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Adding altitude applied base becomes called chord circle circumference common cone construction contained cos.a Cosine Cotang describe determine diameter difference distance divided draw drawn edges equal equation equivalent expressed extremities faces fall feet figure formed four frustum given gives greater half Hence the theorem hypotenuse included inscribed intersect length less logarithm magnitudes means measured meet multiplied opposite parallel parallelogram parallelopipedon pass perpendicular placed plane polygon prism PROBLEM produced proportion PROPOSITION prove pyramid radius rectangle regular represent respectively right angles right-angled triangle segment sides similar sin.a sin.c sine solid sphere spherical triangle square straight line suppose surface taken Tang tangent third triangular vertex vertical volume whole
Page 322 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 123 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Page 58 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 29 - If one side of a triangle is produced, the exterior angle is equal to the sum of the two interior and opposite, angles; and the three interior angles of every triangle are equal to two right angles.
Page 41 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 96 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 65 - 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.
Page 77 - FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi.