## The Elements of Spherical Trigonometry |

### From inside the book

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**circle**. Let O be the centre of the sphere , A PBA a section made by a plane passing through it , draw F OC to the ...**circle**. If the cutting plane pass through the centre , the radius of the section is evidently equal to the radius of ... Page 4

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**circle**, that is a + b + c > 360 , and since any two sides of a triangle is greater than the third , we have a + b > c ; b + c > a ; a + c > b . ON THE POLAR OR SUPPLEMENTAL TRIANGLE . 7. If three arcs of great**circles**be described from ... Page 17

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**circle**through the vertex of the triangle and the middle of the base , we divide it into two right - angled tri angles , equal in all respects , and in each of which we know two elements besides the right angle , then the isosceles ... Page 23

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**circle**DHD ' ; take CD less than 90 ° , and draw the arcs of great**circles**CB , CB ' , CH . . . . from the point C to the different points of the circumference DHD ' . Produce CD , making C'D CD , and join C'B . The triangles CDB , C'DB ... Page 27

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**circle**. If any two sides of a triangle be equal to each other , their opposite angles will be equal , and vice versa . Since cos a cos b cos c sin b sin c cos A = cos b Cos a co8 C cos B = sin a sin c If ba , these expressions are each ...### 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...

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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...