The Elements of Plane and Solid Geometry

Longmans, Green, and Company, 1872 - 285 sider

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Side 107 - Through a given point to draw a straight line 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 line BC.
Side 132 - 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.
Side 23 - If two triangles have two sides of the one equal to two sides of the other, each to each, and" have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them, of the other.
Side 228 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Side 194 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Side 210 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 34 - Any two angles of a triangle are together less than two right angles.

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