An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books
James Munroe, 1846 - Geometry - 161 pages
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ABCD Axes base bounded called centre chord circle circumference coincide common connected consequently construct contained corner cube curved line cylinder describe describe a circle diagonals diameter direction distance divided division Draw edge entire equal equal angles equivalent erect example extents exterior angles faces fall feet figure fore found by multiplying give given greater half hexagon horizontal inches inscribed intersect isosceles triangle length less line passes magnitude manner means measure meet middle number of points opposite parallel parallelogram parallelopiped pentagon perpendicular placed plane polygon position preceding proportion pyramid quadrilateral radii radius radius equal ratio regular remark right angle side AC sides similar solidity sphere square straight line suppose surface taken tangents third triangle ABC triangular prism unequal unit vertex vertices whole
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.