BodY B atter the ShocK, MalI
be equal ro A B, the Velocier oF che Body a bC
Pore ir, and consequenely rhe P’oints P and A beine
coincident, A P che Velocies ot che morins Body
alter the Impulie or Stock, will be = 0; Thac is.
none ac aII. Wrhich also mas be casilr MeW
thus; Because the Bodies A and B are equal, A C
will bc = CB = C D = C F; Wheretore the
poine  Will coincide wich A, and consequenes che
Body A atrer che Shock, Will be ac rett, and ctic
Pod B will more rich che Velocier F B Or
Is iberesore a persecttos Flasticte Dody stribe directus
acainst another equal to it, end which is at rest; af-
ter the Shock, the movins Body vill lose all its morion
and the duiescent move on with the Velocity of the
former.
COR. 3
tecte Bodies A and B are equat, aud bortimove
che Pame war, as in Line che Ach oF thie Figure:
thier vill move also boch che lame way afcex che
Stock, and wich chemurual exchange ot their Ve-
locities.
FOr (nCC CF = CD: and A C = C B: C F
A C, chac is F A, must bc = CD -- C B Or
10 B D. and consequenely the Velocier oFche Body
atrer the Stock will be equal rothar OFB, betore
ic. Besides, lince P A = BD, F. B will bC = AD
and cheretore che Velocirr otche Body B atrer IC
Shock, must be equalro thar oF A betore ic.
COR. 4.
Iche equal Bodies B and A move wich contrary
directions, as in Line the porh of theFisure, chey
vill also aster the Concourse and Shock, move
Concrary wars, and wich cheir Velocities counter
Chariscd.
FOr sincc AC = CB, and CF = CD, AC
=CE, ThaFis, A F must be equal tOC B - CD
Or TOBD; and cheretore che Velocier oFcheBody
A atrer che Strock Will be equal eo that et B, bc-
Fore ir. Besides, since F. A = = BD, AD ril bC
E B. BIE A D expresses che Velociey oF che
Bodr A Betore the Shock, and F. B the Velociry oE
B aster ic, Wheretore che rrurh oE chis Corrollary i5
plain.
Astex chis he Mems a very easie merhod eo bring
chele Theorems ro Practice by a Calcularion in
Numbers.
For suppose (1) che Bodies A and B boch move
ihè lame Way, and. chac che Velocirs os ue precedemt.
Bod7
D E MONS FR AFFO N.
Since che commion Center Oi GraritY OF anY B0-
dies, prores on wich elic lame uniform. Progrestion.
and wich the Pame Velociry boch betore and alter
che Sheet and Impulle, 25 he prores in Theorem 18.
and chac in a Fime equalro chac in whieh che B0
dy A mores che lensch A D, Or the C enter OF GT2
vicy Cmores the lengrh CD; and alrer che Con-
courle, che same Point C Will more che lensch DH
WDC. This beins (0, let R a betatcen equas
Eo CA; then since by Cor. Ot the precedins Theo-
rem, tatins equal Pimes bols Detore and aiter cne
Impulle, che distances oF the Bodiestrom the com-
mon Center of Grariey, Will alivays be equal;
then de Whac cime rhe common Center ol Graviey
wilt De in IE, che Bodr A will be Found to be in a,
ane Cheretore alter the Impulse, ies morion will BC
From D corrards a and irs Velocier will be exprel
sed b)D a, which is che lensch run over in chac
Finte: Buc becanse CF = C D Or rD B C, anc
CA -= F a the disterence berween che righ
Lines CL and C A Will bc equal tothe difference
berween the righe Lines R D and R a; thac is,
F A = D a: Bur the rishe Linc D a expresses the
Velocier ot the Body A alier che Stock or Impulse.
and conseguenls irs Velocur will al(o bC. ex
pressed BV the rigHE Linc F A; Besices, MH. CC MC
relacire relocier of chele Bodies remains the laHe
boch belore and atcer the Strock, and chat cherighe
Line F. A denores che Velocier oF the BOdY A, ThC
Velociry oF the Body B must necessarils atrer the
Impulse be denored by che Line F B, and che di-
ration ot ihe meriom will be crem F. romards B.