 | George Hutton (arithmetic master, King's coll. sch.) - 1844 - 276 pages
...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... | |
 | James Bates Thomson - Algebra - 1844 - 272 pages
...a-\-m=b-\-h. So in the proportion, 12 •• 10 : : 11 •• 9, we have 12+ 9=10-|-11. 325. Again if three quantities are in arithmetical proportion, the sum of the extremes is equal to double the mean. If a ., b : : b •• c, then, a — 6=6 — c And transposing — b and — c, a-|-c=26.... | |
 | Francis Henney Smith - Arithmetic - 1845 - 710 pages
...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.... | |
 | Francis Henney Smith - Arithmetic - 1845 - 300 pages
...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.... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...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... | |
 | James Bates Thomson - Arithmetic - 1847 - 426 pages
...is called descending; as, J 1, 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,... | |
 | James Bates Thomson - Arithmetic - 1847 - 432 pages
...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,... | |
 | Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...a-\-m=b-\-h. So in the proportion, 12- 10:: 11 •• 9, we have 12+ 9=10-[-ll. 325. Again if three quantities are in arithmetical proportion, the sum of the extremes is equal to double the mean. If a •• b : : b •• c, then, a — 6=6 — c And transposing — b and —... | |
 | Horatio Nelson Robinson - Algebra - 1848 - 354 pages
...perceive by inspection that the sum of the extremes is double the mean. When there are four terms, the sum of the extremes is equal to the sum of the means, by (Art. 1 1 6.) To facilitate the solution of problems, when three terms are in question, let... | |
 | Uriah Parke - Arithmetic - 1849 - 414 pages
...propositions as are connected with it. PROPOSITION 38. If four numbers are arithmetically proportional, the sum of the extremes is equal to the sum of the means. 2, 4, 6, 8. 2+8=4 + 6. Here the common difference is embraced once in the 2nd term, and twice... | |
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When four quantities are in arithmetical proportion, the sum of the extremes is equal to the sum of the two mean terms. 
