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

### From inside the book

Results 1-5 of 22

Page 64

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**ellipse**that can be inscribed in the area common to the two circles , is л2 ( - · 1 ) . PUBLICATIONS RECEIVED . - We have received various Educational Periodicals for which we tender our thanks , though our space will not permit us even ... Page 79

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**ellipse**, the section is two**ellipses**whose semi axes are R and ( Ra2 + b3 ) , a and b being the semi axes of the generating**ellipse**. So with a hyperbolic generatrix , we obtain hyperbolas whose semi axes are R and √ ( R2 — a — b3 ) ... Page 89

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**ellipse**that can be inscribed in the area common to the two circles , is r2 ( ) . " SOLUTION BY HENRY HEATON , DES MOINES , IOWA . LET 2a = the distance between the centers of the circles . The distance between the center of the**ellipse**... Page 90

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**ellipse**and x , y , and dy ÷ de of the circle coincide . Combining the above equa- tions we get A = . ' . AB = · ax ) ( * = 9 ) ] , - ах and B = √ ( r2 — ax ) . ( ~ 2 — ax ) | ( 2 = a ) . .. . d ( AB ) = ~ ( r2 — ax ) √ ( ~ ~ a ) -a ... Page 91

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**ellipse**, we have 2r A = S * пxу.2пzdz S2 2nzdz π 2r2 *。 2r xyzdz . • ( 10 ) Substituting in ( 10 ) from ( 8 ) and ( 9 ) , and observing that when z = 0 , x = r , and when z = 2r , x = 0 , we have Απ A = ጕ 2 . S x4dx o ( 2r2 - x2 ) ...### 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