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2x dx a/dx algebraic function algebraic quantities arithmetic progression becomes clear constant differential constant quantity denominator differential calculus differential dx differential equation differential is assumed differential is equal dx dx dx dy dx is constant dxdy dy d2x easily equal to zero example exponent find the differential finite difference finite equation finite quantity follows formula fraction function of x Furthermore geometric ratio given equation given expression given function given series Hence higher differentials higher order homogeneous homogeneous function infinite number infinite series infinitely divisible infinitely large quantity infinitely small quantity infinity integral calculus let dy logarithm method obtain paragraph partial sum pd2x polynomial powers of dx Q dy qdx2 quotient reason relationship rule second and higher second difference second differential set constant similar sine subtracted term third differences three variables vanishing increments x2dy
Page v - Those quantities that depend on others in this way, namely, those that undergo a change when others change, are called functions of these quantities. This definition applies rather widely and includes all ways in which one quantity can be determined by others.
Page vii - To many who have discussed the rules of differential calculus, it has seemed that there is a distinction between absolutely nothing and a special order of quantities infinitely small, which do not quite vanish completely but retain a certain quantity that is indeed less than any assignable quantity.
Page vi - Therefore, differential calculus is concerned not so much with vanishing increments, which indeed are nothing, but with the ratio and mutual proportion. Since these ratios are expressed as finite quantities, we must think of calculus as being concerned with finite quantities.
Page x - I have nothing new to offer, and this is all the less to be required, since in other works I have treated this subject so fully.
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