## The Analyst: A Monthly Journal of Pure and Applied Mathematics, Volumes 3-4Pierson & Blair, 1876 |

### From inside the book

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Page 186

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**force**requires time for its transmission through space , it can be easily proved , by the well known principle of the parallelogram of velocities and**forces**, that every planetary body must be accelerated in its**orbit**, and ... Page 187

... forces are equal in circular orbits ; and if a is equal to the semi - major axis of the earth's orbit ; and v , g and r are re- spectively equal to the orbital velocity , intensity of the

... forces are equal in circular orbits ; and if a is equal to the semi - major axis of the earth's orbit ; and v , g and r are re- spectively equal to the orbital velocity , intensity of the

**orbital force**of grav- ity , and the etherial ... Page 15

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**orbital forces**and R , R ' , the required resisting forces . With the distances d and s form a right - angled parallelogram , the diag- onal of which will represent the compound force of gravity ; this force may be resolved into two ... Page 16

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**orbital force**, exerted upon the earth . The earth moves in its orbit 8976.11926 miles , while gravity is transmitted over the distance d ; hence we have or 8976.11926 91430000 :: 1 : 10185.91635788 ,**orbital force**central force = 1 ... Page 17

... force . Let d and d ' be the distances from the focal force of any two points in an ellipse ; let V , V ' be the ...

... force . Let d and d ' be the distances from the focal force of any two points in an ellipse ; let V , V ' be the ...

**orbital force**, in an elliptic orbit , varies inversely as the cube of the distance from the focal force ...### Other editions - View all

### Common terms and phrases

5th degree a₁ algebraic ANALYST angle ARTEMAS MARTIN assumed axis b₁ C₁ circular coefficients common logarithms constant curve denote determine differential distance E. B. SEITZ ellipse Elliptic Functions equal equation expression factor formula function given circle gives hence hyperbola integral intersection inverse Lagrange's Theorem locus logarithms method multiply observations orbital orbital force ORSON PRATT oxen parabola parallel perpendicular plane points at infinity position probable error quadrics quadrilateral radius ratio reduce represent result roots sides SOLUTION BY PROF SOLUTIONS of problems sphere square substitution surface tangent Taylor's Theorem Theorem tion triangle UNION SPRINGS unknown quantities values velocity whence zero