Plane and Solid Geometry: Suggestive Method |
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Common terms and phrases
A B and C D A B C and D E F A B sustain A C equals adjacent angles altitude angles are equal apothem arc A B bisects chord circumference circumscribed Compare the ratios Compare Zs construct COROLLARY cylinder diagonal diameter dihedral angles distance draw drawn equal circles equal in area equally distant equals the ratio frustum Give auth given line given point Hence hypotenuse inscribed angle intersect isosceles triangle lateral area lateral edges Let A B C represent line A B locus middle point number of sides parallel lines parallelogram parallelopiped perimeter perpendicular plane M N polyhedron prism Prop PROPOSITION XVIII pyramid radii radius rectangle regular polygon respectively right angles right triangle SCHOLIUM segment slant height sphere spherical polygon spherical triangle subtended tangent THEOREM triangles A B C trihedral unit of measure vertex vertices volume
Popular passages
Page 137 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Page 48 - If two triangles have two sides of one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 138 - ... 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 59 - 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 292 - 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 211 - 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 119 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 96 - It is read the ratio of a to b equals the ratio of c to d, or briefly, a is to b as c is to d.
Page 254 - 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 three...
Page 263 - That is, the lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases.