A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page 261
... drawn to the angles , the sum of their squares is a minimum . Take A , one of the angular points , see fig . 20 , of the triangle , for the origin ; and let the base AB = a , and the coordinates to c be h , k ; and let the coordinates ...
... drawn to the angles , the sum of their squares is a minimum . Take A , one of the angular points , see fig . 20 , of the triangle , for the origin ; and let the base AB = a , and the coordinates to c be h , k ; and let the coordinates ...
Page 301
... drawn to the star from the earth , at the two positions of it , are to all appearance parallel straight lines . 187. ] In corroboration also of what has here been stated , the following are a few out of a great many striking instances ...
... drawn to the star from the earth , at the two positions of it , are to all appearance parallel straight lines . 187. ] In corroboration also of what has here been stated , the following are a few out of a great many striking instances ...
Page 303
... drawn through a parallel to the axis of y , and when x is nearly 3 , y is ∞ but when a is greater than 3 , y is ; that is , the curve has crossed the asymptote at the pole of the circle of infinite radius opposite to A , and has ...
... drawn through a parallel to the axis of y , and when x is nearly 3 , y is ∞ but when a is greater than 3 , y is ; that is , the curve has crossed the asymptote at the pole of the circle of infinite radius opposite to A , and has ...
Page 304
... drawn from it , equal in length to a times the linear unit , will fulfil the requirements of the single symbol a . But inas- much as an indefinite number of equal lines may be drawn from any one point , thus far we have no means of ...
... drawn from it , equal in length to a times the linear unit , will fulfil the requirements of the single symbol a . But inas- much as an indefinite number of equal lines may be drawn from any one point , thus far we have no means of ...
Page 305
... drawn from o towards the right hand . Now since , as we said above , any line drawn from o , a times the linear unit in length , will be symbolized by a , it is necessary to fix on some origi- nating direction ; suppose this to be oa ...
... drawn from o towards the right hand . Now since , as we said above , any line drawn from o , a times the linear unit in length , will be symbolized by a , it is necessary to fix on some origi- nating direction ; suppose this to be oa ...
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Common terms and phrases
a₁ algebraical angles b₁ becomes Calculus change of sign changes sign circle coefficients constant cosec curve d2F d2F d²u d²x d²y d³u d³y derived function determine differential equation dr dr dr dy dx dx dx dy dx² dy dx dy dy dy dz dy² dz dx equal equicrescent explicit function expression F(xo F(xo+h factor finite quantity fraction func given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithms loge Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions positive primitive equation radius replaced result right-hand member roots Similarly sin x singular value Sturm's Theorem substituting suppose symbols Theorem tion vanish variables variation versin whence zero