The Elements of Plane TrigonometryJ. Weale, 1854 - 119 páginas |
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Página 1
... circumference of a circle is known to be about 3.14159 times its diameter , or , in other words , the ratio of the circumference to the diameter is represented by 3.14159 ; for this number writers generally put the Greek letter π . B ...
... circumference of a circle is known to be about 3.14159 times its diameter , or , in other words , the ratio of the circumference to the diameter is represented by 3.14159 ; for this number writers generally put the Greek letter π . B ...
Página 2
James Hann .. circumference : = TD ; where D is the diameter , or 2πr , where r is the radius of the circle Hence the length of the arc of a quadrant is πr of a semi- 2 3πη circle , or 180 ° , is πr ; and of 270 ° , or three quadrants ...
James Hann .. circumference : = TD ; where D is the diameter , or 2πr , where r is the radius of the circle Hence the length of the arc of a quadrant is πr of a semi- 2 3πη circle , or 180 ° , is πr ; and of 270 ° , or three quadrants ...
Página 76
... circumference = 3.141592653589793 = π , and when the radius is unity the semicircumference = π , and since there are 64800 seconds in 180 ° , we shall have in parts of the radius arc 10 " = π 64800 = ' 000048481368110 . Now in very ...
... circumference = 3.141592653589793 = π , and when the radius is unity the semicircumference = π , and since there are 64800 seconds in 180 ° , we shall have in parts of the radius arc 10 " = π 64800 = ' 000048481368110 . Now in very ...
Página 91
... circumference of o moC 3.1416 × 2 = 1.5708 = = arc mo , 4 4 1.5708 × 1 sector Com = = 7854 , 2 2.8958 1.8546 * 7854 sum of sectors = 5.5358 AC BC 4 × 3 AABC = = = 2 2 6 ; ... space nmo △ ABC – sum of sectors = - • 4642 . ( 14 ) Given ...
... circumference of o moC 3.1416 × 2 = 1.5708 = = arc mo , 4 4 1.5708 × 1 sector Com = = 7854 , 2 2.8958 1.8546 * 7854 sum of sectors = 5.5358 AC BC 4 × 3 AABC = = = 2 2 6 ; ... space nmo △ ABC – sum of sectors = - • 4642 . ( 14 ) Given ...
Página 93
... circumference of a circle , O its centre , from C draw , a tangent to the circle meeting the radius OA produced , in P , join PD ; then if CP = a , DP = b , 0 = angle formed by DP and a tangent at D , a2- b2 prove that r = of the circle ...
... circumference of a circle , O its centre , from C draw , a tangent to the circle meeting the radius OA produced , in P , join PD ; then if CP = a , DP = b , 0 = angle formed by DP and a tangent at D , a2- b2 prove that r = of the circle ...
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Términos y frases comunes
A+ cot a+b+c AB² AC² angle ACB angle of elevation AO² AP AP Asin BOP₁ centre circumference circumscribed cos A cos cos² cos³ cosec cosine cot A cot cot A+ cot² OPA cot³ diameter distance Divide equation feet formula given height hence hexagon inscribed circle logarithms negative nth root number of sides Oa cot OA² OB² perimeter perpendicular plane triangle quadrant r² cot radii radius ratio regular polygon right angle right-angled triangle sec² sector shew sin A cos sin A sin sin-¹ sin² sin² 18 sin³ sine sine and cosine square subtend subtracted tan-¹ tan² tan³ tangent triangle ABC unity ηφ
Pasajes populares
Página 97 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple, equal to 40° ; then from another window, 18 feet directly above the former, the like angle was 37° 30'.
Página 97 - Wanting to know the height of an inaccessible tower; at the least distance from it, on the same horizontal plane, I took its angle of elevation equal to 58°; then going 300 feet directly from it, found the angle there to be only 32°: required its height, and my distance from it at the first station?
Página 86 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Página 51 - It depends on the principle, that the difference of the squares of two quantities is equal to the product of the sum and difference of the quantities.
Página 63 - If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from, the point of their intersection lines be drawn perpendicular to the sides which contain the opposite angle...
Página 87 - The square on the side of a regular pentagon inscribed in a circle is equal to the sum of the squares on the sides of the regular hexagon and decagon inscribed in the same circle.
Página 93 - To THEIR DIFFERENCE ; - So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 98 - Wanting to know my distance from an inaccessible object 0, on the other side of a river; and having no instrument for taking angles, but only a chain or cord for measuring distances; from each of two stations, A and B, which were taken at 500 yards asunder, I measured in a direct line from the object 0 100 yards, viz. AC and BD each equal to 100 yards ; also the diagonal AD measured 550 yards, and the diagonal BC 560. What then was the distance of the object 0 from each, station A and B ? . C AO...
Página 97 - Being on a horizontal plane, and wanting to know the height of a tower placed on the top of an inaccessible hill : I took the angle of elevation of the top of the hill 40°, and of the top of the tower 51°; then measuring in a line directly from it to the distance of 200 feet farther, I found the angle at the top of the tower to be 33° 45'.
Página 101 - The hypotenuse AB of a right-angled triangle ABC is trisected in the points D, E; prove that if CD, CE be joined, the sum of the squares on the sides of the triangle CDE is equal to two-thirds of the square on AB.