CONTINUAL Proportionals

, are a series of three or more quantities compared together, so that the ratio is the same between every two adjacent terms, viz between the 1st and 2d, the 2d and 3d, the 3d and 4th, &c. As 1, 2, 4, 8, 16, &c, where the terms continually increase in a double ratio; or 12, 4, 4/3, 4/9, where the terms decrease in a triple ratio.

A series of continual or continued proportionals, is otherwise called a progression.

CONTINUED Quantity, or Body, is that whose parts are joined and united together.

CONTINUED Proportion, is that in which the consequent of the first ratio is the same with the antecedent of the second; as in these, 3 : 6 :: 6: 12. See Continual Proportion.

On the contrary, if the consequent of the first ratio be different from the antecedent of the second, the proportion is called discrete: as 3 : 6 :: 4 : 8.

CONTRA-Harmonical Proportion, that relation of three terms, in which the difference of the first and second is to the difference of the 2d and 3d, as the 3d is to the first. Thus, for instance, 3, 5, and 6, are numbers contra-harmonically proportional; for 2 : 1 :: 6 : 3.

CONTRA-Mure, in Fortification, is a little wall built before another partition wall, to strengthen it, so that it may receive no damage from the adjacent buildings.

CONTRATE-Wheel, is that wheel in watches which is next to the crown, whose teeth and hoop lie contrary to those of the other wheels; from whence comes its name.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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* CONTINUAL Proportionals