A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page 30
... suppose we consider the arc of a quadrant of a circle of radius a ; its length is , which if we resolve into ... Let us now investigate these properties with greater 30 ON THE GENERATION OF CONTINUOUS QANTITY . [ 16 . Differentiation of.
... suppose we consider the arc of a quadrant of a circle of radius a ; its length is , which if we resolve into ... Let us now investigate these properties with greater 30 ON THE GENERATION OF CONTINUOUS QANTITY . [ 16 . Differentiation of.
Page 31
Bartholomew Price. 17. ] Let us now investigate these properties with greater ... suppose these increments to become infinitesimal , in which case we shall ... let the differ- ence between them be noticed . Also let it be observed , that ...
Bartholomew Price. 17. ] Let us now investigate these properties with greater ... suppose these increments to become infinitesimal , in which case we shall ... let the differ- ence between them be noticed . Also let it be observed , that ...
Page 43
... let us suppose in two circles of unequal radii , which we will assume to be concentric , although this assumption is un- necessary , two regular polygons of the same number of sides to be inscribed ; then the perimeters of these ...
... let us suppose in two circles of unequal radii , which we will assume to be concentric , although this assumption is un- necessary , two regular polygons of the same number of sides to be inscribed ; then the perimeters of these ...
Page 56
... suppose the function to be compound , and thus to depend on x , not ... let us first take the case in which only two func- tions are involved : viz ... Let ( x ) = 2 , • [ ¥ ( x ) ] = $ ( z ) = U , .. dz = \ ' ( x ) dx , ... du = ' ( z ) ...
... suppose the function to be compound , and thus to depend on x , not ... let us first take the case in which only two func- tions are involved : viz ... Let ( x ) = 2 , • [ ¥ ( x ) ] = $ ( z ) = U , .. dz = \ ' ( x ) dx , ... du = ' ( z ) ...
Page 70
... let us consider a tree , and let us suppose its growth to depend on three circumstances which are independent of each other , viz . the fertility of the soil , the rain that waters it , and the heat of the sun : then , if the relation ...
... let us consider a tree , and let us suppose its growth to depend on three circumstances which are independent of each other , viz . the fertility of the soil , the rain that waters it , and the heat of the sun : then , if the relation ...
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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