Chauvenet's Treatise on Elementary Geometry |
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Common terms and phrases
ABCD adjacent angles altitude angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane angle plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle rectangular parallelopiped regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 38 - The sum of the three angles of any triangle is equal to two right angles.
Page 133 - The area of a rectangle is equal to the product of its base and altitude.
Page 249 - 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 vertices of the inclined section.
Page 117 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 29 - The perpendicular is the shortest line that can be drawn from a point to a straight line.
Page 282 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.
Page 214 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.
Page 54 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector is unequally distant from the sides of the angle...
Page 79 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.
Page 52 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.