geometers
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In 1943 - 1945, he worked in the Institute for Advanced Study at Princeton. Having arrived in the United States for two months, he finished his famous paper entitled "A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds", which inspired other differential geometers.
抵美两个月后,即完成其著名的论文──《闭曲面流形高斯--博内公式(Gauss-Bonnet Formula)的一个简单的内蕴证明》,对於后来微分几何的发展和微分几何学者的研究影响深远。
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The theorems of Ibn al-Haytham, Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals , including the Lambert quadrilateral and Saccheri quadrilateral , were the first theorems on elliptical geometry and hyperbolic geometry , and along with their alternative postulates, such as Playfair's axiom , these works had a considerable influence on the development of non-Euclidean geometry among later European geometers, including Witelo , Levi ben Gerson , Alfonso , John Wallis , and Giovanni Girolamo Saccheri .
定理伊本Haytham,欧玛尔海亚姆和纳西尔基地丁铝土司上quadrilaterals ,包括德兰伯特四边形和萨凯里四边形,是第一个椭圆形的几何定理和双曲几何,并连同其替代假设,如普莱费尔的公理,这些作品有相当发展的影响非欧几里德几何之间稍后欧洲geometers ,包括Witelo ,列维本格森,阿方索,约翰瓦利斯和乔瓦吉罗拉莫萨凯里。
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The synthetic geometers were developing projective geometry.
综合几何学家们在发展射影几何学。
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The upshot of the controversy is that the pure geometers reasserted their role in mathematics.
论战的结局是纯粹几何学家重申了他们在数学中的作用。
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Ever since Plato, philosophers have envied geometers their certitudes. So it's not surprising that the story about philosophy being conceptual analysis was well received all the way from Oxford to Berkeley, with many intermediate stops.
自柏拉图以来,哲学家们就在嫉妒几何学家所拥有的确信无疑,所以,&哲学即概念分析&这一信条,从牛津到伯克利,一路凯旋而至,就丝毫不足为奇了。
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