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" When any number of terms is continued in Geometrical Progression, the product of the two extremes will be equal to any two means, equally distant from the extremes : As 2, 4, 8, 16, 32, 64, where 64X2=4X32=8X16=128. "
A New System of Arithmetick: In which the Rules are Familiarly Demonstrated ... - Page 241
by William Ruger - 1832 - 263 pages
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Arithmetic in Epitome: Or, a Compendium of All the Rules, Both Vulgar and ...

William Webster - Arithmetic - 1767 - 262 pages
...in any rank of numbers in Geometrical Progreffien, confifting of four, or any even number of terms, the product of the two extremes will be equal to the product of the two middle numbers, or of any two means equally diftant from the faid extremes. 2, 4, 8, 1 6, 32,...
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A Compendium of Practical Arithmetick

John Thomas Hope - Arithmetic - 1790 - 430 pages
...= 45 x IJ each being 675, Hence if ever fo many numbers are in geometrical prpgrefTion, the produft of the two extremes will be equal to the product of any two means, that are didanc from the extremes, As in thefe 3, 9, 27, St, 243, 729, Here 3 x 729 = 9 x 24.1 =27...
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 1

Mathematics - 1801 - 446 pages
...any geometrical series, when it consists of an even number of terms, the product of the extremes is equal to the product of any two means, equally distant from the extremes ; and, when the number of terms is odd, the product of the extremes is equal to the square of the mean...
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A New System of Mercantile Arithmetic: Adapted to the Commerce of the United ...

Michael Walsh - Arithmetic - 1807 - 290 pages
...: As 2, 4, 8, 10, increase by ihe multiplier 2, and 10, 8, 4-, 2, decrease by the divisor 2. NOTE. When any number of terms is continued in Geometrical...Progression, the product of the two extremes will be equal to any two means, equally distant from the extremes : As 2, 4, 8, 16', 32, 64, where 6'4 x 2=4 x 32 =...
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The Schoolmaster's Assistant: Being a Compendium of Arithmetic Both ...

Thomas Dilworth - Arithmetic - 1818 - 222 pages
...the multiplier 2 — and 24, 12, 6, 3, decrease by the divisor 2, Note. 1. If any number of terms be continued in Geometrical Progression, the product...equal to the product of any two means equally distant trom the extremes, as in 3, 6, 12, 24 ; where 3X24, are=tiX 12=72 ; and so of any larger number of...
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Staniford's Practical Arithmetic ...: Adapted Principally to Federal Currency

Daniel Staniford - Arithmetic - 1818 - 332 pages
...three of which being known, the others may be found. NOTE. 1. If any three numbers are in Geomctrical Progression, the product of the two extremes will be equal to the square of the mean or middle number, thus, 4 . 8 . 16 ; 4x16=64=8x8=64. 2. If four numbers are in Geomctrical...
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The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - Arithmetic - 1822 - 354 pages
...usually called the extremes, and the common multiplier or divisor the ruth. Note 1. If three numbers be in geometrical progression, the product of the two extremes will be equal to the square of the mean. Thus, if 3. 9. 27. be in geometrical progression. Then will 3x21=9x9. 2. If four...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 210 pages
...contains the like part of the fourth. THEOREM 39. 113. If four quantities, a, b, c, d, are proportionals, the product of the two extremes will be equal to the product of the two means. Let the first, a, contain the wth part of the second b, m times ; then, by the definition,...
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The Schoolmaster's Assistant: Being a Compendium of Arithmetic, Both ...

Thomas Dilworth - Arithmetic - 1825 - 214 pages
...24, 12, 6, 3, deerease by the divisor 2. Note 1. If any number of terms be continued in Gcomctrieal Progression, the product of the two extremes will...of any two means equally distant from the extremes, as in 3, 6, 12,24; where 3x24, are=6x 12=72, and so of any larger number of terms. 2. If the number...
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The Schoolmaster's Assistant: Being a Compendium of Arithmetic, Both ...

Thomas Dilworth - Arithmetic - 1825 - 218 pages
...the divisor 2. Note ). If any number of terms he continued in Geometrical Progression, the product af the two extremes will be equal to the product of any two means equally distant from the extremes, as iu 3, 6,' 12, 24; where 3x24, are=6x 12=72, and so of any larger number of terms. 2. If the number...
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