A Treatise on Infinitesimal Calculus ... |
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Page xxi
... curve . 166. Determination of the equation of a curve when 8 is a given function of x and y 167 , 168. The intrinsic equation of a curve 210 211 212 214 217 219 SECTION 5. - Involutes of Plane Curves . 169 , 170. Investigation of ...
... curve . 166. Determination of the equation of a curve when 8 is a given function of x and y 167 , 168. The intrinsic equation of a curve 210 211 212 214 217 219 SECTION 5. - Involutes of Plane Curves . 169 , 170. Investigation of ...
Page xxiv
... curve , its evolute , and two bounding radii of curvature 316 .. 317 SECTION 3. - Quadrature of Surfaces of Revolution . 232. Investigation of the surface - element .. 319 233. The area of a surface , when the generating plane curve ...
... curve , its evolute , and two bounding radii of curvature 316 .. 317 SECTION 3. - Quadrature of Surfaces of Revolution . 232. Investigation of the surface - element .. 319 233. The area of a surface , when the generating plane curve ...
Page xxvi
... curve of pos- sibility 374 .. 268. On combination of errors of observation ; and the measure of precision of observation .. 376 269. The curve of probability 379 379 380 .. 270. The probability of a given error of observation determined ...
... curve of pos- sibility 374 .. 268. On combination of errors of observation ; and the measure of precision of observation .. 376 269. The curve of probability 379 379 380 .. 270. The probability of a given error of observation determined ...
Page 110
... curve whose equation is y = F ( a , x ) ; let oмx , Oм , x ,, then , as explained in Art . 3 , the area Mo Mn Pn Po = = f ** x ' ( a , x ) dx . xo Let the parameter a vary , and first let the element - function alone vary , and let the ...
... curve whose equation is y = F ( a , x ) ; let oмx , Oм , x ,, then , as explained in Art . 3 , the area Mo Mn Pn Po = = f ** x ' ( a , x ) dx . xo Let the parameter a vary , and first let the element - function alone vary , and let the ...
Page 142
... curve represented in fig . 16 ; let OM , X。, OM = x , OM1 = x1 ; MN dx , MP = y = F ( x ) : so that r ' ( x ) dr expresses n ; = dx the area of MPQN , when MN = dx = an infinitesimal . Evidently therefore will curve , the extreme ...
... curve represented in fig . 16 ; let OM , X。, OM = x , OM1 = x1 ; MN dx , MP = y = F ( x ) : so that r ' ( x ) dr expresses n ; = dx the area of MPQN , when MN = dx = an infinitesimal . Evidently therefore will curve , the extreme ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ angle application axis Beta-function bx dx consequently convergent convergent series coordinates cosec cx² cycloid definite integral denoted determined double integral dx a² dx dx dx dy dx² dy dz dy² dz dy dx e-ax element-function ellipse equal evaluation examples expressed fraction function Gamma-function geodesic geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation length let us suppose limits of integration logr multiple integral plane curve preceding problem proper fraction quantity radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variables variation x-integration x₁ x2 dx x²)¹ x²)³