...perfectly well. • Phi. Then you are to obferve as follows. OBS ERv. i. Any three Numbers in Geometrical Proportion, the Product of the Extremes is equal to the Square of the Mean ; that is, equal to the middle Term multiplied by or into itfelf. Let the 3 Numbers be 4, 16, and 64....

...proportion. When B = C, the equidifference is said to be continued ; the same is said of proportion, when b = c. We have in this case that is, in continued equidifference...extremes is equal to double the mean ; and in proportion, tlie product of liie extremes is equal to the square of the mean. From this we deduce the quantity...

...product of the extremes and means may then be taken reciprocally for each other. And in a continued proportion, the product of the extremes is equal to the square of the mean term: because, the two mean terms being equal, their product is the square of either. Then, to find...

...take the product of the extremes for that of the means, and reciprocally. Therefore, in the continued proportion, the product of the extremes is equal to the square of the mean term; for the two means being equal, their product is the square of one of them. Therefore, to have...

...proportion, the other two are means, and conversely. (359.) COR. 4. — If three quantities be in continued proportion,' the product of the extremes is equal to the square of the mean.1 Let а:Ъ — Ъ:с, then ac = bb = № (360.) Hence when the extremes are known, the square...

...= - ; whence a : b : : c : d or c : d : : a : b. ao PROP. II. If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean, and conversely. Let a:b::b:c; then axc = bxb or ac — b*. Conversely. If the product of any two quantities...

...numbers are proportional ; that is, 5 : 6 : : 10 : 12. (215.) If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean. If a:b::b:c. Then, by Art. 212, ac = bb = b\ Conversely, if the product of two quantities is equal...

...dividing by bd, we have a с . b=d Or, • , в : 6 : : с : d. 44. If three magnitudes be in continual proportion, the product of the extremes is equal to the square of the mean. If a : b : : b : c, then ac = ¿>3. ab *-? Multiply by be, and ac = №. 45. If four quantities be...

...numbers are proportional ; that is, 5 : 6 : : 10 : 12. (215.) If three quantities are in continued proportion, the product of the extremes is equal to the square of the mean. If a:b::b:c. Then, by Art. 212, ac — bb= V. Conversely, if the product of two quantities is equal...

...then dividing by bd, we have a с b=d Or, a : b : : с : d. 44. If three magnitudes be in continual proportion, the product of the extremes is equal to the square of the mean. If a : b : : b : c, then ac = b3. ab *~? Multiply by be, and ac = b*. 45. If four quantities be proportionals,...