 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 whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple...  The First Six Books with Notes - Page 168by Euclid - 1822 - 179 pagesFull view - About this book
 | Euclid - Geometry - 1845 - 218 pages
...ratio to the second, than the fifth has to the sixth. PROPOSITION XIV. THEOR. — If the first has the same ratio to the second which the third has to the fourth; then, if the first be greater than the third, the second shall be greater than the fourth ; and if... | |
 | Dennis M'Curdy - Geometry - 1846 - 168 pages
...having some common property ^ can have a ratio to one another. 5. The first of four magnitudes has the same ratio to the second which the third has to the fourth, when equimultiples of the first and third, also of the second and fourth, being taken ; if the multiple... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...multiple, &c. QED Recite (a) definitions 1, 2, A of b 5 -B D-0 H4 Th. If the first of four magnitudes have the same ratio to the second which the third has to the fourth ; then any equimultiples of the antecedents shall have the same ratio as any equimultiples of the consequents.... | |
 | Euclides - 1846 - 292 pages
...has a greater ratio to the second than the fifth has to the sixth. PROP. XIV. THEOR. If the first has the same ratio to the second which the third has to the fourth, then, if the first be greater than the third, the second shall be greater than the fourth, and if equal,... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...two numbers. Let A=mB, and B=nC ; then A=mnC. PROP. IV. THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of the first and third, and any whatever of the second and... | |
 | Euclides - 1848 - 52 pages
...of the second, and the other of the fourth. PROP. IV. THEOREM. If the first of four magnitudes has the same ratio to the second which the third has to the fourth; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...fourth D. If, therefore, the first, etc. QED PROPOSITION IV. THEOB. If the first of four magnitudes has the same ratio to the second which the third has to the fourth, then any equimultiples •whatever of the first and third shall have the same ratio to any equimultiples... | |
 | Euclides - Geometry - 1853 - 334 pages
...is no necessity for all four to be of the same kind. OBS. 3. When the first of four magnitudes has the same ratio to the second which the third has to the fourth, the third clearly has the same ratio to the fourth which the first has to the second. Such will appear... | |
 | Euclides - Geometry - 1853 - 176 pages
...If, therefore, the first, &c. QED PROPOSITION IV. — THEOREM. If the first of four magnitudes has the same ratio to the second which the third has to the fowrth ; then any equimultiples whatever of tlie first and third shall have the same ratio to any equimultiples... | |
 | Euclides - 1855 - 230 pages
...b = 6, which is the first case in Euclid. PROPOSITION A. THEOREM.—If the first of four magnitudes have the same ratio to the second which the third has to the fourth, then, if the first be greater than the second, the third is also greater than the fourth ; and if equal,... | |
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