Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 14.
Σελίδα 79
... observed from A , is 5 ° 30 ' ; and , as observed from B , is 10 ° 45 ' ; the distance from A to B being 100 yards . Find the distance BC , and the height of the pole . 14. Prove that the area of a circle is equal to the pro- duct of ...
... observed from A , is 5 ° 30 ' ; and , as observed from B , is 10 ° 45 ' ; the distance from A to B being 100 yards . Find the distance BC , and the height of the pole . 14. Prove that the area of a circle is equal to the pro- duct of ...
Σελίδα 112
... observation of the expanded form of— ( 1 + 2 + 3 .. + n ) 2 , prove that the sum of the products of the first n numbers two and two together is 24 n ( n + 1 ) ( 3n + 2 ) ( n - 1 ) . 11. Find the coefficient of x " in the expansion of 1 ...
... observation of the expanded form of— ( 1 + 2 + 3 .. + n ) 2 , prove that the sum of the products of the first n numbers two and two together is 24 n ( n + 1 ) ( 3n + 2 ) ( n - 1 ) . 11. Find the coefficient of x " in the expansion of 1 ...
Σελίδα 117
... observed from two stations a mile apart , and from a point half way between them to be 60 ° , 30 ° , and 45 ° respectively . Prove that the height of the balloor in yards is 440✓√6 . 12. The adjacent sides AC and CB of the base of a ...
... observed from two stations a mile apart , and from a point half way between them to be 60 ° , 30 ° , and 45 ° respectively . Prove that the height of the balloor in yards is 440✓√6 . 12. The adjacent sides AC and CB of the base of a ...
Σελίδα 249
... observed to be 22 ° 37 ′ and 58 ° 7 ' respectively . Find BC , having given L sin 80 ° 44 ′ = 9.994295 , L sin 58 ° 7 ′ = 9.928972 , log 4.08 = 610660 , and log 3.51 = 545337 . 4. A pole is fixed on the top of a mound , and the angles ...
... observed to be 22 ° 37 ′ and 58 ° 7 ' respectively . Find BC , having given L sin 80 ° 44 ′ = 9.994295 , L sin 58 ° 7 ′ = 9.928972 , log 4.08 = 610660 , and log 3.51 = 545337 . 4. A pole is fixed on the top of a mound , and the angles ...
Σελίδα 250
... observed by a ship at sea to bear SE .; after the ship had sailed NE . for 12 miles , the light- house was observed to bear 15 ° E. of S. Find the distance of the lighthouse from each position of the ship . 9. An object 10 ft . high is ...
... observed by a ship at sea to bear SE .; after the ship had sailed NE . for 12 miles , the light- house was observed to bear 15 ° E. of S. Find the distance of the lighthouse from each position of the ship . 9. An object 10 ft . high is ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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.