Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States
A.S. Barnes & Company, 1872 - Geometry - 455 pages
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ABCD altitude base Book called centre chord circle circumference circumscribed coincide common cone consequently construct corresponding Cosine Cotang cylinder denote described diameter difference distance divided draw drawn edges equal EXAMPLES extremity faces feet figure find the area formed Formula four frustum given greater half hence homologous inscribed intersection less logarithm manner mean measured meet middle multiplied opposite parallel parallelogram pass perpendicular placed plane plane MN polyedron polygon position principle prism PROBLEM proportional PROPOSITION proved pyramid radii radius rectangle regular right angles RULE Scholium segment shown sides similar Sine solution sphere spherical triangle square straight line surface taken Tang tangent THEOREM third triangle triangle ABC unit vertex vertices volume whence
Page 101 - The area of a parallelogram is equal to the product of its base and altitude.
Page 92 - PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point 0 (Prob.
Page 48 - 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.
Page 45 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Page 106 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 33 - THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles.
Page 18 - A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle GH I.
Page 30 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the third sides will be unequal; and the greater side will belong to the triangle which has the greater included angle.
Page 8 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 156 - DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar arcs are to each other as their radii, and similar sectors are to each other as the squares of their radii.