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" It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes. "
Elements of Algebra: Being an Abridgement of Day's Algebra Adapted to the ... - Σελίδα 210
των Jeremiah Day - 1844 - 252 σελίδες
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1814 - 303 σελίδες
...quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the...of the means equal to the product of the extremes. • It is evident, in the first place, that any alteration in the arrangement, which will not affect...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1827 - 332 σελίδες
...quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the...of the means equal to the product of the extremes. It is evident, in the first place, that any alteration in the arrangement, which will not affect the...

A New Introduction to the Science of Algebra...

Silas Totten - 1836 - 304 σελίδες
...fractions being equal, and the denominators the same, the numerators must also be equal ; and hence, the product of the means equal to the product of the extremes. (66.) The property of geometrical proportions which has just been proved, is the fundamental principle...

A Practical and Theoretical System of Arithmetic: Containing Several New ...

George Willson - 1838 - 192 σελίδες
...is there between the product of the means, and the product of the extremes of a proportion ? Why is the product of the means equal to the product of the extremes ? ' What rule is founded on this equality ? Explain the common method of stating in the Single Rule...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1839 - 332 σελίδες
...demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will lea*e the product of the means equal to the product of the extremes. It is evident, in. the first place, that any alteration in the arrangement, which will not affect the...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1842 - 332 σελίδες
...proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of ihe ratios; or which will leave the product of the means equal to the product of the extremes. It is evident, in the first place, that any alteration in the arrangement, which will not affect the...

A New Practical and Theoretical Arithemtic: In Which, in Addition to the ...

Horatio Nelson Robinson - 1845 - 288 σελίδες
...is there between the product of the means, and the product of the extremes of a proportion ? Why is the product of the means equal to the product of the extremes ? What rule is founded on this equality ? Explain the common method of stating in the Single Rule of...

The first principles of algebra, for the use of the boys of the Royal ...

Admiralty - 1845
...equation, Divide by 13 .-. ж=12 61. An equation may be formed from 4 proportional quantities, by making the product of the means equal to the product of the extremes. Let the proportional quantities be x, y, a, b ; or x : y : : a : b. Vy-J (Art. 15.) .-. bx=ay. (Art....

An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - 1845 - 294 σελίδες
...:: D : C; B : D : : A : C, &c. &c. From each of which we may readily derive the equation AD= CB, or the product of the means equal to the product of the extremes. Many other properties might be presented, but we limit ourselves to this short discussion, and proceed...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1846 - 332 σελίδες
...quantity, or the proposition which we wish to demonstrate. It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to fhe product of the extremes. It is evident, in the first place, that any alteration in the arrangement,...




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