 | Mathematics - 1801 - 658 pages
...equal to the difference of the squares of the semiaxe^ Or, the square of the distance between the foci is equal to the difference of the squares of the two axes. That is, CF'^CA^S^Ca*, or, F/* — AB1— «i». • For, to the focus F draw the ordinate FE ; which, by the... | |
 | Colin MacLaurin - Calculus - 1801 - 428 pages
...ca1, as CA* + caz to ca1; consequently CtP + CL1 is equal toCAx+c«% or CA^ + CD1; that is, the sum of the squares of any two conjugate diameters is equal to the sum of the squaresof theaxis ABaod DE. 617. Any rectangle gh/k (Jig. 273) in the plane of the circle... | |
 | Charles Hutton - Mathematics - 1807 - 464 pages
...the Difference of the Squares of the Seijiiaxes ; Or, the Square of the Distance between the Foci, is equal to the Difference of the Squares of the two Axes. That is, CF1 = CA* - ca% or pf * = AB* — ab*. For, to the focus F draw the ordinate FE ; which, by the definition,... | |
 | Robert Simson - Conic sections - 1809 - 220 pages
...together with the rectangle EFD, that is, to the (5. 2. Elem.) square of CD. •CoR. 3. Hence the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axes. Let CD, CL be the semi-axis, and CA, C1J conjugate semi-diameters ;... | |
 | Charles Hutton - Mathematics - 1811 - 442 pages
...to the Difference of the Squares of the Semiaxes ; Or, the Square of the Distance between the Foci, is equal to the Difference of the Squares of the two Axes. That is, CF* = CAZ - ca% or Ff Z = ABZ - ab*. b For, to the focus F draw the ordinate FE ; which, by the definition,... | |
 | Charles Hutton - Mathematics - 1811 - 494 pages
...to the Difference of the Squares of the Semiaxes; Or, the Square of the Distance between the Foci, is equal to the Difference of the Squares of the two Axes. Ft, That is, CF* = CAl — ca1, or Ff 1 = AB1 — ab1. For, to the focus F draw the ordinate FE ; which,... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...the Difference of the Squares of the Semiaxes ; . . Or, the Square of the Distance between the Foci, is equal to the Difference of the Squares of the two Axes. That is,cp* = CA* — ca9, or *f* = AB* — ab*. b F6r, to the focus F draw the ordinate »i ; which, by.... | |
 | Robert Simson - Conic sections - 1817 - 298 pages
...together with the rectangle EFD, that is, to the (5. 2. Elem.) square of CD. COR. 3. Hence the sum of the squares of any two conjugate diameters is equal to the sum of the squares of the axis. Let CD, CL be (he semiaxes, and CA, CB conjugate semidiameters ; let... | |
 | Abram Robertson - 1818 - 196 pages
...Fig. 83,84. conjugate diameters is equal to the sum of the squares of the axes ; but in an hyperbola the difference of the squares of any two conjugate...diameters is equal to the difference of the squares of the axes. For the rest remaining, as in the last two articles, let AB, DE be the axes, and then the angles... | |
 | William Nicholson - Natural history - 1819 - 406 pages
...semi-diameter, which is conjugate to that passing through the point of contact. 8. In every ellipsis, the sum of the squares of any two conjugate diameters is equal to the sum of the. squares of the two axes. 9. In every .ellipsis, the angles F GI, /GH, (fig. 1), made by... | |
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Fig. 83,84. conjugate diameters is equal to the sum of the squares of the axes ; but in an hyperbola the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes. 
