Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 43
Page ix
... of the Differential Calculus to Geometry of Three Dimensions 200 XIV . Envelops to Lines and Surfaces XV . General Theorems in the Differential Calculus ......... 224 237 PART II . INTEGRAL CALCULUS . CHAPTER PAGE I. Integration.
... of the Differential Calculus to Geometry of Three Dimensions 200 XIV . Envelops to Lines and Surfaces XV . General Theorems in the Differential Calculus ......... 224 237 PART II . INTEGRAL CALCULUS . CHAPTER PAGE I. Integration.
Page 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 ...
Page 110
... is of more importance geometrically than analytically ; and I may add , that in geometry the failure Annales de Gergonne , Vol . 11. 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 . 11. p . 132 . • of Lagrange's condition indicates that there is a maximum for 110 MAXIMA AND MINIMA .
Page 114
... geometric progression . Let each of these ratios be equal to plying them together , a = b n 1 Then , multi- n b \ or n = , a Let log uv , then proceeding to the second differentials we get , on substituting for x , y , ≈ the values na ...
... geometric progression . Let each of these ratios be equal to plying them together , a = b n 1 Then , multi- n b \ or n = , a Let log uv , then proceeding to the second differentials we get , on substituting for x , y , ≈ the values na ...
Page 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 ...
Other editions - View all
Common terms and phrases
a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx 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 radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³