A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Results 1-5 of 78
Page xvi
... involving partial derived- functions into their equivalents in terms of other variables 107 , 108. Examples illustrative of the preceding principles .... CHAPTER IV . 180 182 CERTAIN RELATIONS BETWEEN FUNCTIONS AND DERIVED - FUNCTIONS ...
... involving partial derived- functions into their equivalents in terms of other variables 107 , 108. Examples illustrative of the preceding principles .... CHAPTER IV . 180 182 CERTAIN RELATIONS BETWEEN FUNCTIONS AND DERIVED - FUNCTIONS ...
Page xxv
... involving two and three arbitrary constants . Examples ..... 465 311. Conditions under which a circle can have contact of the third order . . . . 468 312. Contact of curves with given curves 469 SECTION 2. - The theory of envelopes ...
... involving two and three arbitrary constants . Examples ..... 465 311. Conditions under which a circle can have contact of the third order . . . . 468 312. Contact of curves with given curves 469 SECTION 2. - The theory of envelopes ...
Page 3
... involve only two unknown quantities , say and ; bc- x 2 cause each equation may be divided through by z ; hence it is evident that a relation exists between the coefficients : this = relation is to be determined ; and may be B 2 ...
... involve only two unknown quantities , say and ; bc- x 2 cause each equation may be divided through by z ; hence it is evident that a relation exists between the coefficients : this = relation is to be determined ; and may be B 2 ...
Page 19
... involve each other . a 13 " ... i " , a in Now although generally infinities and infinitesimals are sym- bolized respectively by ∞ and 0 , yet it is manifest that all of each kind are not equal ; not only do infinitesimals differ from ...
... involve each other . a 13 " ... i " , a in Now although generally infinities and infinitesimals are sym- bolized respectively by ∞ and 0 , yet it is manifest that all of each kind are not equal ; not only do infinitesimals differ from ...
Page 20
... involve each other , if i and x are so related that x = 1 i 1 or i == . X These , it is to be observed , are the definitions of the orders of infinities and infinitesimals . Similarly , if x be the infinity - base , x , x3 , x2 ...
... involve each other , if i and x are so related that x = 1 i 1 or i == . X These , it is to be observed , are the definitions of the orders of infinities and infinitesimals . Similarly , if x be the infinity - base , x , x3 , x2 ...
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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