The English works of Thomas Hobbes of Malmesbury, Volume 01 (of 11)
Thomas Hobbes · en
Secondly, I define IMPETUS, _or quickness of motion, to be the swiftness
or velocity of the body moved, but considered in the several points of
that time in which it is moved. In which sense_ impetus _is nothing else
but the quantity or velocity of endeavour. But considered with the whole
time, it is the whole velocity of the body moved taken together
throughout all the time, and equal to the product of a line representing
the time, multiplied into a line representing the arithmetically mean_
impetus _or quickness_. Which arithmetical mean, what it is, is defined
in the 29th article of chapter XIII.
And because in equal times the ways that are passed are as the
velocities, and the _impetus_ is the velocity they go withal, reckoned
in all the several points of the times, it followeth that during any
time whatsoever, howsoever the _impetus_ be increased or decreased, the
length of the way passed over shall be increased or decreased in the
same proportion; and the same line shall represent both the way of the
body moved, and the several _impetus_ or degrees of swiftness wherewith
the way is passed over.
And if the body moved be not a point, but a strait line moved so as that
every point thereof make a several strait line, the plane described by
its motion, whether uniform, accelerated, or retarded, shall be greater
or less, the time being the same, in the same proportion with that of
the _impetus_ reckoned in one motion to the _impetus_ reckoned in the
other. For the reason is the same in parallelograms and their sides.
For the same cause also, if the body moved be a plane, the solid
described shall be still greater or less in the proportions of the
several _impetus_ or quicknesses reckoned through one line, to the
several _impetus_ reckoned through another.