| Charles Davies - Algebra - 1860 - 320 pages
...(1.) ac Clearing of fractions, we have, bc = ad (2.) Hence, 1 . If four quantities are in proportion, **the product of the means is equal to the product of the extremes.** Conversely, if we divide both members of ( 2 ) by ca, we shall have, - — - ; or, a : b : : c : d.... | |
| James Bates Thomson - Arithmetic - 1860 - 422 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
...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 - 422 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... | |
| 1863
...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 - 420 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 - 420 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 - 240 pages
...then, 55 — x= the other. By the question, x : 55 — x : : 2 : 3. Then, since, in every proportion, **the product of the means is equal to the product of the extremes,** we have 3x=2(55 — x)=H0 — 2x. 5z=110 3x Or, thus : Let x= one part; then, -^-= the other. ' ' I'... | |
| Joseph Ray - Algebra - 1866 - 406 pages
...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 - 240 pages
...then, 55 — £= the other. By the question, x : 55 — x : : 2 : 3. Then, since, in every proportion, **the product of the means is equal to the product of the extremes,** we have 3a;=2(55 — 2)=110 — 2x. 5z=110 3=22, and 55— 3=33, as before. Or, thus : Let x= one part;... | |
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