| 1821 - 425 pages
...semi-circle, whose diameter is the bar. Find the inclination of the bar to the horizon, upon supposition **that the semi-circle is devoid of weight. 2. Prove,...required to find the content of a solid, formed by** drawing lines from a given point without the plane, :to every .part of its surface. V 4. The inclination... | |
| Harvey Goodwin (bp. of Carlisle.) - 1847 - 80 pages
...ratio а : b, that it may become equal to the ratio с : d? 4. If four quantities are proportional, **the sum of the greatest and least is greater than the sum of the other two.** 6. If a : b :: с : d, then a + b : a - b :: с + d : с - d. 7. Given that у œ x, and that when... | |
| James Pryde - 1855
...then ma + nb : a : : mc + nd : c. 12. If four quantities of the same kind be proportional, prove that **the sum of the greatest and least is greater than the sum of the other two.** 13. Itx:y :: a" :b4, ando: 6 : : j/(c + x) : tf(d + y), shew that cy = dx. IÍ. If a : 6 : : с : d,... | |
| James Pryde - 1855
...nc 4- nd we have = . ac 12. If four quantities of the same kind be proportional, prove that the sura **of the greatest and least is greater than the sum of the other two.** Let the four proportional quantities be a : b : : с : d, of which a is the greatest, and consequently... | |
| James Elliot - 1860
...proportions, 6 : 1 2 : : 10 : 20, and 9 : 12 : : 15 : 20, form one, by this corollary. THEOREM IX. **If four Quantities are Proportionals, the Sum of the...and least is greater than the Sum of the other two.** DEM. If a : b : : c : d, then, since ad±bc, if a is the greatest, d is the least. But (Th. 6, Cor.... | |
| Euclides - 1860
...manner, if A ^LB it can be demonstrated that A + B:BA::C + D:DC. If four magnitudes be proportional, **the sum of the greatest and least is greater than the sum of the other two.** (tici.il that A : B : : C : D, and that A is the greatest. term; to prove that A + D -?• B + a (Dem.)... | |
| Harvey Goodwin - 1862 - 141 pages
...QW a + ba + 2b ' 2. Compare the ratios, -= and — . 4. If four quantities are proportional, the Bum **of the greatest and least is greater 'than the sum of the other two.** 5. If a : I '.'. c : d, and a be the greatest of the four quantities a, J, c, d, then a™ + dm is... | |
| Thomas Kimber - 1865 - 192 pages
...roots of those quantities are proportional. VIII. [Eu. V., 2o. 148. If four quantities be proportional, **the sum of the greatest and least is greater than the sum of the other two.** a being the greatest of the four terms in a proportion, d will be the least, and (a + d) > (b + c)... | |
| Samuel H. Winter - 1877
...the numbers. 69. Expand (a2— a;2)-2 to 6 terms by the binomial theorem. 70. If four magnitudes be **proportionals, the sum of the greatest and least is greater than the sum of the other two.** 71. The number of combinations of n things, taken 4 together, is to the number taken 2 together as... | |
| 1877
...roots of those quantities are proportional. VIII. [Eu. V., 25. 148. If four quantities be proportional, **the sum of the greatest and least is greater than the sum of the other two.** a being the greatest of the four terms in a proportion, d will be the least, and (a + d) > (b + c)... | |
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