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ABCD adjacent angles altitude apothem base bisects centre of similitude chord circumference circumscribed coincide common cone convex Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw equally distant equilateral equivalent exterior angle faces figure find the locus fixed point frustum given circles given plane given point given straight line hence homologous hypotenuse indefinitely inscribed angle isosceles Let ABC measure medial lines middle point number of sides one-half opposite sides parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume
Sivu 348 - 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...
Sivu 46 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Sivu 127 - The areas of two rectangles are to each other as the products of their bases by their altitudes.
Sivu 129 - The area of a parallelogram is equal to the product of its base and altitude. Let...
Sivu 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Sivu 219 - 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.
Sivu 261 - Any side of a spherical triangle is less than the sum of the other two.
Sivu 95 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.