## The Elements of Spherical Trigonometry |

### From inside the book

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**sines**and cosines of a spherical tri- angle in terms of the**sines**and cosines of the sides . Let O be the centre of the sphere on which the triangle ABC is situated , draw the radii OA , OB , OC ; from OA draw the perpendiculars A D and ... Page 6

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**sines**are positive . As the second member remains constant when we change A and a into B and b , & c ,, we have sin A sin B sin C • sin a sin b sin c Hence in any spherical triangle , the**sines**of the angles are to each other as the**sines**... Page 11

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**sine**of the middle part is equal to the product of the tangents of the extremes conjunct . * Thus , if in figure page 12 we suppose BC , the angle B , and the side A B to be the quantities that are to be used ; now as they lie all toge ... Page 12

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**sine**, and the tangent of a complement is a co - tangent , and vice versa . 21. CASE 1. When the hypothenuse B C and the base AB are given to find the remaining parts of the triangle . Let us first proceed to find AC . Here the ... Page 15

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**sine**, and we see that this really ought to be the case . In fact , if the triangle BAC ( fig . p . 12 ) right - angled at A , satisfy the equation ; produce BA and BC till they inter- sect in D , then take DA ' : BA , and DC ' = BC ...### Other editions - View all

### Common terms and phrases

acos agrees with equation bcos circle comp cos b cos cos b sin cosē cosc cosines cot a cot cot BC cotē disjoined extremes conjunct extremes disjunct find the angle find the hypothenuse formula Given the side Given the three greater than 90 hence hypothenuse BC I. F. Heather less than 90 log cos log cot log sin log sin AC log sin blog log tan AC logarithm middle Napier's Analogies oblique angles opposite angles perpendicular plane angles Plane Trigonometry polar triangle polygon radius regular polyhedron right-angled spherical triangle right-angled triangle SERIES OF RUDIMENTARY side AC sin a sin sin AB sin c cos sin(A sines six right solid angle solution sphere spherical triangle SPHERICAL TRIGONOMETRY Substituting surface taking the complements three angles three circular three sides TREATISE triangle ABC triangle is equal values

### Popular passages

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Page 55 - 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.

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Page 4 - ... 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.

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Page 46 - He did not even understand the rule I made use of for finding the excess of the sum of the three angles of a spherical triangle above...