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ABCD axis base calculation cask centre circle circular segment circumference column cone cosecant cosine cotangent course cylinder decimal departure diameter Diff difference of latitude difference of longitude distance divided earth equal equator errour feet figure find the area find the solidity frustum given side gles greater half horizon hypothenuse inches JEREMIAH DAY length less line of chords logarithm measured Mercator's Merid meridian meridional difference middle latitude miles minutes multiplied number of degrees number of sides object oblique opposite parallel of latitude parallelogram parallelopiped perimeter perpendicular plane sailing polygon prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right cylinder rithms rods root secant segment sine slant-height sphere spherical spirit level square subtract surface tables tance tangent term theorem trapezium triangle ABC Trig trigonometry whole
Pàgina 75 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Pàgina 108 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Pàgina 89 - III. Two sides and the included angle being given ; to find the other side and angles. Draw one of the given sides. From one end of it lay off the given angle, and draw the other given side. Then connect the extremities of this and the first line. Ex. 1. Given the angle A 26° 14', the side b 78, and the side c 106 ; to find B, C, and a.
Pàgina 125 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Pàgina 36 - Icosaedron, whose sides are four triangles ; six squares ; eight triangles ; twelve pentagons ; twenty triangles.* Besides these five, there can be no other regular solids. The only plane figures which can form such solids, are triangles, squares, and pentagons. For the plane angles which contain any solid angle, are together less than four right angles or 360°. (Sup. Euc. 21, 2.) And the least number which can form a solid angle is three.
Pàgina 50 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
Pàgina 129 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.