Plane Trigonometry ...1860 |
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Page 5
... its second revolution ; the angle will be eight right angles and a half if AP be supposed in its third revolution ; and so on . 12. The straight lines CAE and BAD form by their MEASUREMENT OF ANGLES BY DEGREES OR GRADES . 5.
... its second revolution ; the angle will be eight right angles and a half if AP be supposed in its third revolution ; and so on . 12. The straight lines CAE and BAD form by their MEASUREMENT OF ANGLES BY DEGREES OR GRADES . 5.
Page 6
... third quad- rant , and EAB the fourth quadrant . Now suppose any angle formed by the fixed line AB and the moveable line AP ; if AP is situated in the first quadrant , the angle BAP is said to be in the first quadrant ; if AP is ...
... third quad- rant , and EAB the fourth quadrant . Now suppose any angle formed by the fixed line AB and the moveable line AP ; if AP is situated in the first quadrant , the angle BAP is said to be in the first quadrant ; if AP is ...
Page 13
... third is 30 grades , and the sum of the first and second is 36 degrees . Determine the three angles . 5. Express five - sixteenths of a right angle in circular measure , in degrees and decimals of a degree , and in EXAMPLES . 13 CHAPTER ...
... third is 30 grades , and the sum of the first and second is 36 degrees . Determine the three angles . 5. Express five - sixteenths of a right angle in circular measure , in degrees and decimals of a degree , and in EXAMPLES . 13 CHAPTER ...
Page 25
... third of a right angle , and we denote the former by the -B P ' π positive fraction the latter may be denoted by the negative 6 ' fraction -7 . 44. We shall now give our extended definitions of the APPLICATION OF ALGEBRAICAL SIGNS . 25.
... third of a right angle , and we denote the former by the -B P ' π positive fraction the latter may be denoted by the negative 6 ' fraction -7 . 44. We shall now give our extended definitions of the APPLICATION OF ALGEBRAICAL SIGNS . 25.
Page 34
... third , and fourth quadrants respectively . In every case it will be seen that the triangles PAM and PAM ' are geometrically equal in all respects ; also P'M ' and AM are of the same sign , and AM ' and PM are of opposite sign . Thus ...
... third , and fourth quadrants respectively . In every case it will be seen that the triangles PAM and PAM ' are geometrically equal in all respects ; also P'M ' and AM are of the same sign , and AM ' and PM are of opposite sign . Thus ...
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.