A System of Plane and Spherical Trigonometry: To which is Added a Treatise on LogarithmsJ. & J.J. Deighton, 1831 - 330 Seiten |
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Seite 7
... subtending an angle A at the centre , A = For A a ..A == = 180 ° α four right angles . ( Euc . VI . 33 ... subtended at the centre . If a be the value of a ' when r = a linear unit - 1 , A = 180 ° π π π 4 ' 5 ' a ; and a , or the arc ...
... subtending an angle A at the centre , A = For A a ..A == = 180 ° α four right angles . ( Euc . VI . 33 ... subtended at the centre . If a be the value of a ' when r = a linear unit - 1 , A = 180 ° π π π 4 ' 5 ' a ; and a , or the arc ...
Seite 12
... subtending that angle at the centre of a circle , divided by the radius of the circle . 27. PROP . If the angle AOP ... subtended by π and 2 are 180 ° and 360 ° , if A be the angle subtended by a , then , by the Prop . the formula ...
... subtending that angle at the centre of a circle , divided by the radius of the circle . 27. PROP . If the angle AOP ... subtended by π and 2 are 180 ° and 360 ° , if A be the angle subtended by a , then , by the Prop . the formula ...
Seite 13
... subtending A ; therefore by Def . XV . α sin A = C AC 31. COR . Sin ( 90 ° - A ) = sin B = AB b ..cos A = a 32. PROP . Tan A = 3 ? cot A = b α For , by describing a circle with centre A and radius AC ( = b ) BC ( = a ) would PLANE ...
... subtending A ; therefore by Def . XV . α sin A = C AC 31. COR . Sin ( 90 ° - A ) = sin B = AB b ..cos A = a 32. PROP . Tan A = 3 ? cot A = b α For , by describing a circle with centre A and radius AC ( = b ) BC ( = a ) would PLANE ...
Seite 14
... subtending A , therefore a tan A = b Also tan ( 90 ° AC - A ) = tan B - BC b .. cot A = a 33. COR . Sec A AB = = AC с b cosec A sec B = AB C = BC a 34. PROB . Any formula consisting of trigonometric func- tions of an arc having been ...
... subtending A , therefore a tan A = b Also tan ( 90 ° AC - A ) = tan B - BC b .. cot A = a 33. COR . Sec A AB = = AC с b cosec A sec B = AB C = BC a 34. PROB . Any formula consisting of trigonometric func- tions of an arc having been ...
Seite 182
... subtending a spherical angle at its pole , the spherical angle radius of the sphere being = 1 . 180 = a ; π Let the spherical angle = A , then it is obvious that A is as often contained in 180 ° , as a is in the semi - circumference of ...
... subtending a spherical angle at its pole , the spherical angle radius of the sphere being = 1 . 180 = a ; π Let the spherical angle = A , then it is obvious that A is as often contained in 180 ° , as a is in the semi - circumference of ...
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Häufige Begriffe und Wortgruppen
A+B+C a+n ß a+ß a₁ B₁ base C₁ centre chord cosec cot cot diameter equal equations formula four right angles given greater or less hence hypothenuse integer intersection less than 90 Let the sides logarithm loge method Napier's rules nearly negative perpendicular plane angles plane triangle polar triangle pole PROB PROP quadrant quantity R₁ radius unity regular polyhedrons right-angled triangle Similarly sin A sin sin ß sines and cosines small circle solid angle sphere spherical angle spherical polygon spherical triangle ß₁ subtending sum the series suppose tangent trigonometric functions values vers α₁ Απ Δα ηβ π α π π
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 191 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Seite 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.
Seite 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.
Seite 189 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 181 - An arc of a great circle may be drawn through any two points on the surface of a sphere.
Seite 45 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Seite 9 - The Versed Sine of an arc, is the part of the diameter intercepted between the arc and its sine.