A Treatise on Trigonometry, and on Trigonometrical Tables and Logarithms: Together with a Selection of Problems and Their SolutionsJ. & J.J. Deighton, and T. Stevenson, 1841 - 151 páginas |
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Página 41
... proportional to the increments of the angles ; the calculations being precisely similar to those employed in treating of the logarithms of numbers . As this is a point which will be fully illustrated when we come to speak of the ...
... proportional to the increments of the angles ; the calculations being precisely similar to those employed in treating of the logarithms of numbers . As this is a point which will be fully illustrated when we come to speak of the ...
Página 46
... proportional to the differences of the angles ; and this proportion , though inexact , gives in general a sufficient approximation . 77. The following Examples will sufficiently illustrate the mode of proceeding in the first Problem ...
... proportional to the differences of the angles ; and this proportion , though inexact , gives in general a sufficient approximation . 77. The following Examples will sufficiently illustrate the mode of proceeding in the first Problem ...
Página 53
... proportional to cos A , is greater than the variation of the cosine produced by the same variation of the angle , which is proportional to sin A ; and vice versa when the angle is greater than 45 ° ; we may expect to obtain an angle ...
... proportional to cos A , is greater than the variation of the cosine produced by the same variation of the angle , which is proportional to sin A ; and vice versa when the angle is greater than 45 ° ; we may expect to obtain an angle ...
Página 54
... proportional to the increment of the angle . In fact we find in the tables L tan 89 ° .58 ' = 13.2352438 L tan 89 ° . 58 ' . 10 ′′ 13.2730324 = L tan 89 ° . 58 ′ . 20 ′′ = 13 · 3144251 where the differences are not nearly equal . diff ...
... proportional to the increment of the angle . In fact we find in the tables L tan 89 ° .58 ' = 13.2352438 L tan 89 ° . 58 ' . 10 ′′ 13.2730324 = L tan 89 ° . 58 ′ . 20 ′′ = 13 · 3144251 where the differences are not nearly equal . diff ...
Página 108
... proportional to the differences of the numbers , and the above process would be rigorously exact . Now the inspection of the tables ( see p . 113 ) shews us that the difference of the logarithms of consecutive whole numbers is very ...
... proportional to the differences of the numbers , and the above process would be rigorously exact . Now the inspection of the tables ( see p . 113 ) shews us that the difference of the logarithms of consecutive whole numbers is very ...
Outras edições - Ver tudo
A treatise on trigonometry and on trigonometric tables and logarithms John Hymers Visualização integral - 1812 |
Treatise on Trigonometry and Trigonometrical Tables and Logarithms; Together ... John Hymers Pré-visualização indisponível - 2012 |
Palavras e frases frequentes
ABC fig acute angle BAC arcs bisected calculation circular measure circumscribed circle consequently cos² cos³ cosec cotangent decimal point denoted determined diff difference digits distance equal equation expressed find the angle formula given angle Hence horizontal hypothenuse included angle inscribed integer intersect less than 90 log-cos log-cosine log-sin log-tan loga logarithms magnitude multiple negative opposite angles perpendicular pole polygon positive produced quadrant quantities radius regular polygon right angle right-angled triangle sec² shew side opposite Similarly sin a sin sin² sin³ sines and cosines solid angle solution sphere spherical triangle Spherical Trigonometry subsidiary angle subtends subtracting suppose tables tan² tan³ tangent telescope three sides triangle ABC Trigono Trigonometrical Ratios values Vernier zero
Passagens conhecidas
Página 3 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Página 95 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 127 - suffice to afford such an approximation to it as shall be of use in the ' present stage of the reader's knowledge, and help him to many just ' conceptions, on which account we shall exemplify its application in ' numbers. Now, it appears by observation, that two points, each ten...
Página 50 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Página 49 - ... these elements must be given, one of which must be a side, in order to solve a plane triangle. The solution of plane triangles depends upon the following FUNDAMENTAL PROPOSITIONS. 109. In a right-angled triangle, the side opposite to an acute angle is equal to the product of the hypothenuse into the sine of the angle ; and the side adjacent to an acute angle is equal to the product of the hypothenuse into the cosine of the angle. Let...
Página 25 - В; by means of which we can express the sine and cosine of the sum or difference of two angles in terms of the sines and cosines of the angles themselves.
Página 17 - OP — sin A cos B + cos A sin B. OM_OQ-QM_OQ NR '" OP~ OP ~ OP OP _ OQ_ ON_NR NP "ON'OP~WP'"OP =^cos A cos .B- sin .4 sin B. 77. To express the sine and cosine of the difference of two angles in terms of the sines and cosines of the angles themselves.