The English works of Thomas Hobbes of Malmesbury, Volume 01 (of 11) — Thomas Hobbes — John Shaqi
The English works of Thomas Hobbes of Malmesbury, Volume 01 (of 11)
Thomas Hobbes · en
4. The moment of any ponderant applied to one point of the beam, to the
moment of the same or an equal ponderant applied to any other point of
the beam, is as the distance of the former point from the centre of the
scale, to the distance of the latter point from the same centre. Or
thus, those moments are to one another, as the arches of circles which
are made upon the centre of the scale through those points, in the same
time. Or lastly thus, they are as the parallel bases of two triangles,
which have a common angle at the centre of the scale.
Let A (in fig. 2) be the centre of the scale; and let the equal
ponderants D and E press the beam A B in the points B and C; also let
the strait lines B D and C E be diameters of equiponderation; and the
points D and E in the ponderants D and E be their centres of
equiponderation. Let A G F be drawn howsoever, cutting D B produced in
F, and E C in G; and lastly, upon the common centre A, let the two
arches B H and C I be described, cutting A G F in H and I. I say, the
moment of the ponderant D to the moment of the ponderant E is as A B to
A C, or as B H to C I, or as B F to C G. For the effect of the ponderant
D, in the point B, is circular motion in the arch B H; and the effect of
the ponderant E, in the point C, circular motion in the arch C I; and by
reason of the equality of the ponderants D and E, these motions are to
one another as the quicknesses or velocities with which the points B and
C describe the arches B H and C I, that is, as the arches themselves B H
and C I, or as the strait parallels B F and C G, or as the parts of the
beam A B and A C; for A B. A C:: B F. C G:: B H. C I. are proportionals;
and therefore the effects, that is, by the 4th definition, the moments
of the equal ponderants applied to several points of the beam, are to
one another as A B and A C; or as the distances of those points from the
centre of the scale; or as the parallel bases of the triangles which
have a common angle at A; or as the concentric arches B H and C I; which
was to be demonstrated.
[Sidenote: The moments of unequal ponderants have their proportion to
one another compounded of the proportions of their weights
and distances from the centre of the scale.]
5. Unequal ponderants, when they are applied to several points of the
beam, and hang at liberty, that is, so as the line by which they hang be
the diameter of equiponderation, whatsoever be the figure of the
ponderant, have their moments to one another in proportion compounded of
the proportions of their distances from the centre of the scale, and of
their weights.