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ABCD altitude approaches base bisects called centre chord circle circumference circumscribed coincide common cone construct cylinder diagonals diameter distance divided Draw line drawn edges equal equal respectively equally distant equivalent extended extremities faces fall feet figure Find follows foot formed frustum Given Given line given point greater homologous hypotenuse inches included indefinitely inscribed intersecting isosceles joining lateral area length limit line drawn mean measured meeting middle point multiplied Note oblique opposite parallel parallelogram parallelopiped passes perimeter perpendicular placed plane polygon prism Proof PROP proportional Prove pyramid quadrilateral radii radius ratio rectangle Required respectively right angles segments sides similar sphere spherical square straight line surface tangent THEOREM third trapezoid triangle unit vertex vertices volume whence
Σελίδα 168 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Σελίδα 138 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Σελίδα 168 - Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii.
Σελίδα 50 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.
Σελίδα 128 - In any triangle, the product of any two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle, plus the square of the bisector.
Σελίδα 265 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Σελίδα 282 - A zone is a portion of the surface of a sphere included between two parallel planes.
Σελίδα 241 - Every section of a cylinder made by a plane passing through an element is a parallelogram. Given ABCD, a section of cylinder AC, made by plane through element AB.