On the Vis viva. 273 
acquire or lose quantities of the wis viva, 
which are as the momenta acquired or lost by 
them in equal intervals of time, because the 
motive force of gravity is as the matter on 
which it acts. 
Turorem II. Suppose two mediums, 
whose powers of resistance, P and p, act 
uniformly, to be penetrated by any mechani- 
cal means whatever, to the depths S and s: 
Put R and r for the quantities of resistance 
surmounted in penetrating them; and we 
have as R:r:: PS: ps. 
‘For since P and p are magnitudes by ax. 1, 
they may be represented by right lines: 
Assume the right line AC, (plate 4, fig. 1) in 
which take CB, making AC: CB::P:p; 
also make CE perpendicular to AC ; in which 
take CT—S and CV=s; also let CE measure 
both CT and CV: complete the parallelograms 
CT Aa, CVBb, and draw EG parallel to AC, 
meeting Aa in G, and Bb in H: lastly divide 
the lines CV, CT, by means of the common 
measure CE into the equal parts CE, EL, IV, 
VL and LT. 
In the first place, let P=p; then CA=CB; 
let n= quantity of resistance required to pene- 
trate the medium having the resistance p, 
from C to E, by def. 5; and the same quan- 
tity will be again demanded to carry the work 
Mm 
