 | Roswell Chamberlain Smith - 1842 - 320 σελίδες
...extremes 7 and 6 added together are equal to the means 5 and 8 added together, and universally — 23. IN ARITHMETICAL PROPORTION THE SUM OF THE EXTREMES is EQUAL TO THE SUM OF THE MEANS. 24. GEOMETRICAL1 PROPORTION IS AN EQUALITY OF GEOMETRICAL RATIOS, AND ARITHMETICAL PROPORTION AN EQUALITY... | |
 | Jeremiah Day - 1842 - 356 σελίδες
...proportion, the sum of the extremes is It will be proper, however, to observe that, if four quantiequal to the sum of the means. Thus if a.. b : : h.. m, then a+m=6+ h For by supposition, a - b=h - m And transposing - 6 and - m, a+ro=6+h sum of the extremes... | |
 | George Hutton (arithmetic master, King's coll. sch.) - 1844 - 276 σελίδες
...thus 3 : 5 : : 7 : 9 are quantities in arithmetical proportion, for 5-3=2, and 9—7=2. 4. Hence also, in arithmetical proportion, the sum of the extremes is equal to the sum of the means; thus if 3 : 5 : : 7 : 9, 3 + 9=12, and 5+7=12 ; and if from the sum of the means, either of the extremes be... | |
 | Jeremiah Day - 1845 - 358 σελίδες
...however, to observe that, if four quantities are in arithmetical proportion, the sum of the extremes ii equal to the sum of the means. Thus if a. . b: : h....supposition, a - b — h — m And transposing - b and - m, a-\-m = b-\- h So in the proportion, 12•• 10: :11••9, we have 12+9 = 10+11. Again if three... | |
 | Francis Henney Smith - 1845 - 300 σελίδες
...geometrical ratio be made equal ? 178* The fundamental property of an arithmetical proportion is, that the sum of the extremes is equal to the sum of the means. Thus, in the proportion 3 . 7 : 8 . 12 3 + 12=7 + 8; and this is true for every similar proportion. For,... | |
 | Francis Henney Smith - 1845 - 710 σελίδες
...geometrical ratio be made equal ? 178» The fundamental property of an arithmetical proportion is, that the sum of the extremes is equal to the sum of the means. Thus, in the proportion 8.7:8.12 3 + 12=7+8; and this is true for every similar proportion. For, if the first... | |
 | Jeremiah Day - 1846 - 356 σελίδες
...separate consideration. The proportion a . . b : : c . . d It will be proper, however, to observe that, if four quantities are in arithmetical proportion,...extremes is equal to the sum of the means. Thus if o . . b : : h . . m, then a+ m=b-\-h For by supposition, a — b=h — m And transposing - b and -... | |
 | Jeremiah Day - 1846 - 356 σελίδες
...however, to observe that, if four quantities are in arithmetical proportion, the sum of the extremes ia equal to the sum of the means. Thus if a . . b : : h . . m, then a+m=b+h For by supposition, a — b=:h — m And transposing - b and-m, a-\-m=b-\-h So in tiie proportion, 12 . . 10: : 1 1 . . 9,... | |
 | Horatio Nelson Robinson - 1846 - 276 σελίδες
...extremes must be double of tha mean. Thus, a, (o+d), (a+2d).a+(a+2d)=2(a+d) When there are four terms, the sum of the extremes is equal to the sum of the means, by (Art. 116.) To facilitate the solution of problems, when three terms are in question, let them be... | |
 | James Bates Thomson - 1847 - 432 σελίδες
...series is called descending ; as, 11, 9, 7,5, &c. 598. When four numbers are in arithmetical progression the sum of the extremes is equal to the sum of the means. Thus, if 5—3=9—7, then will 5+7=3+9. Again, if three numbers are in arithmetical progression, the sum «f... | |
| |
It will be proper, however, to observe that, if four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the means. Thus if a . . b : : h... 
