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代微积拾级：修订间差异
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第1,399行：
English=
原文如下：
{{from|A<span style{{=}}"font-size: 70%;>RTICLE</span> (157.) I<span style{{=}}"font-size: 70%;>N</span> the Differential Calculus, as in Analytical Geometry, there are two classes of quantities to be considered, viz., ''variables'' and ''constants''.<br><br>Variable quantities are generally represented by the last letters of the alphabet, ''x'', ''y'', ''z'', etc., and any values may be assigned to them which will satisfy the equations into which they enter.<br><br>Constant quantities are generally represented by the firstletters of the alphabet, ''a'', ''b'', ''c'', etc., and these always retain the same values throughout the same investigation.<br><br>Thus, in the equation of a straight line, <br><center><math>y=ax+b</math>,</center>the quantities a and b have but one value for the same line, while ''x'' and ''y'' vary in value for every point of the line.<br><br>(158.) '''One variable is said to be a ''function'' of another variable, when the first is equal to a certain algebraic expression containing the second.''' Thus, in the equation of a straight line <br><center><math>y=ax+b</math>,</center>''y'' is a function of ''x''. <br><br>So, also, in the equation of a circle, <br><center><math>y=\sqrt{R^2-x^2}</math>;</center>and in the equation of the ellipse, <br><center><math>y=\frac{B}{A}\sqrt{2Ax-x^2}</math>.</center>(159.) When we wish merely to denote that ''y'' is ''dependent'' upon ''x'' for its value, without giving the particular expression which shows the value of ''x'', we employ the notation<br><center><math>y=F(x)</math>, or <math>y=f(x)</math>,
|''Elements of Analytical Geometry and of The Differential and Integral Calculus'', Differential Calculus, Section I}}
<center>[[File:Elements of Analytical Geometry and of The Differential and Integral Calculus.pdf|page=124|300px]][[File:Elements of Analytical Geometry and of The Differential and Integral Calculus.pdf|page=125|300px]]</center>
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第1,417行 ⟶ 第1,419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}}
<center>[[File:Elements of Analytical Geometry and of The Differential and Integral Calculus.pdf|page=131|300px]]</center>
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>。
第1,427行 ⟶ 第1,431行：
在卷十七，定义了积分：
{{from|積分爲微分之還原，其法之要，在識別微分所由生之函數。如已得 天<sup>二</sup> 之微分爲 二天{{RareChar|𢓍|⿰彳天}}，則有 二天{{RareChar|𢓍|⿰彳天}}，即知所由生之函數爲 天<sup>二</sup>，而 天<sup>二</sup> 即爲積分。<br><br>'''已得微分所由生之函數爲積分。'''而積分或有常數附之，或無常數附之，既不能定，故式中恒附以常數，命爲{{RareChar|𠰳|⿰口丙}}。{{RareChar|𠰳|⿰口丙}}或有同數，或爲〇，須攷題乃知。<br><br>來本之視微分，若函數諸小較之一，諸小較并之，即成函數。故微分之左係一禾字，指欲取諸微分之積分也。如下式 禾二天{{RareChar|𢓍|⿰彳天}}<math>\xlongequal{\qquad} 天^二 \bot</math>{{RareChar|𠰳|⿰口丙}}。來氏說今西國天算家大率不用，而惟用此禾字，取其一覽了然也。|《代微積拾級·卷十七 積分一·
<center>[[File:Elements of Analytical Geometry and of The Differential and Integral Calculus (Chinese, 1859, 3).pdf|page=3|300px]]</center>
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English=
第1,434行 ⟶ 第1,439行：
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。
<center>[[File:Elements of Analytical Geometry and of The Differential and Integral Calculus.pdf|page=228|300px]]</center>
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