Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 páginas |
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Página 61
... prove that log.blog , a = 1 . 15. Show that log ( ) = = rlogm ― r logn , and find the logarithms of ' 0625 and 14.4 ... Prove the rule for finding the greatest common measure of two algebraical expressions . 5. Find the greatest common ...
... prove that log.blog , a = 1 . 15. Show that log ( ) = = rlogm ― r logn , and find the logarithms of ' 0625 and 14.4 ... Prove the rule for finding the greatest common measure of two algebraical expressions . 5. Find the greatest common ...
Página 68
... Prove that an + b " is divisible by a + b without remainder , when n is an uneven number . Resolve into their simple factors the expressions ( 1. ) 6 ( x − 1 ) +5 . ( 2. ) ( a2 − 1 ) x2 + ( 3a − 1 ) x + a — a2 . 2. State and prove ...
... Prove that an + b " is divisible by a + b without remainder , when n is an uneven number . Resolve into their simple factors the expressions ( 1. ) 6 ( x − 1 ) +5 . ( 2. ) ( a2 − 1 ) x2 + ( 3a − 1 ) x + a — a2 . 2. State and prove ...
Página 74
... prove that the sum of the two sides containing the right angle is equal to the sum of the diameters of the inscribed and circum- scribed circles . 4. A and B are fixed points , and P is a movable point such that PA always bears a fixed ...
... prove that the sum of the two sides containing the right angle is equal to the sum of the diameters of the inscribed and circum- scribed circles . 4. A and B are fixed points , and P is a movable point such that PA always bears a fixed ...
Página 76
... Prove that cos ( A - B ) = cos A cos B + sin A sin B , and employ this formula to find the value of cos 15 ° . 10. Prove the following equalities : ( 1. ) Sin ( 60 ° + A ) —sin ( 60 −A ) = sin A. ( 2. ) ( Cos A + sin A sin 2A ) 2 ...
... Prove that cos ( A - B ) = cos A cos B + sin A sin B , and employ this formula to find the value of cos 15 ° . 10. Prove the following equalities : ( 1. ) Sin ( 60 ° + A ) —sin ( 60 −A ) = sin A. ( 2. ) ( Cos A + sin A sin 2A ) 2 ...
Página 78
... prove that equiangular parallelograms have to one another the ratio which is com- pounded of the ratios of their ... prove that the three common chords , or these chords produced , pass through one and the same point . Given a circle ...
... prove that equiangular parallelograms have to one another the ratio which is com- pounded of the ratios of their ... prove that the three common chords , or these chords produced , pass through one and the same point . Given a circle ...
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Arithmetic axis ball base bisected body cent centre of gravity circle coefficient of friction compound interest cone cost crown 8vo cube cubic foot curve Define determine diameter Divide dwts ellipse English equal equilibrium expression feet Find the area Find the centre Find the distance Find the equation Find the number Find the sum Find the value fluid forces acting fraction geometrical Grammar horizontal plane hyperbola inches inclined plane inscribed Integrate isosceles latus rectum least common multiple length logarithms miles Multiply parabola parallel particle perpendicular pressure Prove pulleys radius ratio rectangle rectangular Reduce right angles sides simple interest sin² sine spherical triangle square root straight line string subtended Subtract surface tangent theorem tons tower triangle ABC velocity vertical vulgar fraction weight yards
Pasajes populares
Página 123 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 10 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Página 184 - If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other.
Página 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 184 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third (20.
Página 184 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 163 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 184 - In right angled triangles the square on the side subtending the right angle is equal to the (sum of the) squares on the sides containing the right angle.
Página 154 - If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F, D : As AE is to EB, so is CF to FD.