 | Sir John Leslie - 1821 - عدد الصفحات: 518
...conjugate &, as the tame & to the parameter of 'IV. It follows that in the parabola, the parameter of a diameter is equal to four times the distance of its vertex from the focus. For GM and gM being joined, the right angled triangles MLT and FLT are evidently equal, and ML ia equal... | |
 | John Radford Young - 1830 - عدد الصفحات: 390
...obviously includes equation (1), p. 122, in which the value of r, the radius vector of the origin, is m. equal to 4m, the coefficient of x, in the equation...property in (100), viz. that the abscissas are as the squares of the ordinates, is obviously true for every system of conjugate axes. Since, in the condition... | |
 | John Radford Young - 1833 - عدد الصفحات: 310
...the origin, is m. (104.) In article (100), it was found that the principal parameter is equal to 4>n, the coefficient of x, in the equation of the curve,...ordinate, corresponding to the abscissa x =r . We shall hereafier see that this double ordinate always passes through the focus. The property in (100), viz.... | |
 | Henry Parr Hamilton - 1834 - عدد الصفحات: 272
...passing through the' focus is called the parameter of the corresponding diameter ; hence 80. COR. 2. The parameter of any diameter is equal to four times the distance of its vertex from the focus. 81. COR. 3. Hence also, the square of the ordinate to any diameter is equal to the parameter multiplied... | |
 | Henry Parr Hamilton - 1834 - عدد الصفحات: 240
...passing through the focus is called the parameter of the corresponding diameter ; hence 80. COE. 2. The parameter of any diameter is equal to four times the distance of its vertex from the focus. 81. COR. 3. Hence also, the square of the ordinate to any diameter is equal to the parameter multiplied... | |
 | John Radford Young - 1835 - عدد الصفحات: 298
...vector of the point A', therefore representing it by r, equation (2) becomes, by substitution, i/2 = 4rx .... (5). This, therefore, is the equation of...the double ordinate, corresponding to the abscissa z=r. We shall hereafter see that this double ordinate always passes through the focus. The property... | |
 | Alexander Jamieson - 1837 - عدد الصفحات: 516
...curve, we have D p = \p ; therefore, by addition, it is But since by the property of the parabola, the parameter of any diameter, is equal to four times the distance between the vertex of that diameter and the focus, we have P and by the equation to the curve, it is... | |
 | Charles Davies - 1838 - عدد الصفحات: 366
...-fji or its equal 2p', is called the parameter of the new diameter A'X!. PROPOSITION VII. THEOREM. The parameter of any diameter is equal to four times the distance from the vertex of that diameter to the directrix, or four times the distance from the vertex to the... | |
 | Charles Davies - 1839 - عدد الصفحات: 366
...sin* or its equal 2p', is called the parameter of the new diameter A'X'. PROPOSITION VII. THEOREM. The parameter of any diameter is equal to four times the distance from the vertex of that diameter to the directrix, or four times the distance from the vertex to the... | |
 | Charles Hutton - 1843 - عدد الصفحات: 570
...17). Some of the most material of these are demonstrated in the following propositions. PROP. IX. Пе parameter of any diameter is equal to four times the distance of the vertex of that diameter from the focus of the parabola. LET CM be any diameter different from the... | |
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In article (100), it was found that the principal parameter is equal to 4m, the coefficient of x, in the equation of the curve, when referred to rectangular conjugates. By analogy, the coefficient 4r, when any system of conjugates are employed, is called... 
