The Elements of Spherical Trigonometry |
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Page 29
... 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 ...
... 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 ...
Page 30
... cot B tan AC ; log cot B = log sin AB log tan AC +10 9.8278843 + 10 10.1105786 = 9.7173057 , which is the log cot 62 ° 27 ′ ; .. B 62 ° 27 ' , = which is acute , like its opposite side . To find the angle C. Here AC is the middle part ...
... cot B tan AC ; log cot B = log sin AB log tan AC +10 9.8278843 + 10 10.1105786 = 9.7173057 , which is the log cot 62 ° 27 ′ ; .. B 62 ° 27 ' , = which is acute , like its opposite side . To find the angle C. Here AC is the middle part ...
Page 31
James Hann. log cos BC = log cos AB + log cos AC - 10 9.8691301 + 9.7872317 10 - = 9.6563613 , which is the cosine 62 ... cot B ; log sin AB = log tan AC + log cot B = 10.1547732 + 2 · 6532976 · 10 9.8080708 , which is the sin 40 ...
James Hann. log cos BC = log cos AB + log cos AC - 10 9.8691301 + 9.7872317 10 - = 9.6563613 , which is the cosine 62 ... cot B ; log sin AB = log tan AC + log cot B = 10.1547732 + 2 · 6532976 · 10 9.8080708 , which is the sin 40 ...
Page 32
... cot C ; log AC = log tan AB + log cot C 10 - log tan AB = log sin AC — log cot C + 10 = 9.9121207-9.9554535 + 10 = 9 · 9566672 which is the tangent of 42 ° 8 ′ 46 ′′ ; .. AB 42 ° 8 ′ 46 ′′ which is acute , like its opposite angle . To ...
... cot C ; log AC = log tan AB + log cot C 10 - log tan AB = log sin AC — log cot C + 10 = 9.9121207-9.9554535 + 10 = 9 · 9566672 which is the tangent of 42 ° 8 ′ 46 ′′ ; .. AB 42 ° 8 ′ 46 ′′ which is acute , like its opposite angle . To ...
Page 33
... cot BC ; log cos C = log tan AC + log cot BC- - 10 ; ... log cot BC = log cos C - log tan AC 10 9.8260715 10.1510145 + 10 - = 9.6750570 , which is the cotangent of 64 ° 40 ′ 34 ′′ ; .. BC 64 ° 40 ′ 34 ′′ . QUADRANTAL TRIANGLES . 39 ...
... cot BC ; log cos C = log tan AC + log cot BC- - 10 ; ... log cot BC = log cos C - log tan AC 10 9.8260715 10.1510145 + 10 - = 9.6750570 , which is the cotangent of 64 ° 40 ′ 34 ′′ ; .. BC 64 ° 40 ′ 34 ′′ . QUADRANTAL TRIANGLES . 39 ...
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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 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.
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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...