III. _Weight_ is the aggregate of all the endeavours, by which all the points of that body, which presses the beam, tend downwards in lines parallel to one another; and the body which presses is called the _ponderant_. IV. _Moment_ is the power which the ponderant has to move the beam, by reason of a determined situation. V. _The plane of equiponderation_ is that by which the ponderant is so divided, that the moments on both sides remain equal. VI. _The diameter of equiponderation_ is the common section of the two planes of equiponderation, and is in the strait line by which the weight is hanged. VII. _The centre of equiponderation_ is the common point of the two diameters of equiponderation. SUPPOSITIONS. [Sidenote: Suppositions.] I. When two bodies are equally poised, if weight be added to one of them and not to the other, their equiponderation ceases. II. When two ponderants of equal magnitude, and of the same species or matter, press the beam on both sides at equal distances from the centre of the scale, their moments are equal. Also when two bodies endeavour at equal distances from the centre of the scale, if they be of equal magnitude and of the same species, their moments are equal. [Sidenote: Two planes of equiponderation are not parallel.] 2. No two planes of equiponderation are parallel. Let A B C D (in fig. 1) be any ponderant whatsoever; and in it let E F be a plane of equiponderation; parallel to which, let any other plane be drawn, as G H. I say, G H is not a plane of equiponderation. For seeing the parts A E F D and E B C F of the ponderant A B C D are equally poised; and the weight E G H F is added to the part A E F D, and nothing is added to the part E B C F, but the weight E G H F is taken from it; therefore, by the first supposition, the parts A G H D and G B C H will not be equally poised; and consequently G H is not a plane of equiponderation. Wherefore, no two planes of equiponderation are parallel; which was to be proved. [Sidenote: The centre of equiponderation is in every plane of equiponderation.] 3. The centre of equiponderation is in every plane of equiponderation. For if another plane of equiponderation be taken, it will not, by the last article, be parallel to the former plane; and therefore both those planes will cut one another. Now that section (by the 6th definition) is the diameter of equiponderation. Again, if another diameter of equiponderation be taken, it will cut that former diameter; and in that section (by the 7th definition) is the centre of equiponderation. Wherefore the centre of equiponderation is in that diameter which lies in the said plane of equiponderation. [Sidenote: The moments of equal ponderants are to one another as their distances from the centre of the scale.]