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Elements of Geometry: Containing Books I, to Vi, and Portions of Books XI ...
J. Hamblin Smith
No preview available - 2018
ABCD base bisected Book called centre chord circle circumference coincide common construction described diagonals diameter difference distance divided double draw drawn equal equiangular Euclid extremities fall figure formed four given point given straight line greater half Hence inscribed intersect isosceles triangle join length less Let ABC magnitudes measure meet method multiple Note opposite sides parallel parallelogram pass perpendicular placed plane polygon position Problem produced proof Prop proportional Proposition prove quadrilateral radius ratio rect rectangle contained regular respectively right angles segment shew shewn sides similar Similarly square suppose Take taken tangent Theorem third touch triangle triangle ABC twice vertex vertical whole
Page 51 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 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...
Page 104 - 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.
Page 44 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Page 88 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle, is greater than the squares on 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 angle, Let ABC be an obtuse-angled triangle, having the obtuse angle...
Page 89 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Page 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 42 - 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.