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代微积拾级：修订间差异
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第1,376行：
在卷十的开头，可以看到那句经典名句：
{{from|微分之數有二，一曰常數，一曰變數；變數以天地人物等字代之，常數以甲乙子丑等字代之。<br><br>凡式中常數之同數俱不變。如直線之式爲<math>地
原文如下：
第1,382行：
“凡此变数中函彼变数，则此为彼之函数”（One variable is said to be a function of another variable, when the first is equal to a certain algebraic expression containing the second.）这句话，往往被讹传为出现在李善兰另一译作《代数学》中，其实并非如此，出处就是《代微积拾级》。
== 微分 ==
同样是卷十，我们可以看到微分的定义：
{{from|'''函數與變數之變比例俱謂之微分'''，用彳號記之。如 <math>戌\xlongequal{\qquad}天^三</math>，則得比例 {{RareChar|𢓍|⿰彳天}} : 彳戌<math>:: 一 : 三天^二</math>。{{RareChar|𢓍|⿰彳天}}彳戌，爲天與戌之微分。后皆仿此，用表天與戌之變比例。以一四兩率相乘，二三兩率相乘，則得彳戌<math>\xlongequal{\qquad}三天^二</math>{{RareChar|𢓍|⿰彳天}}。此顯函數戌之變比例，等于 三天<sup>二</sup> 乘變數天之變比例。以{{RareChar|𢓍|⿰彳天}}約之，得{{sfrac|{{RareChar|𢓍|⿰彳天}}|彳戌}}<math>\xlongequal{\qquad}三天^二</math>。此顯變數之變比例，約函數之變比例，等于函數之微係數也。如戌爲天之函數，三天 爲戌之微係數，此舉立方以㮣其餘。|《代微積拾級·卷十 微分一·例》}}
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><br>then<br><center><math>dx:du::1:3x^2</math></center>.<br>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><br>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><br>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}}
[[分类:数学]]
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