A Treatise on Special Or Elementary Geometry
Sheldon, 1872 - 201 pages
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ABCD adjacent altitude applied axis base bisect called centre chord circle circumference coincide common conceive cone consequently construct Converse corresponding DEM.-Let demonstration describe diagonals diameter diedral difference direction distance divided draw drawn edges equal equiangular equivalent extremities faces facial angles fall feet figure four given given line greater Hence homologous inches included inscribed intersect joining latter length less lune manner mean measured meet oblique opposite parallel parallelogram passing perpendicular plane pole polygon position prism produced PROP proportional PROPOSITION pyramid quadrilateral radii radius ratio reason rectangle represent respectively revolve right angles sides similar solid sphere spherical triangle square straight line student supplement surface tangent Theorem.-The third triangle triedral unit vertex vertices volume whence
Page 217 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 109 - If the diagonals of a parallelogram are equal, the figure is a rectangle.
Page 72 - Dn the same side of the secant line is equal to two right angles, the two lines are parallel.
Page 33 - ... two, or equal to the difference ? Ex. 5. If you have two triangles with only one side and one angle in the one equal to one Side and one angle in the other, can y^ou apply one as a pattern and make it fit on the other ? Cut out two such triangles and try it. Ex. 6. If you have two triangles with only two sides of one respectively equal to two sides of the other, can you make one fit as a pattern on the other ? Try it. Ex. 7. If you have two triangles with two sides in one equal respectively to...
Page 136 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Page 125 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having the greater included angle.
Page 69 - If two lines are cut by a third, and the sum of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced.
Page 2 - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.