Plane Trigonometry ...1860 |
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Page 92
... logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number . The logarithm of n to the base a is written log.n ; thus logan = x expresses the same relation as a * = ne ...
... logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number . The logarithm of n to the base a is written log.n ; thus logan = x expresses the same relation as a * = ne ...
Page 94
... log , 10 " = log1N - n . log 10 10 " = 10 That is , if we know the logarithm of any number we can determine the ... given base . - a * = { 1 + ( a − 94 LOGARITHMS AND LOGARITHMIC SERIES ,
... log , 10 " = log1N - n . log 10 10 " = 10 That is , if we know the logarithm of any number we can determine the ... given base . - a * = { 1 + ( a − 94 LOGARITHMS AND LOGARITHMIC SERIES ,
Page 101
... given log 2 = 301030 . 5 . 6 . Given log 224 = a and log 125 = b , find log 2 and log 7 . Required the characteristics of log , 725 , and of log , 5 / ( 0725 ) . 7. Given log 2 = 301030 , log 405 = 2.607455 , find log 003 . 8. Given log ...
... given log 2 = 301030 . 5 . 6 . Given log 224 = a and log 125 = b , find log 2 and log 7 . Required the characteristics of log , 725 , and of log , 5 / ( 0725 ) . 7. Given log 2 = 301030 , log 405 = 2.607455 , find log 003 . 8. Given log ...
Page 105
... given number . If the number be contained in the Table we have merely to take the decimal part of the logarithm ... log 5342-7275413 . log 5340047275413 , log 0534-2.7275413 . In the last example the characteristic is - 2 , USE OF LOGARITHMIC ...
... given number . If the number be contained in the Table we have merely to take the decimal part of the logarithm ... log 5342-7275413 . log 5340047275413 , log 0534-2.7275413 . In the last example the characteristic is - 2 , USE OF LOGARITHMIC ...
Page 106
... given number is not contained in the Table ; the Table for instance may give ... log 5340300 = 6.7275657 log 5340200 = 6.7275575 difference = • 0000082 ... ́log 23454000 = 7.3702169 Proportional Parts . log 23453000 = 106 USE OF LOGARITHMIC.
... given number is not contained in the Table ; the Table for instance may give ... log 5340300 = 6.7275657 log 5340200 = 6.7275575 difference = • 0000082 ... ́log 23454000 = 7.3702169 Proportional Parts . log 23453000 = 106 USE OF LOGARITHMIC.
Common terms and phrases
approximately base calculated called centre chapter circle circular measure cloth College contained corresponding cos² cos³ cosec cosine Crown 8vo decimal denote determine difference distance divided Edition English equal equation error example expression factors feet figure formula four functions give given greater half height Hence included increases inscribed integer known length less lies limit logarithm method minutes multiple nearly negative object observed obtain opposite perpendicular places plane polygon positive preceding present proceed produced proportional prove quadrant quantity radius respectively right angle root Schools secant shew shewn sides Similarly sin² sin³ sine solve student subtend suppose Table taken tangent tower Treatise triangle Trigonometrical Ratios unity universally
Popular passages
Page 9 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Page 18 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 1 - Mr Smith's Work is a most useful publication. The Rules are stated with great clearness. The Examples are well selected and worked cut with just sufficient detail without being encumbered by too minute explanations; and there prevails throughout it that just proportion of theory and practice, which is the crowning excellence of an elementary work.
Page 22 - The author has endeavoured to connect the history of the New Testament Canon with the growth and consolidation of the Church, and to point out the relation existing between the amount of evidence for the authenticity of its component parts, and the whole mass of Christian literature.
Page 4 - Mathematics. Each chapter is followed by a set of Examples: those which are entitled Miscellaneous Examples, together with a few in some of the other sets, may be advantageously...
Page 221 - From eight times the chord of half the arc, subtract the chord of the whole arc, and divide the remainder by 3, and the quotient will be the length of the arc, nearly.
Page 93 - The logarithm of any power, integral or fractional, of a number is equal to the product of the logarithm of the number by the index of the power. For let m = a"; therefore m' = (a")
Page 94 - ... is some number between — 2 and — 3 ; that is, — 3 plus a fraction ; and so on. 5. In the common system, as the logarithms of all numbers which are not ^exact powers of 10 are incommensurable with those numbers, their values can only be obtained approximately, and are expressed by decimals. 6. The integral part of any logarithm is called the CHARACTERISTIC, and the decimal part is sometimes called the MANTISSA.
Page 51 - To express the cosine of the sum of two angles in terms of the sines and cosines of the angles themselves.