PROPORTION ( Lat. proportio, proportion, symmetry, ana logy, from pro, before, for + port io, connected with pars, part). In nmthe unities, an equality of ratios. Thus the ratio of 12 to 3 equals the ratio of S to 2; hence 12:3= 8:2 is a proportion. In general if a:b=c:d, a, b, e, d arc said to be in proportion. An equal ity of several ratios, as 1:2=4:8=9:18, is called a continued proportion. An equality between the products of ratios, as i•2=1,•y, is called a compound proportion. In the proportion a:b= 1:11, a, b, e, d are called the terms, a and d the and b and c the means. The term if is called the fourth proportional to a, b, c. In the proportion a:b=b :c, b is called the mean pro portional between a and C. and c is called the third proportional to a and b. If one quantity varies directly as another, the two are said to be directly proportional, or simply proportional. E.g. the price of a given quality of sugar varies directly as the weight; the price is then propor tional to the weight. Thus at 4 cents a pound. 12 pounds cost 48 cents, and 4 cents : 48 eents = 1 pound : 12 pounds. If one quantity varies inversely as another, the two are said to be inversely proportional. E.g. in general, the
temperature being constant. the volume of a gas varies inversely as the pressure, and the volume is therefore said to be inversely proportional to the pressure.
A proportion, being an equation, can be solved so as to express any term by means of the other three. of the fundamental properties of proportion are: (I) The product of the extremes equals the product of the means; (2) the terms are in proportion by composition. i.e. if 0:b= c:d, (a+b) :a= (c+d ) :c or (a+b) :b= (e+d ) :d: (3) the terms are in proportion by division, i.e. if a:b=e:d, (a—b)—d):c or (a—b) :b= (e—d) :11; (4) the terms are in proportion by composition and division, i.e. if a:b=c:d, ( (1+1)) : (a—b ) = ( : (c—d) ; (5) in a tinued proportion, a ce mau pe° 9e°- – — — k= b d + pi" + 9P+ r The theory of proportion, often called the rule of three' or 'golden rule.' is as old as Plato's time and was called by the I becks civalloTta. Euclid in the fifth, eighth, and ninth hooks of the Elements gives a rigorous treatment of the sub ject, in which the magnitudes arc regarded as either commensurable or ineommensurable. See