Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 62
Сторінка 102
... ( fig . 1 ) , to draw two straight lines to a point P in a given line ON such that AP + BP shall be a minimum . Take the given line as the axis of x , O the origin . Let OP , and let the co - ordinates of A and B be a , b , a1 , b1 . Then ...
... ( fig . 1 ) , to draw two straight lines to a point P in a given line ON such that AP + BP shall be a minimum . Take the given line as the axis of x , O the origin . Let OP , and let the co - ordinates of A and B be a , b , a1 , b1 . Then ...
Сторінка 103
... ( fig . 4 ) and BD being parallel , it is required to draw from C a line CXY , such that the sum of the triangles ACX and BXY shall be a minimum . If AC = a , AB = b , AX = x , it is easily seen that the area of the triangle ACX is ...
... ( fig . 4 ) and BD being parallel , it is required to draw from C a line CXY , such that the sum of the triangles ACX and BXY shall be a minimum . If AC = a , AB = b , AX = x , it is easily seen that the area of the triangle ACX is ...
Сторінка 104
Duncan Farquharson Gregory. ( 27 ) OM , OP ( fig . 5 ) are two arcs of great circles on a sphere , and the arc PM is drawn perpendicular to OM ; find when the difference between OP and OM is the greatest . Let POM = a , OP = 4 , OM = 0 ...
Duncan Farquharson Gregory. ( 27 ) OM , OP ( fig . 5 ) are two arcs of great circles on a sphere , and the arc PM is drawn perpendicular to OM ; find when the difference between OP and OM is the greatest . Let POM = a , OP = 4 , OM = 0 ...
Сторінка 105
... ( fig . 6 ) be the base of the prism , PQRS one of the faces of the terminating solid angle passing through the angles P , R. Let S be the vertex of the pyramid . Draw SO perpendicular to the upper surface of the prism . Join OM , RP , SQ ...
... ( fig . 6 ) be the base of the prism , PQRS one of the faces of the terminating solid angle passing through the angles P , R. Let S be the vertex of the pyramid . Draw SO perpendicular to the upper surface of the prism . Join OM , RP , SQ ...
Сторінка 106
... ( fig . 7 ) be the cone BC = a , AC - b , BN = x . Then DN = b a x , and EN = ( ax − x2 ) 3 . 4 3 The area of the parabola is EN . DN , or 4 b - - 3 a x ( ax - x2 ) , which is to be a maximum . Whence x = За , and the area of the ...
... ( fig . 7 ) be the cone BC = a , AC - b , BN = x . Then DN = b a x , and EN = ( ax − x2 ) 3 . 4 3 The area of the parabola is EN . DN , or 4 b - - 3 a x ( ax - x2 ) , which is to be a maximum . Whence x = За , and the area of the ...
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a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³