The Elements of Spherical Trigonometry |
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Page 4
... AC PC ; hence the section APBA is a circle . If the cutting plane pass through the centre , the radius of the ... sides , and are the same as the inclinations of the planes of those great circles to one another . 5. Any two sides of a ...
... AC PC ; hence the section APBA is a circle . If the cutting plane pass through the centre , the radius of the ... sides , and are the same as the inclinations of the planes of those great circles to one another . 5. Any two sides of a ...
Page 11
... AC be the quantities , then since the right angle does not separate the sides , A B is the middle part , and the ... side A B is said to separate A C from the angle B , that part AC which is separated from both the others , call the ...
... AC be the quantities , then since the right angle does not separate the sides , A B is the middle part , and the ... side A B is said to separate A C from the angle B , that part AC which is separated from both the others , call the ...
Page 12
... AC . Here the hypothenuse and the two sides are the three circular parts . C ' B a b A B A The hypothenuse being ... side AB is separated from the hypothenuse by the angle B , and it is separated from the angle C by the side AC , then ...
... AC . Here the hypothenuse and the two sides are the three circular parts . C ' B a b A B A The hypothenuse being ... side AB is separated from the hypothenuse by the angle B , and it is separated from the angle C by the side AC , then ...
Page 13
... AC ; taking the complement of BC , cos a = cos b cos c ; which is the same as equation ( 1 ) ; To find angle C ... side AB ; calling AC the middle part , then BC and angle B are extremes disjunct . sin AC cos BC cos B ; taking the ...
... AC ; taking the complement of BC , cos a = cos b cos c ; which is the same as equation ( 1 ) ; To find angle C ... side AB ; calling AC the middle part , then BC and angle B are extremes disjunct . sin AC cos BC cos B ; taking the ...
Page 14
... side AC or b and the opposite angle B to find a , c , C. 1. To find the hypothenuse BC or a . Here b or AC is separated from the hypothenuse by the angle C , and from the angle B by the side AB ; calling then AC the middle part , the ...
... side AC or b and the opposite angle B to find a , c , C. 1. To find the hypothenuse BC or a . Here b or AC is separated from the hypothenuse by the angle C , and from the angle B by the side AB ; calling then AC the middle part , the ...
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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
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...