## The Elements of Spherical Trigonometry |

### From inside the book

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Page 27

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**comp**. log sin b**comp**. log sin c 2 log sin A log sin A 9.6871552 9.5047412 0.0275078 0.0062623 19.2256665 9.6128332 A = 24 ° 12 ′ 27 ′′ -9 , or A = 48 ° 24 ′ 56 ′′ . 37. The following properties of spherical triangles we shall premise ... Page 29

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**comp**. log . 63 ° 56 ′ 7 ′′ ; 9.8546469 ; .. C 45 ° 41 ′ 21 ′′ . The angle C is acute , the hypothenuse and given side being of the same affection . When the two sides are given . Given the side SPHERICAL TRIGONOMETRY . 29. Page 31

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**comp**. log 0.2414087 + 10 9.8546494 = log sin 45 ° 41 ′ 21 ′′ ; .. C 45 ° 41 ′ 21 ′′ . The angle C is ambiguous ; as it cannot be determined by the data alone whether , AB , C , and BC are greater or less than 90 ° . To find the side AB ... Page 35

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**comp**log sin 58 °**comp**log sin 79 ° 17 ′ 14 ′′ log sin 9,8445513 log sin = 9,9595173 0,0715795 0,0076359 2 ) 19,8832840 log sin 60 ° 57 ′ 28 ′′ = 2 9,9416420 121 54 56 equals the required angle A. By a similar operation the angles B and ... Page 42

... two remainders , and the

... two remainders , and the

**comp**. log of the sines of each of the adjoining angles . Half the sum of these four logarithms will give the cosine of half the required side ; thus 121 ° 54 ′ 56 ′′ 50 62 34 6 42 SPHERICAL TRIGONOMETRY ,### 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 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.

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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.

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 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...