Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 26
Сторінка 105
Duncan Farquharson Gregory William Walton. ( 31 ) To find the point in the line ... axis of the prism in order that for a given content the total surface may be ... cut off from the prism is equal to the part included in the pyramid SPR ...
Duncan Farquharson Gregory William Walton. ( 31 ) To find the point in the line ... axis of the prism in order that for a given content the total surface may be ... cut off from the prism is equal to the part included in the pyramid SPR ...
Сторінка 106
... cut from a given cone . Let AC ( fig . 8 ) = a , major axis of the ellipse . CD = b , CN = x , BP being the Then the condition that the area of the ellipse shall be a maximum gives x = 2b ( a2 — b2 ) ± b ( a1 — 14a2b2 + b1 ) * 3 ( a2 + ...
... cut from a given cone . Let AC ( fig . 8 ) = a , major axis of the ellipse . CD = b , CN = x , BP being the Then the condition that the area of the ellipse shall be a maximum gives x = 2b ( a2 — b2 ) ± b ( a1 — 14a2b2 + b1 ) * 3 ( a2 + ...
Сторінка 135
... cut the axis of a at distances 4a , 6a , & c . , -2a , -4a , & c . from the origin . The farther these points are removed from the origin the more nearly is the curve perpendicular to the axis of x , the value of dy da π at the ...
... cut the axis of a at distances 4a , 6a , & c . , -2a , -4a , & c . from the origin . The farther these points are removed from the origin the more nearly is the curve perpendicular to the axis of x , the value of dy da π at the ...
Сторінка 145
... axes cut off between the origin and the tangent , or the intercepts of the tangent , are dy y ----- x along the axis of y . da dx - -y along the axis of x . dy These I shall call yo , a respectively . Ex . ( 1 ) . The equation to the ...
... axes cut off between the origin and the tangent , or the intercepts of the tangent , are dy y ----- x along the axis of y . da dx - -y along the axis of x . dy These I shall call yo , a respectively . Ex . ( 1 ) . The equation to the ...
Сторінка 154
... cuts the axis of y at a distance a and that of ≈ at a distance - from the origin , and as it is therefore inclined at an a , its equation is 3 angle of 45 ° to the axis of a y = x + - 3 ( 14 ) Let the equation to the curve be y2 = x3 + ...
... cuts the axis of y at a distance a and that of ≈ at a distance - from the origin , and as it is therefore inclined at an a , its equation is 3 angle of 45 ° to the axis of a y = x + - 3 ( 14 ) Let the equation to the curve be y2 = x3 + ...
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Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³