 | Euclides - 1874 - 342 pages
...Proportion consists in three terms at least. 10. When three magnitudes are proportionals, the first is said to have to the third, the duplicate ratio of that which it has to the second. 11. When four magnitudes are continual proportionals, the first is said to have to the fourth,... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...because as .BCis to EF, so EFto BG; and that if three straight lines be proportionals, the first is said to have to the third, the duplicate ratio of that which it has to the second : (v. def. 10.) therefore BChas to BG the duplicate ratio of that whichSChasto EF: but as BCis... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...Proportion consists in three terms at least. 10. When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio Of that which it has to the second. [The second magnitude is said to bo a mean proportional between the first and the third.] 11.... | |
 | 1882 - 486 pages
...duplicate ratio of their homologous sides. (a) "When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. (Definition, Book V.) (b) Euclid, Book VI., Prop. 19. 6. If the four sides of any quadrilateral... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...Proportion consists in three terms at least. 10. "When three magnitudes are proportionals, the first Ja said to have to the third the duplicate ratio of that which it has to the second. [The second magnitude is said to be a mean proportional between the first and the third.] 1... | |
 | Euclides - 1885 - 340 pages
...proportion is 4 : 6 : : 6 : 9. x. When three magnitudes are continual proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. xi. When four magnitudes are continual proportionals, the first is said to have to the fourth... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...proportion is 4 : 6 : : 6 : 9. x. When three magnitudes are continual proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. xi. When four magnitudes are continual proportionals, the first is said to have to the fourth... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...Proportion consists in three terms at least 10. When three magnitudes are proportionals the first is said to have to the third the ' duplicate ratio ' of that which it has to the second. Thus if A : B :: B : C, then the ratio of A : C is called the ' duplicate ' of the ratio A:... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...T, -, -, - we ocae HSE , Definition 13. When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. Thus if a : b : : b : c, then a : c is said to be the duplicate of the ratio a : 6. NOTE. In... | |
 | Euclid - Mathematics, Greek - 1908 - 456 pages
...in three terms is the least possible. 9. When three magnitudes are proportional, the first is said to have to the third the duplicate ratio of that which it has to the second. 10. When four magnitudes are < continuously > proportional, the first is said to have to the... | |
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When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. 
