## Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and References |

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acting amount angle Arithmetic axis ball base body Book cent centre of gravity circle coefficient common contained cost crown 8vo cubic curve decimal Define described determine diameter difference direction distance Divide drawn ellipse English equal equation equilibrium Explain expression feet Find fixed fluid foot force four fraction given greater greatest half History horizontal horizontal plane hour inches inscribed interest least length logarithms means measure miles moving Multiply observed parallel passing perpendicular placed plane position pressure produced projected Prove radius ratio Reduce respectively rest resultant right angles roots sides smooth square straight line string Subtract surface taken tangent tons tower triangle uniform velocity vertical weight whole yards

### Popular passages

Page 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.

Page 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.

Page 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.

Page 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 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.

Page 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.

Page 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.

Page 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.

Page 6 - Text-Books of Science, Mechanical and Physical, adapted for the use of Artisans and of Students in Public and other Schools.

Page 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.