## The Elements of Spherical Trigonometry |

### From inside the book

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**B C**and the base AB are given to find the remaining parts of the triangle ...**cot**a tan c , which corresponds with ( 8 ) , and therefore the rule is ...**BC**cos C ; taking the complements of**BC**and C , sin c sin a sin C. This agrees with ... Page 13

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**BC**cos AB cos AC ; taking the complement of**BC**, cos a = cos b cos c ; which ...**cot**c ; which agrees with ( 9 ) ; tan c or tan C - sin b To find the angle B ...**cot**B , which agrees with ( 4 ) ; tan b or tan B sin c 23. CASE 3. Given the ... Page 14

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**BC**; taking the complements of B and**BC**, .. tan c = cos B**cot**a 3. To find C. cos B tan c**cot**a ; cos B tan a , which agrees with equ . ( 8 ) . Here the circular parts lie all together , the hypothenuse being in the middle ; call it ... Page 16

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**cot**c ; sin b tan C , which agrees with equ . ( 9 ) . 3. To find the angle B. Since the angle B is separated from 6 by the side AB , and from the angle C by the hypothenuse**BC**...**BC**. Here a , B and C all lie together , a or**BC**being in the ... Page 29

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**cot BC**; log cos B = log tan AB + log**cot B C**= - 10 log tan 40 ° + log cot 63 ° 56 ′ 7 ′′ = 9.9238135 + 9.6894258-10 = 9.6132393 ; .. B 65 ° 46 ′ 5 ′′ . = The angle B is acute , as the hypothenuse and given side are of the same ...### 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

Page 1 - ... principles untouched. The only method of avoiding this error is to confide to men, who are masters of their respective subjects, the task of drawing up Popular Introductions to the several branches of Science. The Publisher trusts that the following list of names will be a sufficient guarantee to the Public that what he proposes to attempt in the cause of Popular Instruction will be done well, and that these little treatises will fully answer the purpose for which they are intended, namely, to...

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...

Page 1 - Popular treatises are to Science what boats are to large ships ; they assist people in getting aboard ; but as no one would trust himself to a weak or inefficient boat, so no one ought to begin the study of Science with an imperfect guide. It sometimes happens that popular treatises are made to appear easy by the omission of those very details which are most essential to be known : they state...

Page 1 - Course for the easy comprehension of the leading principles of various Sciences. It has been remarked that " those who are in the ship of Science ought to remember that the disciples cannot arrive without the aid of boats.

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...