Just as euclid illuminates newton and galileo , so they in turn help to make einstein intelligible . The point applies to philosophical books as well .
Although euclid 's algorithm and the problem of finding perfect numbers from the preceding exercise are both drawn from the domain of mathematics , the greeks were fascinated with algorithms of other kinds as well .
尽管前面例子中的欧几里德算法以及需找完美数字的问题都是数学领域的,希腊人还同样擅长其他的领域。
But euclid 's axioms closely resembled reality while the theory of rational expectations and the efficient market hypothesis became far removed from it .
In the examples of euclid 's algorithm to calculate gcd ( x , y ) that appear in this chapter , x is always larger than y. does this condition matter ?
在本章中使用欧几里德算法计算gcd(x,y)的例子中,x总是大于y。
It has been customary when euclid , considered as a textbook , is attacked for his verbosity or his verbosity or his obscurity or his pedantry , to defend him on the ground that his logical excellence is transcendent , and affords an invaluable training to the youthful powers of reasoning .
He engaged in feverish bouts of self-improvement , studying euclid and grammar at all hours .
他沉迷于自我完善,整日整夜地研究欧几里德和语法学。
In this article , we discuss some questions with respect to number theory in the works of euclid and diophantus .
在本文中,我们讨论了欧几里得和丢番图著作中与数论有关的某些问题。
It has been too often assumed that " proof " must be what kant called " apodeictic " that is of the kind that we used to be familiar within euclid , where the argument could be concluded with a triumphant q.e.d. because every rational person who understands the propositions is compelled to accept the inference .