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alſo equal alternate angles angle ATD angle G angles equal baſe AD baſe cD Becauſe the lines biſe&ts chord compoſed cone conſequently cube demonſtrated deſcribe draw the line Draw the right drawn equal number equiangular exterior angles fides fimilar figures firſt given line half the arc impoſſible incloſe Let the line line AB line Ac line BA line cD line D meaſured by half oppoſite P R O parallelogram ABCD paſs perpendicular phyſical points plane LM point F point of diviſion priſm produćt pyramid radii radius ct reëtangle right angles right line ſame baſe ſame manner ſame parallels ſame reaſon ſe&tion ſecants ſecond ſee fig ſegment ſhall ſide AB ſide Ac ſide cD ſide FG ſides proportional ſimilar ſince ſmall ſmaller ſolid content ſpace ſphere ſquare ſuch manner ſuppoſed ſuppoſition ſurface tangent Theſe two triangles triangle ABc triple
Page 90 - FGL have an angle in one equal to an angle in the other, and their...
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.