| Dana Pond Colburn - 1860 - 390 pages
...to the quotient obtained by dividing the product of the extremes by the oiher mean. (6.) Hence, in a **proportion — The product of the means is equal to the product of the extremes.** 161. Practical Problems. (a.) The forming of a proportion from the conditions of a probiem is called... | |
| James Bates Thomson - Arithmetic - 1860 - 446 pages
...the work is right. (Art. 500.) Demtrmtral'ian. -If four numbers are proportional, we have seen that **the product of the means is equal to the product of the extremes** ; (Art. 498 ;) therefore the priduct of the second and thin/ terms must be equal to that of the first... | |
| Thomas Sherwin - 1862 - 252 pages
...6 d b and d, we have ad=bc. But a and d are the extremes, and 6 and c are the means. Hence, In any **proportion, the product of the means is equal to the product of the extremes.** (n). Suppose we have the equation ad—be. If we divide both members by 6 and d, we have — = —,... | |
| James Bates Thomson - Arithmetic - 1862 - 436 pages
...work is right. (Art. 500.) Demmatratian. -If four numbers are proportional, we have seen that th« **product of the means is equal to the product of the extremes** ; (Art. 498 ;} therefore the prxiict of the second and third terms must be equal to that of the first... | |
| Robert Johnston (F.R.G.S.) - 1863 - 258 pages
...proportion are called means (9 and 10); the first and fourth extremes (15 and 6). When four numbers form a **proportion, the product of the means is equal to the product of the extremes.** Thus, 6 : 3 : : 8 : 4 ; here, 6x4, the extremes, = 8x3, the means, = 24. If the product of any two... | |
| Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...the extremes is equal to the square of the mean. 2d. When four terms are in geometrical progression, **the product of the means is equal to the product of the extremes.** APPLICATION OF THE FORMULAS. 364. The two primitive equations, ,««. ,given, the other two may be... | |
| Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...the. extremes is equal to the square of the mean. 2d. When four terms are in geometrical progression, **the product of the means is equal to the product of the extremes.** APPLICATION OF THE FOKMULAS. 364. The two primitive equations, contain the five quantities, a, r, l,... | |
| Joseph Ray - Algebra - 1866 - 420 pages
...as 6 to 7? Let 3a;= the first, and 5x= the second number. Then, 3a;+9 : 5z+9 : : 6 : 7. But in every **proportion, the product of the means is equal to the product of the extremes.** (RAY'S ARITH., 3d Book, Art. 200.) Hence, 6(5a;+9)=7(3a;+9). From which the answer is readily found.... | |
| Joseph Ray - Algebra - 1866 - 252 pages
...in proportion? Example. What is the second term called? The third ? 244. Proposition I. — In every **proportion, the product of the means is equal to the product of the extremes.** Let a : 6 : : c : d. Then, since this is a true proportion, we must have bd Clearing of fractions,... | |
| Joseph Ray - Algebra - 1867 - 240 pages
...100—3z= B's gain, and 40z — 200= A's stock. Therefore, 4te— 200 : 20a; : : 3x : 100—3z. Since **the product of the means is equal to the product of the extremes,** 60z2=(40z— 200)(100— 3«). Reducing, z2— J{°x=— i°o°. Whence, z=20; hence, &c=60= A's gain,... | |
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