​    ​兩千多年之前，數學家阿基米德懂得用無窮小寬度的金屬板來計量面積和體積。這是很了不起的數學成就。

    ​    ​兩千多年之後，魯賓遜嚴格定義了什麼是數學的無窮小。隨之，無窮小微積分出現了。

    ​    ​兩千年，彈指一揮間。現今，我們已經進入無窮小數學時代，然而，很不幸的是，我們自己還不知道。

        袁萌  陳啟清 10月16日

附：阿基米德的無窮小方法

阿基米德（Archimedes） (287–212 b.c.), the greatest mathematician of antiquity（地方名）, used another procedure to determine areas and volumes. To measure an unknown figure, he imagined that it was balanced on a 2The more familiar formula A = πr2 results from the fact that π is defined by the relation C = 2πr.

    ​    ​lever against a known figure. To find the area or volume of the former in terms of the latter, he determined where the fulcrum must be placed to keep the lever even. In performing his calculations, he imagined that the figures were comprised of an indefinite number of laminae—very thin strips or plates. It is unclear whether Archimedes actually regarded the laminae （金屬板）as having infinitesimal width or breadth（無窮小寬度）. In any case, his results certainly attest to the power of his method: he discovered mensuration formulae for an entire menagerie of geometrical beasts, many of which are devilish to find, even with modern techniques. Archimedes recognized that his method did not prove his results. Once he had applied the mechanical technique to obtain a preliminary guess, he supplemented it with a rigorous proof by exhaustion