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ABCD base bisected Book called centre chord circle circumference coincide common construction described diagonals diameter difference distance divided double draw drawn equal equiangular equimultiples Euclid extremities fall figure formed four given point given straight line greater half Hence inscribed intersect isosceles triangle join less Let ABC magnitudes measure meet method middle points multiple NOTE opposite sides parallel parallelogram pass perpendicular plane polygon PROBLEM produced Prop PROPOSITION prove Q. E. D. Ex quadrilateral radius ratio rect rectangle contained regular respectively right angles segment shew shewn similar Similarly square suppose Take taken tangent THEOREM third touch triangle triangle ABC twice vertex whole
Pagina 79 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Pagina 158 - 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.
Pagina 7 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Pagina 40 - 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...
Pagina 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Pagina 96 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Pagina 168 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Pagina 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Pagina 275 - 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.
Pagina 81 - 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.