Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten Seconds of the Quadrant: With Other Useful TablesHarper & brothers, 1859 - 150 pages |
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Page 7
... preceding principles may be extended to fractions by means of negative exponents . Thus , since 10 - 1 = 0.1 , -1 is the logarithm of 0.1 10-2-0.01 , -2 66 10--0.001 , -3 in Briggs ' system ; ( 6 0.01 ( 6 66 66 66 } 0.001 ( 6 66 0.0001 ...
... preceding principles may be extended to fractions by means of negative exponents . Thus , since 10 - 1 = 0.1 , -1 is the logarithm of 0.1 10-2-0.01 , -2 66 10--0.001 , -3 in Briggs ' system ; ( 6 0.01 ( 6 66 66 66 } 0.001 ( 6 66 0.0001 ...
Page 12
... preceding logarithms do not pretend to be perfectly exact , but only the nearest numbers limited to six decimal places . Accordingly , when the fraction which is omitted ex- ceeds half a unit in the sixth decimal place , the last figure ...
... preceding logarithms do not pretend to be perfectly exact , but only the nearest numbers limited to six decimal places . Accordingly , when the fraction which is omitted ex- ceeds half a unit in the sixth decimal place , the last figure ...
Page 13
... preceding article ; or , since the value of a fraction is equal to the quotient of the numerator divided by the denominator , we may , according to Art . 3 , subtract the logarithm of the denominator from that of the numerator ; the ...
... preceding article ; or , since the value of a fraction is equal to the quotient of the numerator divided by the denominator , we may , according to Art . 3 , subtract the logarithm of the denominator from that of the numerator ; the ...
Page 15
... preceding rule , is to be understood in its algebraic sense ; therefore , if any of the characteristics of the logarithms are negative , we must take the difference be- tween their sum and that of the positive characteristics , and ...
... preceding rule , is to be understood in its algebraic sense ; therefore , if any of the characteristics of the logarithms are negative , we must take the difference be- tween their sum and that of the positive characteristics , and ...
Page 16
... preceding rule , is to be under- stood in its algebraic sense ; therefore , if the characteristic of one of the logarithms is negative , or the lower one is greater than the upper , we must change the sign of the subtrahend , and ...
... preceding rule , is to be under- stood in its algebraic sense ; therefore , if the characteristic of one of the logarithms is negative , or the lower one is greater than the upper , we must change the sign of the subtrahend , and ...
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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.