Elements of GeometryJ. Johnson, 1787 - 162 Seiten |
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ABCDF alſo equal alternate angles angle ATD angle G angles equal baſe AD baſe LM Becauſe the lines biſected chord circle circumference compoſed conſequently cube deſcribe draw the line draw the right equal baſes equal number equal to half equiangular fide AB fide AC fides proportional fince firſt folid given line half the arc half the product incloſe interfect line AB line BA line CD line D line FG lines AC meaſured 42 meaſured by half muſt oppoſite parallelogram ABCD paſs perpendicular phyſical points plane LM points of diviſion PROP pyramid radii radius rectangle right angles right line ſame baſe ſame manner ſame parallels ſecond ſection ſegment ſhall ſide ſimilar ſimilar figures ſince ſmall ſolid ſolid content ſpace ſphere ſquare ſuch manner ſuppoſed ſurface tangent Theſe two triangles three fides equal triangle ABC triangle DFG triple whence
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Seite 85 - FGL have an angle in one equal to an angle in the other, and their...
Seite 31 - Through a given point to draw a line parallel to a given straight line.
Seite 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...
Seite 86 - 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.
Seite 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.
Seite 125 - 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.
Seite 21 - If a line is perpendicular to one of two parallel lines, it is perpendicular to the other; thus EF (Art.
Seite 127 - 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
Seite 88 - 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.
Seite 122 - 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...