Elements of Geometry and Conic Sections

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Harper & brothers, 1861 - Conic sections - 234 pages
 

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Page 30 - 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.
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Page 10 - 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 32 - 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 22 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page 148 - It will be shown (p. 7,) that every section of a sphere, made by a plane, is a circle...
Page 79 - ACB about the triangle, and produce AD to the circumference in E, and join EC : then because the angle BAD is equal to the angle CAE, and the angle ABD to the angle (21. 3.) AEC, for they are in the same segment : the triangles ABD, AEC, are equiangular to one another : therefore as BA to AD, so is (4.
Page 65 - ... the sides which contain the right angle. Let ABC be a right-angled triangle having the right angle BAC . the square described upon the side BC is equal to the squares described upon BA, AC. On BC describe the square BDEC (1.

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