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代微积拾级：修订间差异
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'''《代微积{{ruby|拾|shè}}级》'''，由英国汉学家、来华传教士{{w|伟烈亚力}}（Alexander Wylie，1815年4月6日－1887年2月10日）口译，清代数学家{{w|李善兰}}（1811年1月22日－1882年12月9日）笔述；1859年由上海{{w|墨海书馆}}（The London Missionary Society Press）出版。原著为美国数学家{{w|伊莱亚斯·罗密士}}（Elias Loomis，1811年8月7日－1889年8月15日）于1851年出版的'''《解析几何和微积分初步》（''Elements of Analytical Geometry and of The Differential and Integral Calculus''）'''。
需要注意的是，这本书中的定义以今天的眼光来看并不严谨。一方面，当时的微积分学基础并不牢固，(ε, δ)-极限定义还未出现，书中仍然只使用未严格定义的无穷小量来定义概念；另一方面，这本书本身就是入门教材，不应过于晦涩难懂。
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第1,391行 ⟶ 第1,393行：
原文如下：
{{from|(170.) '''The rate of variation of a function or of any variable quantity is called its ''differential''''', and is denoted by the letter ''d'' placed before it. Thus, if<br><center><math>u=x^3</math>,</center>then<br><center><math>dx:du::1:3x^2</math>.</center>The expressions ''dx'', ''du'' are read differential of ''x'', differential of ''u'', and denote the rates of variation of ''x'' and ''u''.<br><br>If we multiply together the extremes and the means of the preceding proportion, we have<br><center><math>du=3x^2dx</math>,</center>which signifies that the rate of increase of the function ''u'' is 3''x''<sup>2</sup> times that of the variable ''x''.<br><br>If we divide each member of the last equation by ''dx'', we have<br><center><math>\frac{du}{dx}=3x^2</math>,</center>which expresses the ratio of the rate of variation of the function to that of the independent variable, and is called the ''differential coefficient'' of ''u'' regarded as a function of ''x''.|''Elements of Analytical Geometry and of The Differential and Integral Calculus'', Differential Calculus, Proposition II}}
注意，时至今日，微分号为了与量区别而记作<math>\mathrm{d}</math>，书中的微分号仍然是斜体<math>d</math>。
== 积分 ==
第1,400行 ⟶ 第1,404行：
原文如下：
{{from|A<span style{{=}}"font-size: 70%;>RTICLE</span> (291.) T<span style{{=}}"font-size: 70%;>HE</span> Integral Calculus is the reverse of the Differential Calculus, its object being to determine the expression or function from which a given differential has been derived.<br><br>Thus we have found that the differential of ''x<sup>2</sup>'' is ''2xdx'', therefore, if we have given ''2xdx'', we know that it must have been derived from ''x'', or plus a constant term.<br><br>(292.) '''The function from which the given differential has been derived, is called its ''integral''.''' Hence, as we are not certain whether the integral has a constant quantity or not added to it, we annex a constant quantity represented by C, the value of which is to be determined from the nature of the problem. <br><br>(293.) Leibnitz considered the differentials of functions as indefinitely small differences, and the sum of these indefinitely small differences he regarded as making up the function; hence the letter S was placed before the differential to show that the sum was to be taken. As it was frequently required to place S before a compound expression, it was elongated into the sign ''∫'', which, being placed before a differential, denotes that its integral is to be taken. Thus,<br><center><math>\int 2xdx = x^2+C</math>.</center>This sign ''∫'' is still retained ever by those whu reject the philosophy of Leibnitz. |''Elements of Analytical Geometry and of The Differential and Integral Calculus'', Integral Calculus, Section I}}
实际上，书中的积分号仅仅写作<span style="font-family:serif;">''∫''</span>，没有写得像今天的<math>\int</math>那么长。
[[分类:数学]]
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