 | 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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THEOREM. lf the first 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 first shall also have to the second a greater ratio than the fifth, has to the... 
