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ABCD altitude base 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 formed Formula four frustum functions given greater half height hence homologous included inscribed intersection less logarithm manner mean measured meet multiplied opposite parallel parallelogram parallelopipedon pass perpendicular placed plane plane MN polyedron polygon positive principle prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular remaining right angles RULE Scholium segment shown sides similar sine solution sphere spherical triangle square straight line taken Tang tangent term THEOREM third triangle triangle ABC unit upper vertex vertices volume whence
Page 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 46 - 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 43 - 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 104 - 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 31 - THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles.
Page 16 - A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle GH I.
Page 28 - 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 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 154 - 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.