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If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... - Σελίδα 72
των Jeremiah Day - 1831 - 332 σελίδες
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An Intire System of Arithmetic: Or, Arithmetic in All Its Parts ..., Τόμος 6

Edward Hatton - 1721 - 395 σελίδες
...continually 3 tioies ; fo will the Anfwer be found <f. 20. 80. 320. 1280. Sthly, If four Numbers be given in Geometrical Proportion, the Product of the two Extremes is equal to that of the two Means : fo in the hift Example 5 times 320 is equal to 20 times 80, viz,. 1600: •'"•...

Astronomia Accurata: Or The Royal Astronomer and Navigator. Containing New ...

Robert Heath - 1760 - 412 σελίδες
...Radius : Dif. Long, nearly. J Ltt. : Dif. Longitude. J Mid. Lat. : Dif. Longitude. SINCE the Produft of the two Extremes is equal to the Product of the two middle Terms, in any Proportion, therefore fubftituting in the 5th Proportion Difl. run X Sine Courfe...

Arithmetic, Both in the Theory and Practice: Made Plain and Easy in All the ...

John Hill - 1764 - 416 σελίδες
...by a rank of numbers geometrically proportional. ' And it is to be known, that if three numbers be in geometrical proportion, the product of the two extremes is equal to the fquare of the mean, by the 2oth of the -yth of Euclid. So, on the contrary, if the re&angle contained...

Arithmetic, Both in the Theory and Practice: Made Plain and Easy in All ...

John Hill - 1765 - 416 σελίδες
...performed by a rank of numbers geometrically proportional. And it is to be known, that if three numbers be in geometrical proportion, the product of the two extremes is equal to the fquare of the mean, by the 2eth of the 7th of Euclid. So, on the contrary, if the rectangle contained...

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. When four quantities-are...

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

Jeremiah Paul - 1801 - 222 σελίδες
...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,...

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 muft be equal...

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

Charles Hutton - 1811
...similar to those in Arithmetical Proportion, using multiplication for addition, &c, , - 1. When 1. Wh.en four quantities are in geometrical proportion,...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. br = ar x i, z:...

A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - 1812
...and reason of the practice in the Rule of Three. THEOREM 2. In any continued geometrical progression, the product of the two extremes is equal to the product of any two means that are equally distant from them, or equal to the square of the middle term when there...

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

John Bonnycastle - 1813 - 428 σελίδες
...• — • • » 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...