## A Treatise on Plane and Spherical Trigonometry |

### From inside the book

Results 1-5 of 65

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**results**this general equation , sin . ( 2n + A ) = sin . { ( 2n + 1 ) π − A } , or , what amounts to the same thing , if s be the sine of any arc A , it is also the sine of all arcs comprehended under the two formulæ , ( 2ηπ + Α ) ... Page 15

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**results**may be conveniently represented in a Table , s and c representing the sine and cosine of an arc A. * This hinges on the general doctrine of negative quantities : the scrupulous Student , who is not satisfied with what is here ... Page 18

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**resulting**formula will belong to lines drawn in a circle , of which the radius is r : for instance , tan . A sin ...**result**- ing formula will belong to a circle of which the radius is r . This is the rule ; but , since it would 18 ... Page 19

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**resulting**formula will be true when the radius is = r . Thus , if cos . 3 A = 4.cos.3 3. cos . A ( rad3 . = 1 ) , since cos.3 A , the term of the highest , is of three dimensions , and cos . 3 A , cos . A , are of one dimension , we ... Page 24

... consequently , cos . C = Zap 2ab.cos.C ; a2 + b2-2 2ab If we investigate cos . B , and cos . A , the process will be exactly similar , and the

... consequently , cos . C = Zap 2ab.cos.C ; a2 + b2-2 2ab If we investigate cos . B , and cos . A , the process will be exactly similar , and the

**result**similar , that is cos . B a2 + c2 2ac - 62 , cos . A b2 + c2 - a2 2bc •### Other editions - View all

### Common terms and phrases

1+cos A.cos a+b+c ABDE Acad ANMB arithmetical Astron Astronomy chord circle circumference co-sec co-tan consequently cubic equations deduced determined difference equal equation Euclid Example formula fraction given Hence included angle instance Introduction to Taylor's latter loga logarithmic tangents method of solution multiple arcs multiply negative oblique-angled triangles obtained plane pole preceding methods Prob Problem Prop Proposition quadrant quadratic equation quantity radius registered computations required to express result right angle right ascension right-angled spherical triangles rithms root secant Sherwin's Tables shew similar similarly sin.c sine sine and cosine sphere spherical angle spherical excess Spherical Trigonometry substitute subtract supplemental triangle surface Theorem Third Method Trigonometrical formulæ 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.