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abscissa arithmetical progression axis bisects body catenary centre circle co-ordinates coefficients cone conic section conjugate consequently constant cos2 cubic equation curve cycloid cylinders denote described determine diamedral diameter direction distance divisor draw drawn ellipse equal equation expression force formula fraction given by position given point gravity Hence horizontal hyperbola inclined plane inscribed inscribed circle integral intersection John Baines latitude latus rectum mathematical method motion multiplied obtain ordinate Palaba parabola parallel perpendicular Porism projection prove quantities QUESTION quotient radius ratio respectively right angles right ascension roots second order Second Solution shew sides similar triangles sin1 sin2 sphere spherical square straight line substituting suppose surface tang tangent planes theorem tion transformation triangle variable velocity vertex vertical whence
Page 40 - Having given the hypotenuse of a right-angled triangle, and the radius of the inscribed circle, to construct the triangle. 33. ABC is a triangle inscribed in a circle, the line joining the middle points of the arcs AB, AC, will cut off equal portions of the two contiguous sides measured from the angle A.
Page 190 - The Principles of Bridges ; containing the Mathematical Demonstrations of the Properties of the Arches, the Thickness of the Piers, the Force of the Water against them, &c. together with practicalObservations and Directions drawn from the Whole.
Page 108 - Nutation of lunar orbit. The action of the bulging matter at the earth's equator on the moon occasions a variation in the inclination of the lunar orbit to the plane of the ecliptic. Suppose the plane N/?
Page 114 - Let any plane DE pass through AB, and let CE be the common section of the planes DE...
Page 97 - At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours ; and two hours afterwards met a stage vvaggcn, which was moving at the rate of 9 miles in 4 hours.
Page 53 - In every geometrical progression consisting of an odd number of terms ; the sum of the squares of the terms is equal to the sum of all the terms multiplied by the excess of the odd terms above the even.
Page 134 - The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5.
Page 192 - Calculations to determine at what Point in the Side of a Hill its Attraction will be the greatest.