...of the fourth, equal to it, or less. 6. 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 be...

...f3,ft This condition is evidently equivalent to the definition 5 of the Fifth Book of Euclid, viz.— 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...

...number of metres may make, a greater length can always be found containing an exact number of yards. 5. The first of four magnitudes is said to have the '...when, any equimultiples whatever of the first and third being taken, and any equimultiples whatever of the second and fourth, the multiple of the third...

...greater than, equal to, or less than the multiple of the fourth — under those conditions, the first is said to have the same ratio to the second that the third has to the fourth ; and the four magnitudes are called proportionals. And, conversely, if four magnitudes are proportionals,...

...definition. Euclid's definition of a proportion is: ' 'The first of four magnitudes is said to hare the same ratio to the second that the third has to...second and the fourth, if the multiple of the first IMJ less than that of the second, the multiple of the third is also less than that of the fourth, and...

...quadrilateral (i) inscribed in, (2) described about, a circle. 9. When is the first of four magnitudes said to have the same ratio to the second that the third has to the fourth ? Illustrate this definition by giving Euclid's proof of the proposition that triangles of the same...

...that the third has to the fourth. ' 6. 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 be...

...circle describe a triangle equiangular to a given triangle. 6. When is the first of four magnitudes said to have the same ratio to the second that the third has to the fourth ? Explain the terms — invertendo, ex aequali. Define reciprocal figures. *i '. If a straight line...

...PR0P0RTI0N. ART. 197. Proportion is an equality of ratios. Four numbers are proportional, when the first has the same ratio to the second that. the third has to the fourth. REVIEW. — 19i. How is a ratio affected by multiplying the consequent, or dividing the antecedent...