Plane and Solid Geometry: Suggestive Method |
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A B and C D A B C and D E F A B equals adjacent angles altitude angle formed angles are equal apothem base and altitude bisects chord circumference circumscribed Compare the ratios construct convex COROLLARY cylinder diagonal diameter dihedral angle distance draw drawn equal circles equal in area equals the ratio equilateral faces frustum Give auth given line given point Hence hypotenuse interior angles intersect isosceles triangle lateral area lateral edges Let A B C represent locus middle point number of sides parallel lines parallelogram parallelopiped perimeter perpendicular plane M N polyhedron prism Prop PROPOSITION III PROPOSITION XII pyramid radii radius rectangle regular polygon respectively right angles right triangle SCHOLIUM segment slant height sphere spherical polygon spherical triangle square subtended surface tangent THEOREM triangles A B C trihedral unit of measure vertex volume
Popular passages
Page 189 - Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Page 81 - If two triangles have two sides of one equal to two sides of the other but the third side of the first greater than the thin!
Page 190 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 19 - If two triangles have two sides, and an included angle of the one, equal to two sides and the included angle of the other, each to each, the remaining parts will also be equal.
Page 368 - ADC ; the last two are therefore right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to the base, and bisects the vertical angle.
Page 159 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 275 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection of AB upon plane MN.
Page 75 - The sum of the interior angles of any convex polygon together with four right angles is equal to twice as many right angles as the polygon has sides 266 CONGRUENT TRIANGLES.
Page 320 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism and whose vertices are the...
Page 335 - The lateral or total areas of two similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases; and their volumes are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. Let S and s...