COMMON
, is applied to an angle, line, measure, or the like, that belongs to two or more figures, or other things. As, a common angle, a common side, a common base, a common measure, &c.
Common Measure, or divisor, is that which measures two or more things without a remainder. So of 8 and 12, a common measure is 2, and so is 4.
The greatest Common Measure, is the greatest number that can measure two other numbers. So, of 8 and 12, the greatest common measure is 4.
To find the greatest common measure of two numbers. Divide the greater term by the less; then divide the divisor by the remainder, if there be any; and so on continually, always dividing the last divisor by the last remainder, till nothing remains; and then is the last divisor the greatest common measure sought.
Thus, to find the greatest common measure of 816 and 1488. | Therefore 48 is the greatest common measure of 816 and 1488, thus:
| 48) 816 | (17 | 48) 1488 | (31 |
| 48 | 144 | ||
| 336 | 48 | ||
| 336 | 48 |
The common measure is useful in fractions, to reduce a fraction to its least terms, by dividing those that are given by their greatest common measure. So 816/1488 reduces to 17/31, by dividing 816 and 1488 both by their greatest common measure 48.
COMMUNICATION of Motion, that act of a moving body, by which it gives motion, or transfers its motion to another body.
Father Mallebranche considers the communication of motion, as something metaphysical; that is, as not necessarily arising from any physical principles, or any properties of bodies, but flowing from the immediate agency of God.
The communication of motion results from, and is an evidence of the impenetrability and inertia of matter, as such; unless we admit the hypothesis of the penetrability of matter, advanced by Boscovich and Michell, and ascribe to the power of repulsion those effects which have been usually ascribed to its solidity and actual resistance.
Newton shews that action and reaction are equal and opposite; so that one body striking or acting against another, and thence causing a change in its motion, does itself undergo the very same change in its own motion, the contrary way. And hence, a moving body striking directly another at rest, it loses just as much of its motion as it communicates to the other. For the laws and quantity of motion so communicated, either in elastic or nonelastic bodies, see Collision.
