| Colin MacLaurin - Calculus - 1801
...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 - Mathematics - 1806 - 526 pages
...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 - 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 ;... | |
| Robert Simson - Conic sections - 1817 - 296 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
...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 - 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... | |
| 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 Gl, /GH, (fig. 1), made by the... | |
| Rev. John Allen - Astronomy - 1822 - 508 pages
...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 - Astronomy - 1822 - 516 pages
...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 - Mathematics - 1823 - 576 pages
...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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