 | George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...Proportion consists iu three terms at least. X. "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. If a : I : : Ъ : с, a is said to have to с the duplicate ratio ofthat which it has to 6.... | |
 | Euclides - 1863 - 122 pages
...consists in three terms at least. 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... | |
 | Euclides - 1864 - 448 pages
...Proportion consists in three terms at least. X. 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. XL When four magnitudes are continual proportionals, the first is said to have to the fourth,... | |
 | Euclides - 1865 - 402 pages
...BC is to EF, so is EF to 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 BC has to BG the duplicate ratio of that which BC has to EF; but as... | |
 | Robert Potts - 1865 - 528 pages
...because as BC is to EF, so EFto BG; and that if three straight lines be proportionals, the first is sr.id to have to the third, the duplicate ratio of that which it has to the second: (v. def. 10.) therefore BC has to BG the duplicate ratio of that which BC has tn EF: ImtasBCistoBG,... | |
 | E. M. Reynolds - Geometry - 1868 - 172 pages
...NOTE. Duplicate ratio is thus deftned : 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, A has to C the duplicate ratio of that which it has to B. It will be... | |
 | Robert Potts - 1868 - 434 pages
...Proportion consists in three terms at least. X. 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. XT. When four magnitudes are continual proportionals, the first is said to have to the fourth,... | |
 | William Nathaniel Griffin - Algebra - 1871 - 330 pages
...are aH equal fractions. ba J 310. Def. — If three quantities are in proportion, the first is said to have to the third the duplicate ratio of that which it has to the second. If the quantities be a, b, c, so that a : b = b : c, or ? = b, bc It appears then that the... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...particular case of Proposition xi. DBF. II. 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 here AB has to CE the duplicate ratio of AB to AC. DBF. III. When three magnitudes are... | |
 | Charles Lutwidge Dodgson - 1874 - 96 pages
...three terms at least. This is an Axiom. X. 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. XI. When four magnitudes are continual proportionals, the first is said to have to the fourth,... | |
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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. 
