## The Analyst: A Monthly Journal of Pure and Applied Mathematics, Volumes 1-2Pierson & Blair, 1874 |

### From inside the book

Results 6-10 of 82

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**Hence**, in order that this value of x may be rational , we must make --- - 4 n2 t1 — ( n2 — 1 ) ( d ) 2 = a square = This gives d = x = 8 n s t2 82 + n2 - 1 ' 4 n ( n2 - 1 ) ta 82 + n2 — 1 ' [ 2 n t2 8 ( d ) ] - and then ( b ) The first ... Page 42

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**Hence**r = p4 - 4 2 } = cube = p3 { 222 + r ~ } ° 3 2 p2 6 -- 2 and x = First term = x- p3 - 1 2 Last term = x + p3 - 1 2 The sum of the cubes = { p1 - 3p3 — 2p2 +4 6 p1 + 3p3 — 2p2 - 2 9 6 p ( p - 1 ) ( p + 1 ) ( p2 +2 ) As particular ... Page 47

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**Hence**, ± and y = ± b 2 √ a 2 +63 ( √ ( a − 6 ) 3 — 8 a b ± √ ( a + b ) 3 + 2 ad ) a 2 Va2 + 62 √ ( a − b ) 2 — 2 a b = √ ( a + b ) 2 + 2 a b ) . [ Prof. Knisely writes that the question he sent ( No. 1 ) is , by mistake slightly ... Page 54

A Monthly Journal of Pure and Applied Mathematics.

A Monthly Journal of Pure and Applied Mathematics.

**Hence**in a stable system , there can be no collision and no indefinite separation of the bodies composing it . With this definition of stability we see that , in the problem of two ... Page 61

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**hence**the curve of section is symmetrical about 2 , and this is the axis of the surface . If we move the origin to a point on z half way between the two directrices we obtain a more symmetrical form of the equation . δ Let 2 ' = 2 or 2 ...### Other editions - View all

### Common terms and phrases

A₁ Algebra ANALYST angle ARTEMAS MARTIN axes axis binomial theorem bipolar equation Calculus circle coefficient comet conic constant construction coordinates cubic equation curve denote describe diameter differential distance divided E. B. Seitz ellipse equal expression formula frustrum function G. W. HILL give given Hence hyperbola hyperbolic functions imaginary roots integral intersection limaçon Mathematical motion multiply negative nine-point circle nth root obtain odd number orbits P₁ parabola parallel perpendicular plane pole quadratic quantity r₁ radius represent Robert Adrain RULE OF SIGNS sides SOLUTION BY PROF SOLUTIONS OF PROBLEMS solved sphere square straight line Substituting suppose tangent theorem tion triangle variable velocity whence zero

### Popular passages

Page 157 - SOL UT10N OF A PROBLEM. BY EB SEITZ, GREENVILLE, OHIO. Three circles whose radii are a, b, c, touch each other externally. Within the space enclosed by them a circle is drawn tangent to the three circles, and within this circle three circles are drawn tangent to each other and to the three given circles. Calling the radii of these three circles...

Page 18 - If they be considered, as we have done, as small nebulae, wandering from one solar system to another, and formed by the condensation of the nebulous matter, which is diffused so profusely throughout the universe, we may conceive that when they arrive in that part of space where the attraction of the Sun predominates, it should force them to describe elliptic or hyperbolic orbits. But as their velocities are equally possible in every...

Page 18 - To discover the system which binds together the great members of the creation in the whole extent of infinitude, and to derive the formation of the heavenly bodies themselves, and the origin of their movements, from the primitive state of nature by mechanical laws, seems to go far beyond the power of human reason. On the other hand, religion threatens to bring a solemn accusation against the audacity which would presume to ascribe to nature by itself results in which the immediate hand of the Supreme...

Page 175 - HENRY said, the question of balls and points had not been fully settled. If electricity acts inversely as the square of the distance, then, on the principle of central forces, the induction on a sphere at a distance from the cloud would be the same as if all the matter of the sphere were concentrated in its centre, and consequently the attraction of the ball or sphere on the electricity of the distant cloud would be the same as that of a point. When, however, the inducing body, or the discharge itself,...

Page 14 - MC STEVENS, SALEM, OHIO. In the February number of the Michigan Teacher for 1869, there appeared an article, contributed by Mr. William Wiley of Detroit, entitled, " New Theory of Repetends," in which it is shown that the figures of a repetend are easily deduced from the common fracton successively from right to left, instead of from left to right as is done by the ordinary method. Thinking it deserving of more notice than it received from its publication in that journal, I propose in this article...

Page 119 - No. 11). Other articles on the Diophantine analysis by Mr. Wheeler would have been inserted, if the Mathematical Monthly had been continued. ' The Economy and Symmetry of the Honey-bees' Cells,' by Chauncey Wright (Vol. II, No. 9). Simon Newcomb gives several interesting

Page 172 - Hence : — The differential of the sine of an arc is equal to the \ cosine of the arc, into the differential of the arc, divided by the radius. In a similar manner we may find the following functions to have the respective differentials, viz.

Page 74 - The correspondence between the theoretical and observed values is given below in units of Sun's radius. The values of the secular mean apsides are taken from "Stockwell's Memoirs on the Secular Variations of the Orbits of the Eight Principal Planets.

Page 108 - ... (14) Two equal particles, attracting each other with forces varying inversely as the square of the distance, are constrained to move in two straight lines at right angles to each other ; supposing their motions to commence from rest, to find the time in which each of them will arrive at the intersection of the two straight lines.

Page 175 - ... [No construction of this prob. has been received. — Prof. J. Scheffer writes: "If we describe a circle about one of the extrmities of the lower base of the quadrilateral as a centre, with a radius equal to one of the sides, and another circle about the other extremity of the lower base as a centre, with a radius equal the other side, we reduce the problem to the following: If two circles are given as to magnitude and position, to lay a line of given length between the two circumferences, which...