The English works of Thomas Hobbes of Malmesbury, Volume 01 (of 11)
Thomas Hobbes · en
Secondly, let the parallelogram A K I B not be rectangled; the strait
line I B will nevertheless press the point B perpendicularly in the
strait line B E; and the strait line L G will press the point G
perpendicularly in the strait line G H; and all the rest of the strait
lines which are parallel to I B will do the like. Whatsoever therefore
the moment be which is assigned to the strait line I B, as here, for
example, it is supposed to be B E, if A E be drawn, the moment of the
whole parallelogram A I will be the triangle A B E; and the moment of
the part A L will be the triangle A G H. Wherefore the moment of any
ponderant, which has its sides equally applied to the beam, whether they
be applied perpendicularly or obliquely, will be always to the moment of
a part of the same in such proportion as the whole triangle has to a
part of the same cut off by a plane which is parallel to the base.
[Sidenote: The diameter of equiponderation of figures which are
deficient according to commensurable proportions of their
altitudes and bases, divides the axis, so that the part taken
next the vertex is to the other part as the complete figure
to the deficient figure.]
9. The centre of equiponderation of any figure, which is deficient
according to commensurable proportions of the altitude and base
diminished, and whose complete figure is either a parallelogram or a
cylinder, or a parallelopipedum, divides the axis, so, that the part
next the vertex, to the other part, is as the complete figure to the
deficient figure.
For let C I A P E (in fig. 5) be a deficient figure, whose axis is A B,
and whose complete figure is C D F E; and let the axis A B be so divided
in Z, that A Z be to Z B as C D F E is to C I A P E. I say, the centre
of equiponderation of the figure C I A P E will be in the point Z.