An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |
Contents
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Common terms and phrases
ABCD acute angles adjacent angles angles are equal Bisect called centre chord circumference concave angles convex angle convex surface corner cube curved line cylinder decagonal describe a circle diagonals diameter divided division points draw a line Draw a straight equal altitude equal angles equal bases equal-4 equilateral triangle erect a perpendicular exterior angles find the number found by multiplying given number given square greatest number hexagon inches inscribed isosceles triangle length line angles line passes magnitude measure middle point Multiply the number number of angles number of lines number of points number of straight obtuse angles opposite parallelogram parallelopiped passes 2 points pendicular protractor quadrangular quadrilateral radii radius equal ratio rectangle regular polygon right angles semi-circumference set intersecting side AC similar solid angles sphere straight line suppose tangents triangle ABC triangular prism unequal vertex vertices
Popular passages
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.