Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems
Ivison, Phinney, 1860 - Geometry - 453 pages
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ABCD adding altitude applied base becomes called chord circle circumference common cone construction contained cos.a cos.b 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 N.sine 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.b sin.c sine sphere spherical triangle square straight line suppose surface taken Tang tangent third triangular vertex vertical volume whole
Page 320 - 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 65 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 121 - 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 56 - 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 34 - Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle it itosceles.
Page 126 - To inscribe a regular polygon of a certain number of sides in a given circle, we have only to divide the circumference into as many equal parts as the polygon has sides : for the arcs being equal, the chords AB, BC, CD, &c.
Page 22 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Page 277 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 94 - 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 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.