Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка ix
... Calculus to Geometry of Three Dimensions 200 XIV . Envelops to Lines and Surfaces 224 XV . General Theorems in the Differential Calculus ........................ . 237 CHAPTER I. PART II . INTEGRAL CALCULUS . Integration of.
... Calculus to Geometry of Three Dimensions 200 XIV . Envelops to Lines and Surfaces 224 XV . General Theorems in the Differential Calculus ........................ . 237 CHAPTER I. PART II . INTEGRAL CALCULUS . Integration of.
Сторінка 103
... geometry of the problem . A geometrical solution of this problem is given in the Mathematical Collections of Pappus , Book V. Theor . 16 . ( 26 ) AC ( fig . 4 ) and BD being parallel , it is required to draw from C a line CXY , such ...
... geometry of the problem . A geometrical solution of this problem is given in the Mathematical Collections of Pappus , Book V. Theor . 16 . ( 26 ) AC ( fig . 4 ) and BD being parallel , it is required to draw from C a line CXY , such ...
Сторінка 110
... is of more importance geometrically than analytically ; and I may add , that in geometry the failure * Annales de Gergonne , Vol . III . p . 132 . of Lagrange's condition indicates that there is a maximum for 110 MAXIMA AND MINIMA .
... is of more importance geometrically than analytically ; and I may add , that in geometry the failure * Annales de Gergonne , Vol . III . p . 132 . of Lagrange's condition indicates that there is a maximum for 110 MAXIMA AND MINIMA .
Сторінка 114
... geometric progression . Let each of these ratios be equal to plying them together , α b = 1 n1 or n = - • Then , multi- n ( • Let log u = v , then proceeding to the second differentials we get , on substituting for x , y , ≈ the values ...
... geometric progression . Let each of these ratios be equal to plying them together , α b = 1 n1 or n = - • Then , multi- n ( • Let log u = v , then proceeding to the second differentials we get , on substituting for x , y , ≈ the values ...
Сторінка 118
... Geometry that if lines be drawn joining the points where the perpendiculars from the angles meet the sides , each intersecting pair makes equal angles with the side in which they meet ; consequently the triangle formed by these lines is ...
... Geometry that if lines be drawn joining the points where the perpendiculars from the angles meet the sides , each intersecting pair makes equal angles with the side in which they meet ; consequently the triangle formed by these lines is ...
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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