## A Popular Course of Pure and Mixed Mathematics ...: With Tables of Logarithms, and Numerous Questions for Exercise |

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### Common terms and phrases

ABCD altitude axis base body called centre circle circumference common cone consequently contained curve cylinder described diameter difference direction distance divided draw drawn equal equation example expression fall feet figure fluxion force four give given greater half Hence inches integral join length less logarithm magnitudes manner means measure meet method motion multiplied opposite original parallel parallelogram pass perpendicular plane pole Prob Problem produced projection PROP proportional pyramid quantity radius ratio rays rectangle Reduce remaining represent right angles root rule sides similar sine solid space sphere square straight line suppose surface taken tang tangent Theorem third triangle vanishing weight whence Wherefore whole

### Popular passages

Page 174 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Page 193 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Page 192 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Page 198 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Page 194 - 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 179 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Page 211 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Page 286 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.

Page 288 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Page 181 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.