| 1801 - 658 σελίδες
...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 - 1801 - 428 σελίδες
...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 - 1807 - 464 σελίδες
...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 - 1809 - 220 σελίδες
...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 - 1811 - 442 σελίδες
...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 - 1811 - 494 σελίδες
...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 - 1812 - 620 σελίδες
...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 - 1817 - 298 σελίδες
...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 σελίδες
...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 - 1819 - 406 σελίδες
...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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