Solutions to the mathematical examination papers set for admission to the Royal military academy, Woolwich, and for the Royal military college [&c.] by D. Tierney and H. Sharratt1877 |
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Page 14
... diameters of these circles are to each other in the same ratio as the segments of the base . Let O and O ' ( fig . 5 ) be the centres of the two circles described about the two triangles , and BOD , EO'F diameters of the two circles ...
... diameters of these circles are to each other in the same ratio as the segments of the base . Let O and O ' ( fig . 5 ) be the centres of the two circles described about the two triangles , and BOD , EO'F diameters of the two circles ...
Page 25
... diameter is equal to its conjugate ; therefore CP - CD , and we have SP . HP = CP2 . PURE MATHEMATICS ( 2 ) . TUESDAY , 12TH DECEMBER , 1876. 10 A.M. TO 1 P.M. 1. Prove that the sum of the squares on the three . straight lines drawn ...
... diameter is equal to its conjugate ; therefore CP - CD , and we have SP . HP = CP2 . PURE MATHEMATICS ( 2 ) . TUESDAY , 12TH DECEMBER , 1876. 10 A.M. TO 1 P.M. 1. Prove that the sum of the squares on the three . straight lines drawn ...
Page 35
... diameters passing through the lowest point of the plane are inclined at an angle a to the vertical . 5. Two particles of mass p and q respectively are connected by a string passing over a fixed pulley ; determine the motion of the ...
... diameters passing through the lowest point of the plane are inclined at an angle a to the vertical . 5. Two particles of mass p and q respectively are connected by a string passing over a fixed pulley ; determine the motion of the ...
Page 41
... has been raised . Todhunter's Mechanics , Arts . 192 , 198 . In how many hours would an engine of 18 horse- power empty a vertical shaft full of water , if the diameter G of the shaft be 9 feet , and its depth STATICS . 41.
... has been raised . Todhunter's Mechanics , Arts . 192 , 198 . In how many hours would an engine of 18 horse- power empty a vertical shaft full of water , if the diameter G of the shaft be 9 feet , and its depth STATICS . 41.
Page 67
... diameter . Ans . 1809-5616 square inches . 22. A cylindrical vat 8 feet in diameter contains 960.
... diameter . Ans . 1809-5616 square inches . 22. A cylindrical vat 8 feet in diameter contains 960.
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ABē ABCD acceleration ADē ARITHMETIC axis BCē cent centre of gravity circle coefficient of friction Conic Sections cose cubic curve decimal described diameter Differential Calculus directrix Divide dy dx equal and parallel Euclid expression feet Find the equation forces fraction given straight line hyperbola inches inclined integration intersect Join latus rectum least common multiple logarithmic mechanical advantage METCALFE AND SON moment of inertia Multiply opposite angles parabola parallelogram Parkinson's Mechanics particle perpendicular plane point of bisection Prop prove quadrilateral radius ratio rectangle contained Result right angles roots seconds segments semicircle shew sides Similarly sinē sine square string subtending Subtract tangent Todhunter Todhunter's Trigonometry triangle ABC Trig vertex vertical virtual velocities weight whence whole number yards
Popular passages
Page 55 - If two triangles have two sides of the one equal to two sides of the...
Page 71 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 11 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Page 12 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Page 13 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Page 15 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 13 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Page 62 - In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle.
Page 13 - PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Page 70 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.