Chauvenet's Treatise on Elementary Geometry |
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Common terms and phrases
ABCD adjacent angles altitude angle ABC angle BAC angles are equal arc BC axis base bisect bisector called centre chord circumference circumscribed coincide common constructed convex convex polygon Corollary Definition diagonals diameter dicular diedral angle distance divided draw equal angles equally distant exterior angle faces figure frustum geometry given point given straight line greater hence homologous homologous sides hypotenuse indefinite inscribed inscribed angle intercepted arc isosceles lateral edges less Let ABC measured by one-half middle point number of sides parallelogram parallelopiped pass pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron produced proportion PROPOSITION pyramid quadrilateral radii radius ratio rectangle regular polygon revolving rhombus right angles right triangles Scholium secant secant line segment similar square straight line drawn surface tangent tetraedrons THEOREM triangle ABC triedral vertex vertices
Popular passages
Page 201 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 31 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP
Page 201 - Words, Facts, and Phrases : A Dictionary of Curious, Quaint, and Out-of-the-Way Matters. By ELIEZER EDWARDS.
Page 120 - Any side of a spherical triangle is less than the sum of the other two.
Page 81 - 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 92 - Every point in the bisector of an angle is equally distant from the sides of the angle...
Page 58 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.