 | Alexander Malcolm - 1718 - 396 σελίδες
...fought. Propofition zd, IF four Numbers are in Arithmetical Proportion, whether continued or interrupted; the Sum of the two Extremes is equal to the Sum of the two middle "Terms: And therefore four Numbers with this Property, are Arithmetically proportional.... | |
 | 1811 - 210 σελίδες
...last terms are called the extremes. Note. — In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two teni.b equally distant from them; as m the latter of the above series 6 + 1 =» 4 + 3, and = 5 + 2.... | |
 | Charles Hutton - 1811 - 406 σελίδες
...proportion is contained in the following theorems : 1. When four quantities are in Arithmetical Proportion, the sum of the two extremes is equal to the sum of the two means. Thus, in the arithmeticals 4, 6, 7, 9, the sum 4 + 9 = 6 + 7 = 13: and in the arithmeticals... | |
 | Charles Hutton - 1812 - 620 σελίδες
...contained in the following theorems : THEOREM 1. When four quantities arc in arithmetical proportion, the sum of the two extremes is equal to the sum of the two means. Thus, of the four 2, 4, 6, 8, here 2 + 8 = 4 + 6= 10. THEOREMS. In any continued arithmetical... | |
 | Jeremiah Joyce - 1812 - 274 σελίδες
...term ; as 6, 9, 12, where 6 + 12 = 2 X «f = 18. 2. If four numbers be in arithmetical progression, the sum of the two extremes is equal to the sum of the means; as 5, 8, 11, 14, where 5 + 14 = 8 + 11 = 19. 3. When the number of terms is odd, the double... | |
 | John Bonnycastle - 1813 - 456 σελίδες
...' number (n). of arithmetical means between a and b. 4. In any continued arithmetical progression, the sum of the two extremes is equal to the sum of any two terms that are equally distant from them, or to double the middle term, when the numher of terms is odd.... | |
 | John Bonnycastle - 1813 - 444 σελίδες
...each of the two members, we shall have a + d=b+c. From which it appears, as in the common rule, that the sum of the two extremes is equal to the sum of the two means. And if the third term, in this case, be the same as the second, or c = b, the equi-diflerence... | |
 | Charles Hutton - 1816 - 610 σελίδες
...b, b + d, the sum a + 6 + d = a + 6-\-d. 2. In- any continued arithmetical progression, the sum oi" the two extremes is equal to the sum of any two terms at an equal distance from them. Thus Thus, if th« series be 1, 3, 5, 7, 9, 1 1, &c. Then 1+11=3+9=5... | |
 | 1817 - 214 σελίδες
...last terms are called the extremes. JVote. — In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them ; as in the latter of the above series 6-fl=4-f-3, and=5-{-2. Whei. the number of terms is odd, the... | |
 | John Bonnycastle - 1818 - 284 σελίδες
...=5i. 2 2 And an arithmetical mean between a and b is . 4. In any continued arithmetical progression, the sum of the two extremes is equal to the sum of any two terms that are equally distant from them, or to double the middie term, when the number of terms is odd.... | |
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In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2. 
