Plane TrigonometryLongmans, Green, and Company, 1906 |
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... polar triangles 18. Definitions 19. Convention · 20. Shortest line between two points on a sphere PROBLEMS OF CONSTRUCTION . 22. Problems on great circles 23-24 . Construction of triangles ( six cases ) • CHAPTER II . RIGHT - ANGLED ...
... polar triangles 18. Definitions 19. Convention · 20. Shortest line between two points on a sphere PROBLEMS OF CONSTRUCTION . 22. Problems on great circles 23-24 . Construction of triangles ( six cases ) • CHAPTER II . RIGHT - ANGLED ...
Page 5
... polar axis of the earth and the North and South Poles . b . Propositions relating to great circles . Every great circle bisects the surface of the sphere ; e.g. the equator bisects the surface of a terrestrial globe . Any two great ...
... polar axis of the earth and the North and South Poles . b . Propositions relating to great circles . Every great circle bisects the surface of the sphere ; e.g. the equator bisects the surface of a terrestrial globe . Any two great ...
Page 6
... polar distance of a circle on a sphere is its distance from its pole , the distance being measured along an arc of a great circle passing through the pole . Thus the north polar distance of a parallel of latitude is its distance from ...
... polar distance of a circle on a sphere is its distance from its pole , the distance being measured along an arc of a great circle passing through the pole . Thus the north polar distance of a parallel of latitude is its distance from ...
Page 7
... polar distance must be taken equal to a quadrant of the sphere . 8. Proposition . If a point on the surface of a sphere lies at a quadrant's distance from each of two points , it is the pole of the great circle passing through these ...
... polar distance must be taken equal to a quadrant of the sphere . 8. Proposition . If a point on the surface of a sphere lies at a quadrant's distance from each of two points , it is the pole of the great circle passing through these ...
Page 15
... POLAR TRIANGLES . 16. a . NOTE . Three straight lines on a plane , no two of which are parallel , intersect in three points , and form one triangle . Three great circles on a sphere have six points of intersection , and form eight ...
... POLAR TRIANGLES . 16. a . NOTE . Three straight lines on a plane , no two of which are parallel , intersect in three points , and form one triangle . Three great circles on a sphere have six points of intersection , and form eight ...
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Common terms and phrases
A+B+C acute angle algebraic centre CHAPTER circumscribing computation cos² cosec cotangent deduced denoted Derive diedral angle draw equal equator EXAMPLES expression figure Find the distance formulas geometry given Hence hypotenuse included angle inscribed circle intersection latitude law of cosines law of sines length logarithms mantissa mathematics meridian method NOTE number of degrees number of sides opposite perpendicular plane triangle Plane Trigonometry polar triangle pole positive quadrant radian measure radii radius regular polygon relations respectively right angles right triangles right-angled triangle secant Show sides and angles sin² solid angle solution Solve ABC sphere spherical angle spherical degree spherical excess spherical polygon spherical triangle spherical trigonometry subtended surface tables tan² tangent terminal line three angles tower triangle ABC trigono trigonometric functions trigonometric ratios π π
Popular passages
Page 52 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Page 42 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 108 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 74 - The area of the surface of a sphere is four times the area of a great circle.
Page 108 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 72 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Page 62 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area, F THE RIGHT TRIANGLE.
Page 128 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 200 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.
Page 202 - Find the area of a regular polygon of n sides inscribed in a circle, and show, by increasing the number of sides of the polygon without limit, how the expression for the area of the circle may be obtained. 13. (a) Find the distance at which a building 50 ft. wide will subtend an angle of 3'. (6) A church spire 45 ft. high subtends an angle of 9