A Treatise on Plane and Spherical Trigonometry |
From inside the book
Results 1-5 of 22
Page i
... object , and to other investigations than those of the relations of the sides and angles of Triangles . The collateral uses of the science have become the most numerous , and are not the least important . To the knowledge of many of ...
... object , and to other investigations than those of the relations of the sides and angles of Triangles . The collateral uses of the science have become the most numerous , and are not the least important . To the knowledge of many of ...
Page ii
... objects , not merely curious , but of real interest , we may learn from the history and actual state of the science . The first considerable extension of Trigonometry , beyond its original object , was made about twenty years after the ...
... objects , not merely curious , but of real interest , we may learn from the history and actual state of the science . The first considerable extension of Trigonometry , beyond its original object , was made about twenty years after the ...
Page iv
... object of the science , its propositions are more easily established by the Analytical method than the Geometrical . And , ( at least in the opinion of the Author of this Treatise ) this would be the case , even if there existed no simi ...
... object of the science , its propositions are more easily established by the Analytical method than the Geometrical . And , ( at least in the opinion of the Author of this Treatise ) this would be the case , even if there existed no simi ...
Page 35
... object is to obtain an expression involving tan . A , tan . B , we must divide both numerator and denominator of the above fraction by cos . A. cos . B , an operation which will not change its real value ; beginning then with the ...
... object is to obtain an expression involving tan . A , tan . B , we must divide both numerator and denominator of the above fraction by cos . A. cos . B , an operation which will not change its real value ; beginning then with the ...
Page 41
... object is utility , will feel averse from their investigation , should he suspect them to be mere Trigono- metrical ... object has no concern whatever with the properties of triangles . Yet , the investigation of the properties of ...
... object is utility , will feel averse from their investigation , should he suspect them to be mere Trigono- metrical ... object has no concern whatever with the properties of triangles . Yet , the investigation of the properties of ...
Other editions - View all
Common terms and phrases
a+b+c analytical arithmetical Asin chord circle circumference co-sec co-tan coefficient compute the sines consequently cos.³ COS.C cosine decimal deduced determined difference equal equation Euclid Example formula fraction given Hence horizontal angle included angle instance latter loga logarithmic sines multiple arcs natural sines nearly oblique oblique-angled obtained plane preceding method Prob PROBLEM Prop quadrant quantity rectilinear triangles required to express right angle right ascension rithm root Rule secant Sherwin's Tables sides similar similarly simple arc sin.² sin.³ sin.c sine and cosine sines of arcs solution spherical angle spherical excess spherical triangle Spherical Trigonometry substitute subtract supplemental triangle tangent Theorem Treatise Trigonometrical formulæ Trigonometrical Survey Trigonometrical Tables versed sine versin
Popular passages
Page 191 - The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 126 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Page 127 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Page 142 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 125 - A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre.
Page 171 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 25 - It depends on the principle, that the difference of the squares of two quantities is equal to the product of the sum and difference of the quantities.
Page 138 - ... sun in the meridian. The arches being supposed semi-circular, it is required to find the curve terminating that part of the surface of the water which is illuminated by the sun's rays passing through any arch. 7- It is required to express the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides.
Page 134 - The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles.
Page 188 - From the logarithm of the area of the triangle, taken as a plane one, in feet, subtract the constant log 9-3267737, then the remainder is the logarithm of the excess above 180°, in seconds nearly.* 3.