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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 ... - Page 176
1804 - 130 pages
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Cambridge Problems: Being a Collection of the Printed Questions Proposed to ...

Mathematics - 1821 - 464 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...
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A collection of problems and examples adapted to the 'Elementary course of ...

Harvey Goodwin (bp. of Carlisle.) - Mathematics - 1847 - 136 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...
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Exercises and problems in algebra [by J. Pryde] with answers. without answers

James Pryde - 1855 - 70 pages
...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 - 136 pages
...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, Part 1

James Elliot - 1860 - 252 pages
...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 - 288 pages
...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 - 174 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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...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...
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A mathematical course for the University of London. (2nd)

Thomas Kimber - Mathematics - 1865 - 302 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)...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 452 pages
...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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