A System of Plane and Spherical Trigonometry: To which is Added a Treatise on Logarithms |
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Page xii
... TRIANGLES . ART . PAGE 28- 33. Limits to the magnitude of the sides of spherical triangles and polygons 187 ............. 34- 42. Properties of the polar triangle 189 polygons ......... .......... 193 43- 49. Limits to the magnitudes ...
... TRIANGLES . ART . PAGE 28- 33. Limits to the magnitude of the sides of spherical triangles and polygons 187 ............. 34- 42. Properties of the polar triangle 189 polygons ......... .......... 193 43- 49. Limits to the magnitudes ...
Page xiii
... triangles .... 124-129 . Various problems SECTION VI . ON THE MEASURING OF SOLID ANGLES . 130-131 . The method ... TRIANGLE . 133-140 . On the corresponding small variations of the ele- ments of spherical triangles ... 260 141-151 ...
... triangles .... 124-129 . Various problems SECTION VI . ON THE MEASURING OF SOLID ANGLES . 130-131 . The method ... TRIANGLE . 133-140 . On the corresponding small variations of the ele- ments of spherical triangles ... 260 141-151 ...
Page xiv
... triangle when the sides are small com- 168 . pared with the radius of the sphere..279 To reduce the spherical excess from feet to seconds 284 .... SECTION IX . ON REGULAR POLYHEDRONS , & C . 169-173 . Equations involving the number of ...
... triangle when the sides are small com- 168 . pared with the radius of the sphere..279 To reduce the spherical excess from feet to seconds 284 .... SECTION IX . ON REGULAR POLYHEDRONS , & C . 169-173 . Equations involving the number of ...
Page 3
... triangle AOT = . AO . AT = r . ( arc AP ) ; ... area of the circle ABC = r . ( circumference ABC . ) 6. COR . 1. The area of a circle = = r . ( circumference . ) γ . 2 πν , πγ2 . : 7. COR . 2. When radius = 1 , area π . ON THE DIVISION ...
... triangle AOT = . AO . AT = r . ( arc AP ) ; ... area of the circle ABC = r . ( circumference ABC . ) 6. COR . 1. The area of a circle = = r . ( circumference . ) γ . 2 πν , πγ2 . : 7. COR . 2. When radius = 1 , area π . ON THE DIVISION ...
Page 8
... triangle the acute angles are complements of each other ; and in any triangle one of the angles is the supplement of the sum of the other two . ( Euc . I. 32. ) 21. Definitions of the Trigonometric Functions of an arc . DEF . V. The ...
... triangle the acute angles are complements of each other ; and in any triangle one of the angles is the supplement of the sum of the other two . ( Euc . I. 32. ) 21. Definitions of the Trigonometric Functions of an arc . DEF . V. The ...
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Common terms and phrases
2ί π A₁ base C₁ centre chord circle cos a)2 cos(a cosec cosec a)² cot 2n cot a cot cot cot decimal equal factors find what values Firstly four right angles given greater or less hence imaginary quantities integer less than 90 loga logarithm loge m² n2 mcot Napier's rules nearly negative odd integer perpendicular plane angles polar triangle pole polygon positive integer PROB PROP quadrant radius unity regular polyhedrons sec a)2 Similarly sin a)2 sin sin sin sin ẞ sın solid angle sphere spherical angle spherical polygon spherical triangle substituting subtending sum the series surface tangent trigonometric functions vanish α α α β α+β α₁ αξ Δα ηβ ίπ Μπ π α π π π+α
Popular passages
Page 197 - IF two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases, or third sides, equal ; and the two triangles shall be equal ; and their other angles shall be equal, each to each, viz.
Page 179 - The diameter of a sphere is any straight line which passes through the centre, and is terminated both ways by the superficies of the sphere.
Page 190 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Page 191 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Page 181 - ... poles. 751. COR. 2. All great circles of a sphere are equal. 752. COR. 3. Every great circle bisects the sphere. For the two parts into which the sphere is divided can be .so placed that they .will coincide; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their planes passes through the centre, and is, therefore, a diameter of each circle. 754.
Page 252 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.
Page 189 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 181 - An arc of a great circle may be drawn through any two points on the surface of a sphere.
Page 45 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 9 - The Versed Sine of an arc, is the part of the diameter intercepted between the arc and its sine.