 | Colin MacLaurin - 1801 - 428 sider
...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... | |
 | Isaac Dalby - 1806 - 526 sider
...parallelogram SN, consequently vlC . 2lZ or the rcctang. CG. ZB = the parallelogram SN. 279. The sum of the squares of any two conjugate diameters, is equal to the sum of the squares rf the, two axes. Tliut is, PK '• + HV = CG2 -1- ZB3 : (see the preceding fig.)... | |
 | Robert Simson - 1809 - 220 sider
...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 ;... | |
 | Robert Simson - 1817 - 298 sider
...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 sider
...any two 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...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 sider
...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... | |
 | William Nicholson - 1819 - 408 sider
...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 Gl, /GH, (fig. 1), made by the... | |
 | Rev. John Allen - 1822 - 508 sider
...if the angles contained by the asymtotes be not right, any two conjugate diameters are unequal; and the difference of the squares of any two conjugate...diameters, is equal to the difference of the squares oftheaxes. The sum of the squares of any two conjugate diameters of an ellipse, is equal to the sum... | |
 | Rev. John Allen - 1822 - 516 sider
...within the acute angles, is greater than its conjugate. Cor. In ellipses, the sum, and in hyperbolas, the difference of the squares, of any two conjugate diameters, is equal to the sum or difference, as the case may be, of the squares of any other conjugate diameters, being each,... | |
 | James Mitchell - 1823 - 666 sider
...PM'*=ft». Fourth, CE=^-MP, cuv Filth, rfJ— fr« ~CP*-f. PM« — DE^— CE-i = CM* — CIK Therefore the difference of the squares of any two conjugate diameters is equal to the dillerence of the squares of the two axes. Hence also in the equilateral hyperbola the conjugate diameters... | |
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Fig. 83,84. conjugate diameters is equal to the sum of the squares of the... 
