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### Contents

 Section 1 1 Section 2 17 Section 3 33 Section 4 47 Section 5 61 Section 6 77 Section 7 93 Section 8 109
 Section 12 173 Section 13 189 Section 14 221 Section 15 253 Section 16 269 Section 17 301 Section 18 321 Section 19 325

 Section 9 125 Section 10 141 Section 11 157
 Section 20 333 Section 21 337

### Popular passages

Page 35 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 62 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Page 48 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Page 245 - Prove that the algebraic sum of the moments of two concurrent forces about any point in their plane is equal to the moment of their resultant about the same point.
Page 125 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Page 205 - 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 190 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Page 18 - ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...
Page 287 - If two triangles have two sides of the one equal to two sides of the other...
Page 189 - If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.