Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Σελίδα 11
... = = ab sin c = 2 2 √ c2 sin A sin B { s ( s — a ) ( s — b ) ( s — c ) } = 2 ' sin ( A + B ) p being the r drawn from A to side c ; s = ( a + b + c ) . Area of trapezoid = ( a + b ) h FORMULA . 11 Formulæ in Mensuration.
... = = ab sin c = 2 2 √ c2 sin A sin B { s ( s — a ) ( s — b ) ( s — c ) } = 2 ' sin ( A + B ) p being the r drawn from A to side c ; s = ( a + b + c ) . Area of trapezoid = ( a + b ) h FORMULA . 11 Formulæ in Mensuration.
Σελίδα 12
... drawn from the end of the arc a to radius through its origin . Area of ring between two concentric circles = π ( r ̧2 — r22 ) ( r1 + r2 ) ( r1 - r2 ) . Τι = and 72 being the radii of the outer and inner circles . Surface of solid ...
... drawn from the end of the arc a to radius through its origin . Area of ring between two concentric circles = π ( r ̧2 — r22 ) ( r1 + r2 ) ( r1 - r2 ) . Τι = and 72 being the radii of the outer and inner circles . Surface of solid ...
Σελίδα 62
... drawn . 12. A cube contains 11 cubic feet 675 cubic inches . Find the length ( 1 ) of its edge , ( 2 ) of its diagonal . 13. In order to find the distance of an enemy's position from his battery an artillery officer riding at the rate ...
... drawn . 12. A cube contains 11 cubic feet 675 cubic inches . Find the length ( 1 ) of its edge , ( 2 ) of its diagonal . 13. In order to find the distance of an enemy's position from his battery an artillery officer riding at the rate ...
Σελίδα 65
... drawn up in the form of a hollow square , three deep ; find the number of men in the front of each side of the square . 10. Define the logarithm of a number to a given base , and find the logarithms of 10000 to the base 10 and to the ...
... drawn up in the form of a hollow square , three deep ; find the number of men in the front of each side of the square . 10. Define the logarithm of a number to a given base , and find the logarithms of 10000 to the base 10 and to the ...
Σελίδα 74
... drawn in a circle then AC and BD are equally distant from the centre . 3. Describe a circle about a given triangle . If the triangle be right angled , prove that the sum of the two sides containing the right angle is equal to the sum of ...
... drawn in a circle then AC and BD are equally distant from the centre . 3. Describe a circle about a given triangle . If the triangle be right angled , prove that the sum of the two sides containing the right angle is equal to the sum of ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.