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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... "
New Cambridge Guide; Or, A Description of the University, Town, and County ... - Página 176
1804 - 130 páginas
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Cambridge Problems: Being a Collection of the Printed Questions Proposed to ...

1821 - 425 páginas
...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...
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A collection of problems and examples adapted to the 'Elementary course of ...

Harvey Goodwin (bp. of Carlisle.) - 1847 - 80 páginas
...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...
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Exercises and problems in algebra [by J. Pryde] with answers. without answers

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,...
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Exercises and problems in algebra [by J. Pryde] with answers

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...
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An elementary course of practical mathematics

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....
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

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.)...
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Problems and Examples

Harvey Goodwin - 1862 - 141 páginas
...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...
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A mathematical course for the University of London. (2nd)

Thomas Kimber - 1865 - 192 páginas
...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)...
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Mathematical exercises

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...
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A Mathematical Course for the Matriculation Examination of the ..., Parte1

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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