 | 1821 - Страниц: 464
...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 - Страниц: 136
...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 - Страниц: 70
...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 - Страниц: 136
...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 - Страниц: 252
...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 - Страниц: 288
...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 - Страниц: 174
...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... | |
 | Robert Potts - 1865 - Страниц: 528
...the particular conclusions that may be arrived at by means of Euclid's definition of Proportion. 42. Prove from a property of the circle, that if four...and least is greater than the sum of the other two. 43. " Number and magnitude do not corresp .nd in all their relations." In what relations do they correspond... | |
 | Thomas Kimber - 1865 - Страниц: 302
...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 - Страниц: 452
...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... | |
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Find the inclination of the bar to the horizon, upon supposition that the semi-circle is devoid of weight. 2. Prove, from a property of the circle, that if four quantities are proportionals, the sum of the greatest and least is greater than the sum of... 
