Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 66
Page 102
... angles APM , BPN are equal . ( 23 ) To find the point in the straight line AD ( fig . 2 ) , at which BC subtends the greatest angle ; ABC being per- pendicular to AD . If the angle be a maximum its tangent is also a maximum . Let P be ...
... angles APM , BPN are equal . ( 23 ) To find the point in the straight line AD ( fig . 2 ) , at which BC subtends the greatest angle ; ABC being per- pendicular to AD . If the angle be a maximum its tangent is also a maximum . Let P be ...
Page 103
... angle which it must subtend at the centre in order that the corresponding segment may be a maximum . Let a be the half - length of the arc , the radius of the α circle ; then is the half - angle of the segment . - 20 If u be the segment ...
... angle which it must subtend at the centre in order that the corresponding segment may be a maximum . Let a be the half - length of the arc , the radius of the α circle ; then is the half - angle of the segment . - 20 If u be the segment ...
Page 105
... 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 intersecting each other in N. Then it is easy to see that MN NO and consequently SO ...
... 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 intersecting each other in N. Then it is easy to see that MN NO and consequently SO ...
Page 106
... angles of the faces of the terminating solid angle , and he found them to be 109. 28 ' and 70. 32 " respectively . It occurred to Réaumur that this might be the form , which , for the same . solid content , gives the minimum of surface ...
... angles of the faces of the terminating solid angle , and he found them to be 109. 28 ' and 70. 32 " respectively . It occurred to Réaumur that this might be the form , which , for the same . solid content , gives the minimum of surface ...
Page 107
... angle of the cone must be less than 15o . When this is not the case , the ellipse increases continually till it coincides with the base . It may happen that the maximum value of the section is less than the base of the cone ; and this ...
... angle of the cone must be less than 15o . When this is not the case , the ellipse increases continually till it coincides with the base . It may happen that the maximum value of the section is less than the base of the cone ; and this ...
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