...follows that the same multiples of the first and third being taken, and also of the second and fourth, the multiple of the first is greater than, equal to, or less than, that of the second, according as that of the third is greater than, equal to, or less than, that...

...ELEMENTARY MATHEMATICS equal to that of the fourth ; or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth."1 The other extreme is the purely algebraic plan, the one adopted by most American...

...third is also equal to that of the fourth : and, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. The statement of the above Test in symbols has already been given in Art. 35. Art....

...the third is also equal to that of the fourth, and if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth." (Euclid, Book V.) ac For, let a : b = c ; d; then — oa £2=£5. qh qd Hence...

...the third is also equal to that of the fourth ; or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth." 199 It is worth noticing that this theorem is true whether the parallel meets...

...the third is also equal to that of the fourth, and if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth.' This means in effect that where we cannot speak of a ratio in the strict Pythagorean...