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" In any continued geometrical progression, the product of the two extremes is equal to the product of any two means... "
Practical Arithmetic: In Four Books ... Extracted from the Large and Entire ... - Σελίδα 303
επεξεργασία από - 1813 - 348 σελίδες
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Arithmetic, Both in the Theory and Practice: Made Plain and Easy in All ...

John Hill - 1765 - 416 σελίδες
...96 by 24 ; all being. terms equally diftant. THEOREM IV. In any geometrical progreffion whatfoever, the product of the two extremes is equal to the product of any other two immediate terms of like diftance from both. EXAMPLE. 5, 20, 80, 320, 1280, 5120. So in this...

A Synopsis of Practical Mathematics: Containing Plain Trigonometry ...

Alexander Ewing - 1799 - 328 σελίδες
...antecedents-, and the feconct and fourth terms, 32 and 24, are confequents. In four proportional numbers, the product of the two extremes is- equal to the product of -the two means ; End. B. 6 prop. 16. ; thus^ if -1€ s• 3* • 1 12 ! 24, then 16X24=32X 12 = 384....

The American Preceptor's Assistant: Containing a System of Practical Arithmetic

Jeremiah Paul - 1801 - 222 σελίδες
...multiplier 2 ; and 729, 243, 81, 27, 9,3, 1, decrease by the common divisor 3. In any series of numbers, in Geometrical Progression, the product of the two extremes, is equal to the product of any two means, equally distant therefrom ; or of the product of the middle term by itself: Thus, 1, 3, 9, 27,...

The Elements of Natural Or Experimental Philosophy, Τόμος 1

Tiberius Cavallo - 1803
...multiplied by AS. Then D is the centre of percuflion. And fmce, when four quantities are proportional, the product of the two extremes is equal to the product of the two means; therefore if the weight of A multiplied by AS, be again multiplied by AD, the product...

The Tutor's Guide: Being a Complete System of Arithmetic; with Various ...

Charles Vyse - 1806 - 320 σελίδες
...the common Divisor or Ratio is 3. In any Series of Numbers in Geometrical Prpgression, the Prodjct of the two Extremes is equal to the Product of any two Means that are equally distant from the Extremes. * A. 3. 9. 27. 81. 243. 729. Here 3 X 729 = 27 X...

The Columbian Arithmetician: Or, New System of Theoretical and Practical ...

1811 - 216 σελίδες
...geometrical piogreiSon or proportion ; ie increafing or decreaiing by an У equal ratio •, the produdl of the two extremes, is equal to the product of any two means equally diftant from the extremes, and is equal to the fquare of the middle term ; as, 2,4,8,16,32-,...

A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811
...multiplication for addition, &c, , - 1. When 1. Wh.en four quantities are in geometrical proportion, the product of the two extremes is equal to the product of the two means. As in these, 3, 6, 4, 8, where 3x8=6 X 4 = 24; and in these, a, ar, b, br, where ax....

A Course of Mathematics: For the Use of Academies as Well as ..., Τόμος 1

Charles Hutton - 1812
...contained in the following theorems. THEOREM 1. When four quantities are in geometrical proportion, the product of the two extremes is equal to the product of the two means. Thus, in the four 2, 4, 3, 6, it is 2 X 6 = 3 x 4 = 12. And hence, if the product of...

A Treatise on Algebra, in Practice and Theory: With Notes and Illustrations ...

John Bonnycastle - 1813
...• — • • » 2 ' 6 ' ' 3 • 9' a • b • ' с • d 9. In any continued geometrical series, the product of the two extremes is equal to the product of any two means that are equally distant from them ; or to the square of the mean, when the number of terms is...

An Easy Introduction to the Mathematics: In which the Theory and ..., Τόμος 2

Charles Butler - 1814
...and one for z \ the four theorems for rinding the value of n, may be expressed four proportionals, the product of the two extremes is equal to the product of the two means ; and in three proportionals, the product of the extremes !• opal to the square of...




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