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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. "
Treatise on the elements of algebra - Page 256
by James Bryce - 1837 - 80 pages
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A New Treatise of Arithmetick and Book-keeping ...: The Whole Illustrated ...

Alexander Malcolm - Arithmetic - 1718 - 396 pages
...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....
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The Teachers Assistant. Or, A System of Practical Arithmetic: Wherein the ...

Arithmetic - 1811 - 210 pages
...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....
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 406 pages
...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...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - Mathematics - 1812 - 620 pages
...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...
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A System of Practical Arithmetic: Applicable to the Present State of Trade ...

Jeremiah Joyce - Arithmetic - 1812 - 274 pages
...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...
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A Treatise on Algebra, in Practice and Theory: With Notes and ..., Volume 1

John Bonnycastle - Algebra - 1813 - 456 pages
...' 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....
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A Treatise on Algebra: In Practice and Theory, ... with Notes and ..., Volume 2

John Bonnycastle - Algebra - 1813 - 444 pages
...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...
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816 - 610 pages
...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...
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The Teachers' Assistant, Or, A System of Practical Arithmetic: Wherein the ...

Arithmetic - 1817 - 214 pages
...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...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 284 pages
...=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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