| Industrial arts - 1827 - 600 pages
...Гич г та?bur тК »r :¡ ] i к ^ ALfíBHRAH.AI. «S7 ' uitudes has the same ratio to the secood, **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, equal; if lees, less." Hence, in... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...to B, D, F together. Wherefore, if any number, &c. «. ED PROP. XIII. THEOR. SeeN. If the Jirst has **to the second the same ratio which the third has to the fourth,** but the third to the fourth a greater ratio than the fifth has to the sixth ; the Jirst shall also... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...A : D = A' : D', and so on, whatever be the number of magnitudes. PROPOSITION XXIV. THEOREM. (503) **If the first have to the second the same ratio which the third has to the fourth** ; and the fifth to the second, the same ratio which the sixth has to the fourth ; the first and fifth... | |
| John Warren - Geometry of numbers - 1828 - 302 pages
...opposite direction are called negative quantities. (12.) DEF. The first of four quantities is said to **have to the second the same ratio which the third has to the fourth** ; when the first has in length to the second the same ratio which the third has in length to the fourth,... | |
| Euclid, Robert Simson - Geometry - 1829 - 548 pages
...GB is of E. If therefore two magnitudes, &c. QE IX PROP. A. THEOR. IF the first of four magnitudes **have to the second the same ratio which the third...the fourth: then, if the first be greater than the** second, the third is also greater than the fourth; and if equal, equal; if less, less.* Take any equimultiples... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...to the second, and of the third to the fourth be expressed by the same terms ; the first is said to **have to the second the same ratio which the third has to the fourth** ; and the four magnitudes are called proportionale. IL $ 1.1 For example, let ABC I), and EFGH be two... | |
| John Playfair - Euclid's Elements - 1832 - 356 pages
...Therefore HI A>»B, and mE<nF, wherefore, A: B>E: F (def. 7. 5.). Therefore, &c. QED . PROP. XIV. THEOR. **If the first have to the second the same ratio which the third** hat to the fourth, and if Ihejirst be greater than the third, the second shall be greater than the... | |
| John Playfair - Euclid's Elements - 1833 - 348 pages
...mA7«B, and mE/.nF, wherefore, A : B7E : F (def. 7. 5.) Therefore, &c. QED PROP. XIV. THEOR. If ike **first have to the second the same ratio which the third has to the fourth,** and if the first be greater than the third, the second shall be greater than the fourth ; if equal,... | |
| Robert Simson - Trigonometry - 1835 - 544 pages
...greater ratio to the second than the fifth has to the sixth. PROP. XIV. THEOR. Sec N. If the first has **to the second, the same ratio which the third has...if the first be greater than the third, the second** will be greater than the fourth ; and if equal, equal ; and if leas, less. Let the first A, have to... | |
| Euclid - 1835 - 540 pages
...b2. 5. O H BDET PROP. A. THEOR. Boot V. If the first of four magnitudes has to the second the sec N. **ratio 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, equal ; if less, less. Take any equimultiples... | |
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