## Modern geometry [ed.] with an appendix by W.B. Jack1876 |

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A B C base bisect bisector called centre CHAPTER chord circle circumference common consequently Construct converse corresponding curve DEFINITIONS describe describe a circle determined diagonals diameter difference direction distance divided draw drawn equal equidistant evident example EXERCISE extremities fall figure four given circle given point given straight line greater half height Hence inches inscribed isosceles joining length less line joining magnitudes mark means measure meet middle points moving number of sides opposite opposite sides parallel parallelogram pass perpendicular plane position PROBLEM produced Proof properties proportion propositions proved quadrilateral radius ratio rect rectangle regular polygon respectively right angles segment sides similar square statements Suppose surface tangent termed Theorem third touch triangle true truth twice units whole yards

### Popular passages

Page 242 - 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 240 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 240 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 242 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Page 242 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.

Page 241 - If the first has to the second the same ratio which the third has to the fourth...

Page 240 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 242 - 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 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Page 239 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.