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" The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples... "
College Algebra - Σελίδα 526
των James Harrington Boyd - 1901 - 777 σελίδες
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 σελίδες
...ratio that the third has to the fourth. VI. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on, whatever...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 σελίδες
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the first has the same ratio to the second that the third has to the fourth. We are now arrived very nearly at Euclid's definition ; for, let A, B, C, D be four proportionals,...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 σελίδες
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same...the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth...

The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - 1835 - 513 σελίδες
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same...the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth...

A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 σελίδες
...quantity be contained in a fourth an equal number of times exactly, — then the first quantity has the same ratio to the second that the third has to the fourth. Thus, if the right line j± _ B o ___ JJ AB be contained, say 4 times exactly in CD, and if the triangle...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 σελίδες
...ratio that the third has to the fourth. 6. Magnitudes are said to be proportionals, wheti the first has the same ratio to the second that the third has to the fourth ; and the third to the fouitii the same ratio which the fililí has to the sixth, and soon whatever...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...ratio that the third has to the fourth. 11. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on, whatever...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 σελίδες
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the first has the same ratio to the second that the third has to the fourth. We are now arrived very nearly at Euclid's definition ; for, let A, B, C, D be four proportionals,...

A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...geometrical magnitudes, and therefore it is necessary to substitute another, which is as follows: — Def. The first of four magnitudes is said to have the same...fourth, when any equimultiples whatever of the first and third being taken, and any equimultiples whatever of the second and fourth — if the multiple of the...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...exceed the other. v. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when, any equimultiples whatever of the first and third being taken, and any whatever of the second and fourth, if the multiple of the first be equal...




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