LIKE Quantities
, or Similar Quantities, in Algebra, are <*>uch as are expressed by the same letters, to the same power, or equally repeated in each quantity; though the numeral coefficients may be different.
Thus 4a and 5a are Like quantities, as are also 3a2 and 12a2, and also 6bxy2 and 10bxy2. But 4a and 5b, or 3a2b and 10a2b2, &c, are unlike quantities; because they have not every where the same dimensions, nor are the letters equally repeated. —Like quantities can be united into one quantity, by addition or subtraction; but unlike quantities can only be added or subtracted by placing the signs of these operations between them.
Like Signs, in Algebra, are the same signs, either both positive or both negative. But when one is positive and the other negative, they are unlike signs.
So, + 3ab and + 5cd have Like signs, as have also - 2a2c and - 2ax2; but + 3ab and - 5cd have unlike signs, as also - 2ax and 3ax.
Like Figures, or Arches, &c, are the same as Similar sigures, arches, &c. See Similar.
All Like figures have their homologous lines in the same ratio. Also Like plane figures are in the duplicate ratio, or as the squares of their homologous lines or sides; and Like solid figures are in the triplicate ratio, or as the cubes of their homologous lines or sides.
