...given, — =6; if a, b, and c, are given, — =d; and be if d, b, and c, are given, then -r=a '• 60. If the product of two quantities be equal to the product of two others, then if the terms of one product be made the means, and the terms of the other product...

...three terms in a proportion being given, the fourth may be determined from the equation ad=bc. (175.) If the product of two quantities be equal to the product of two others, the four are proportionals, making the terms of one product the means, and the terms of...

...their numerators are equal, therefore AD=BC; A and D being the extremes, and B and c the means. 12. If the product of two quantities be equal to the product of two others, the four quantities may be turned into a proportion, by making the terms of one product...

...and, therefore, x = Vac. » 110. The converse of each of the preceding theorems is also true, that is, If the product of two quantities be equal to the product of two others, or if the product of two be equal to the square of one, then the FOUR, or the THREE quantities...

...greater than C, thenB is greater than D,if A=C,thenB=D,andif A be less than C, then B is less than D. 33. If the product of two quantities be equal to the product of two other quantities, these four quantities may be turned into a proportion by making the terms of...

...b ; ' c ; d, then will ad = be. Also, if a ; 6 ; rb ; c, then will ac = 62. Whence it follows, that if the product of two quantities be equal to the product of two other quantities, the four quantities will be proportionals, thus, ad=bc, and this is turned into...

...4.), the product of the extremes will be equal to the square of the mean. PROPOSITION II. THEOREM. If the product of two quantities be equal to the product of two other quantities, two of them will be the extremes and the other two the means of a proportion....

...product of the extremes is equal to the square of the mean. For (Art. 39) if a : x :: x : 6, ab = a?. 41. If the product of two quantities be equal to the product of two others, the four are proportionals, making the terms of one product the means, and the terms of...

...proportionate, then - = -; multiply each side и С by ас, and there results be — ad. THEOREM 2. If the product of two quantities be equal to the product of two others, then a proportion may be formed of the four quantities. Let qr = ps ; then, dividing each...

...proportional between a and c ; then ac = b2, or the product of the extremes = the square of the mean. 142. If the product of two quantities be equal to the product of two others, the four are proportionals, making the terms of one product the means, and the terms of...