正是因为有了这些学校，我们的早期技工才普遍能读会写，并精通算术及部分几何和三角，这种情况在新英格兰和大西洋中部各州尤为可见。

especially in the New England and Middle Atlantic states, were generally literate and at home in arithmetic and in some aspects of geometry and trigonometry. （NETEM 1996 Passage 4, paragraph 3）

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在数学学科的很多的领域中算术只是起到次要作用，例如逻辑学和几何学。

There are entire fields of mathematics where numerical manipulation is peripheral: logic and geometry, for example.

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算术、天文和几何本来就是中世纪学校的部分标准课程，这些课程引起了教皇尔贝特的热情本身就是非同一般的，但也不是闻所未闻。

Arithmetic, astronomy and geometry were a standard part of the curriculum in medieval schools, making Gerbert's enthusiasm for these subjects unusual, but not unheard of.

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