Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten Seconds of the Quadrant: With Other Useful Tables |
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Page 20
... sides , a right angle is measured by 90 ° , two right angles by 180 ° , and four right angles are measured by 360 ° . D Cotan . L K Cosine Sec . I Sine Tangent ( 20. ) The complement of an arc is what remains after sub- tracting the arc ...
... sides , a right angle is measured by 90 ° , two right angles by 180 ° , and four right angles are measured by 360 ° . D Cotan . L K Cosine Sec . I Sine Tangent ( 20. ) The complement of an arc is what remains after sub- tracting the arc ...
Page 32
... side , or the cosine of either acute angle to the adjacent side . Let the triangle CAB be right angled at A , then will R : CB :: sin . C : BA :: cos . C : CA. From the point C as a center , with a B radius equal to the radius of the ...
... side , or the cosine of either acute angle to the adjacent side . Let the triangle CAB be right angled at A , then will R : CB :: sin . C : BA :: cos . C : CA. From the point C as a center , with a B radius equal to the radius of the ...
Page 33
... sides ad- jacent to the right angle being called the base , the other side adjacent to the right angle may be called the perpendicular . The three sides will then be called the hypothenuse , base , and perpendicular . The base and ...
... sides ad- jacent to the right angle being called the base , the other side adjacent to the right angle may be called the perpendicular . The three sides will then be called the hypothenuse , base , and perpendicular . The base and ...
Page 36
... sides of a right - angled triangle are given , the third may be found by means of the property that the square of the hypothenuse is equal to the sum of the squares of the other two sides . Hence , representing the hypothenuse , base ...
... sides of a right - angled triangle are given , the third may be found by means of the property that the square of the hypothenuse is equal to the sum of the squares of the other two sides . Hence , representing the hypothenuse , base ...
Page 37
... sides is to their difference , as the tangent of half the sum of the opposite angles is to the tangent of half their difference . Let ABC be any triangle ; then will CB + CA : CB - CA :: tang . A + B : tang . 2 A - B 2 Produce AC to D ...
... sides is to their difference , as the tangent of half the sum of the opposite angles is to the tangent of half their difference . Let ABC be any triangle ; then will CB + CA : CB - CA :: tang . A + B : tang . 2 A - B 2 Produce AC to D ...
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Common terms and phrases
9 I I altitude angle of elevation arithm base chains circle Co-sine Co-tangent complement computed correction cosecant course and distance decimal diameter diff difference of latitude difference of longitude Dist divided equal equator fifth figure find the angles find the area find the Logarithm frustum given number given the angle height Hence horizontal plane hypothenuse inches latitude and departure length LO LO LO logarithmic sine measured meridian middle latitude miles minutes Multiply natural number nautical miles parallel parallel sailing perpendicular places plane sailing Prob Prop proportional quadrant radius Required the logarithmic right-angled spherical triangle right-angled triangle Sandy Hook secant ship sails side AC spherical triangle ABC SPHERICAL TRIGONOMETRY station subtract surface tabular number tang Tangent telescope theodolite Theorem vernier vertical Vulgar Fraction wyll yards zoids ΙΙ ΙΟ
Popular passages
Page 20 - The circumference of every circle is supposed to be divided into 360 equal parts, • called degrees, each degree into 60 minutes, and each minute into 60 seconds, etc.
Page 163 - In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. In the case of right-angled spherical triangles, this proposition has already been demonstrated.
Page 69 - FIND the area of the sector having the same arc with the segment, by the last problem. Find also the area of the triangle, formed by the chord of the segment and the two radii of the sector.
Page 54 - 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.
Page 69 - TO THE NUMBER OF DEGREES IN THE ARC ; So IS THE AREA OF THE CIRCLE, TO THE AREA OF THE SECTOR.
Page 73 - To find the solidity of a pyramid. RULE. Multiply the area of the base by one third of the altitude.
Page vi - The characteristic of the logarithm of ANY NUMBER GREATER THAN UNITY, is one less than the number of integral figures in the given number.
Page 184 - If a heavy sphere, whose diameter is 4 inches, be let fall into a conical glass, full of water, whose diameter is 5, and altitude 6 inches ; it is required to determine how much water will run over ? AHS.