## The Elements of Spherical Trigonometry |

### From inside the book

Results 1-5 of 32

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**cot**a sin b cos b cos C + sin C**cot**A. By permuting the letters , we have in all the following six equations :**cot**a sin b = cos b cos C + sin C**cot**A ......... ( 5 )**cot**b sin a = cos a cos C + sin C**cot**B.**cot**a sin c = cos c cos B + sin ... Page 9

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**cot**C • cos ( a cos ( a + b ) ― b ) ( 16 ) tan ( A - B ) =**cot**C sin ( a ― · b ) • sin ( a + b ) ( 17 ) My able and talented friend , Mr. Reynolds of Chelsea Hos- pital , has sent me the following very neat method of deducing Napier's ... Page 10

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**cot**B**cot**C ............ .. ( 6 ) These six independent formulę are all adapted to logarith- mic calculation . The first gives a relation between the hypothenuse and the two sides containing the right angle ; the second , one side and ... Page 12

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**cot**a tan c , which corresponds with ( 8 ) , and therefore the rule is proved in this case also . To find the angle C. Here the side AB is separated from the hypothenuse by the angle B , and it is separated from the angle C by the side ... Page 13

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**cot**c ; which agrees with ( 9 ) ; tan c or tan C - sin b To find the angle B. The three circular parts all lie together again , AB being in the middle ; calling it the middle part , then AC and angle B will be extremes conjunct . sin AB ...### Other editions - View all

### Common terms and phrases

acos agrees with equation bcos circle comp cos b cos cos b sin cos² cosc cosines cot a cot cot BC cot² 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 2 - JOHN \YEALK (of which Prospectuses have been extensively issued), have realised the anticipated success from that portion of the public who seek the attainment of those objects of Science which belong to the business of life, and the highest and most useful subjects in the Elements of Art and Science. Pursuing the same path, to render further aid to public instruction, and to direct the attention of the Heads and Principals of the several Colleges and Mr.

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.

Page 2 - CONSTRUCTING CRANES for the Erection of Buildings and for Hoisting Goods, by JOSEPH GLYNN, FRS, CE , TREATISE ON THE STEAM ENGINE, by DR. LARDNER, LL.D., Editor of the " Cabinet Cyclopaedia

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.

Page 3 - ... inestimable value, and too many attempts cannot be made to render them perfect and complete." To carry out this new Series successfully and methodically, the most eminent men in scholastic erudition and elementary instruction have been selected, under the able management and editing of Mr. JAMES...

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Page 3 - BRIDGES, tec., more particularly the Conway and Britannia Bridges, describing the Experiments made to determine their form, strength, and efficiency, together with the construction of the same, the floating and raising the tubes, *c 2 li.

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...