Elements of Geometry

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J. Johnson, 1787 - Geometry - 162 pages
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Page 90 - FGL have an angle in one equal to an angle in the other, and their...
Page 31 - Through a given point to draw a line parallel to a given straight line.
Page 3 - The magnitude of an angle does not depend upon the length of its legs, that is, of the straight lines by which it is...
Page 94 - Q. the rectangle of B and C, and R the rectangle of B and D. Then the rectangles P and R, being between the same parallels, are to each other as their bases A and B (th.
Page 15 - ... and D; join C and D cutting AB at E, and the line AB is bisected at E. For C and D being each equally distant from A and B, the line CD must be perpendicular to AB at its middle point (converse of I.
Page 133 - But these two angles are (Defin. 3.) the angles of inclination of the two planes. Therefore the two planes make angles with each other, which are together equal to two right angles.
Page 21 - If a line is perpendicular to one of two parallel lines, it is perpendicular to the other; thus EF (Art.
Page 135 - Hence it follows that the lines BG, AH, are parallel (def. 9). And the line AB being perpendicular to the line AH, is also perpendicular to the parallel line BG (cor th. 12). In like manner it is proved, that the line AB is perpendicular to all other lines which can be drawn from the point B in the plane EF. Therefore the line AB is perpendicular t
Page 96 - Let the four lines meet in a common point, forming at that o point four right angles, and complete the rectangles x, y, z. If the line A be triple of the line B, the line C will be triple of the line D. | * The rectangles .••• and z, being between the same parallels, FI* soi.
Page 130 - CDE, another plane might puss through the point A, to which the line AB would be perpendicular. But this is impossible ; for, since the angles BAG, BAD, are right angles...

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