Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 páginas |
Dentro del libro
Resultados 1-5 de 45
Página 11
... right angles = · 2πr2 = 2π × area of hemisphere . FORMULE IN MENSURATION . Area of rectangle = Area of parallelogram ab ; a and b being adjacent sides . ab sin 0 , a and b being adjacent angle 0 . sides including an Area of triangle ...
... right angles = · 2πr2 = 2π × area of hemisphere . FORMULE IN MENSURATION . Area of rectangle = Area of parallelogram ab ; a and b being adjacent sides . ab sin 0 , a and b being adjacent angle 0 . sides including an Area of triangle ...
Página 79
... angles subtended at the centre by the arcs AC and BD is double of the angle AEC . 3. The diameter AB of a circle is produced to C , and through C the line CD is drawn at right angles to the line ABC : Prove that if the straight line AD ...
... angles subtended at the centre by the arcs AC and BD is double of the angle AEC . 3. The diameter AB of a circle is produced to C , and through C the line CD is drawn at right angles to the line ABC : Prove that if the straight line AD ...
Página 80
... angles of the right - angled triangle ABC the lines BD and AE are drawn to the oppo- site sides of the triangle such that the angles DBC and EAC are each equal to a . Prove that DE = AB tan ɑ . 12. Given A = 40 ° , a = 140 · 5 , b = 170 ...
... angles of the right - angled triangle ABC the lines BD and AE are drawn to the oppo- site sides of the triangle such that the angles DBC and EAC are each equal to a . Prove that DE = AB tan ɑ . 12. Given A = 40 ° , a = 140 · 5 , b = 170 ...
Página 81
... right - angled at A , and DAB and EAC be the triangles similar to ABC having their right angles at D and E respectively , prove that the triangles DAB and EAC will be together equal to the triangle ABC . 5. Define circular measure and ...
... right - angled at A , and DAB and EAC be the triangles similar to ABC having their right angles at D and E respectively , prove that the triangles DAB and EAC will be together equal to the triangle ABC . 5. Define circular measure and ...
Página 83
... angle between these two straight lines passes through the centre of the circle ... right angle . 4. Prove that the area of the square inscribed in any circle ... angles such that their difference is one degree , and their sum is the unit ...
... angle between these two straight lines passes through the centre of the circle ... right angle . 4. Prove that the area of the square inscribed in any circle ... angles such that their difference is one degree , and their sum is the unit ...
Otras ediciones - Ver todas
Términos y frases comunes
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.