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A B C angle applied axis base bisect called centre chord circumference coincide compasses construction contained corresponding describe describe a circle diagonals diameter difference direction distance divide division draw drawn equal equilateral triangle equivalent evident example extremities fall figure Find the area fixed formed four Geometry give given circle given point given straight line greater half height Hence hexagon hypothenuse inscribed intersection isosceles join length less line A B line drawn mark means measure meet method middle point obtained opposite sides parallel parallelogram pass pentagon perpendicular placed plane position problem produced proportional Prove radii radius ratio rectangle regular polygon represents respectively right-angles round ruler segment sides similar square star Suppose surface symmetrical tangent termed third touch triangle twice unit vertical whole yards
Page 33 - Any two sides of a triangle are together greater than the third side.
Page 266 - 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 vi - In my own time," says Seneca, "there have been inventions of this sort, transparent windows, tubes for diffusing warmth equally through all parts of a building, short-hand, which has been carried to such a perfection that a writer can keep pace with the most rapid speaker. But the inventing of such things is drudgery for the lowest slaves; philosophy lies deeper. It is not her office to teach men how to use their hands.
Page 59 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Page 146 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 153 - Describe a circle which shall pass through two given points, and have its centre in a given line.
Page 68 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the transversal is equal to two right angles, (p.
Page 86 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.
Page 264 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.