An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books

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James Munroe, 1846 - Geometry - 161 pages
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Page 82 - If two angles of one triangle are equal to two angles of another triangle...
Page 82 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page iii - While Nature was feeding her pine with plenty of wholesome juices, Education passed a strong rope round its top, and pulling it downwards with all her force, fastened it to the trunk of a neighbouring oak. The pine laboured to ascend, but not being able to surmount the obstacle, it pushed out to one side, and presently became bent like a bow. Still, such was its...
Page 151 - Similar triangles are to each other as the squares of their homologous sides.
Page 139 - Similarly, by placing A A'B'C' on A AB C, so that Z B' shall coincide with its equal, ^the ZB, we may prove that AB:A'B' = BC:B'C'. QED 355. COR. 1. Two triangles are similar if two angles of the one are equal, respectively, to two angles of the other.
Page 101 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.
Page 66 - Two adjacent sides of a parallelogram and the included angle being given, to construct the parallelogram. Draw the straight line AB equal to one of the given sides. At the point A make an angle, BAD, equal to the given angle, and take AD equalj to the other given side..
Page 109 - The surface of a sphere is equal to four times the area of a circle...
Page 101 - An angle formed by a tangent and a chord drawn from the point of contact is measured by half the intercepted arc.
Page 114 - ... of the triangular prism is equal to the product of its base, half of that of the parallelopiped, by its altitude.

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