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Elements of Plane Geometry: For the Use of Schools - Primary Source Edition
Ingen forhåndsvisning tilgjengelig - 2013
ABCD altitude angles ABD antecedent applied B. I. Prop base bisect BOOK called centre chord circle circumference circumscribed coincide common consequently contained cutting describe diagonal diameter difference distances divide draw draw the line equal angles equal B. I. Prop equal Prop equiangular equivalent extremities feet figure formed four given angle given line given point greater half hence hypotenuse inches included angle larger less longer mean measure meet middle multiplied number of sides opposite parallel parallelogram perimeter perpendicular polygon PROBLEM produced proportion prove radii radius ratio rectangle regular remainder respectively equal right angles right-angled triangle Scholium sides similar square straight line subtended suppose surface taken tangent THEOREM third triangles ABC unit vertex yards
Side 31 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Side 70 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Side 53 - In any proportion, the product of the means is equal to the product of the extremes.
Side 87 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Side 54 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Side 81 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Side 61 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.