A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
From inside the book
Page xvi
... positive or negative , so does ƒ ( x ) in- crease and diminish with x , or as x increases , f ( x ) de- creases , and vice versá 187 188 111. The proof that --- F ( x ) − F ( x ) = ( xn− xo ) F ' { xo + 0 ( x − xo ) } , - F ( x ) ...
... positive or negative , so does ƒ ( x ) in- crease and diminish with x , or as x increases , f ( x ) de- creases , and vice versá 187 188 111. The proof that --- F ( x ) − F ( x ) = ( xn− xo ) F ' { xo + 0 ( x − xo ) } , - F ( x ) ...
Page xxii
... positive or negative ... 367 241. Another proof of the same theorem by means of an expansion 368 242. Examples in illustration . 370 243. Interpretation of the preceding results by the infinitesimal method 371 244. Criterion of points ...
... positive or negative ... 367 241. Another proof of the same theorem by means of an expansion 368 242. Examples in illustration . 370 243. Interpretation of the preceding results by the infinitesimal method 371 244. Criterion of points ...
Page 4
... positive number , the sign of inequality remains the same ; that is , the quantity which was greater before the multiplication is the greater after it ; but if the terms are multiplied by a negative number , the sign of the inequality ...
... positive number , the sign of inequality remains the same ; that is , the quantity which was greater before the multiplication is the greater after it ; but if the terms are multiplied by a negative number , the sign of the inequality ...
Page 5
... positive , so that the signs of the above inequalities will not be changed when they are multiplied as follows : a1a ... positive , and let L be the least and & the greatest of the fractions ; then a1 is > L , < G b1 b2 is > L , < G an ...
... positive , so that the signs of the above inequalities will not be changed when they are multiplied as follows : a1a ... positive , and let L be the least and & the greatest of the fractions ; then a1 is > L , < G b1 b2 is > L , < G an ...
Page 7
... a pour objet propre de résoudre toutes les questions de nombres . ” — Philosophie Positive , vol . i . p . 143 . ance with the rules of the science of number , Infinitesimal Calculus considers continuously-varying number.
... a pour objet propre de résoudre toutes les questions de nombres . ” — Philosophie Positive , vol . i . p . 143 . ance with the rules of the science of number , Infinitesimal Calculus considers continuously-varying number.
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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