Complexity had extended itself on immense horizons, and arithmetical ratios were useless for any attempt at accuracy.

复杂性在广阔的视野中扩展， 率对于任何追求准确性的尝试都是无用的。

This possibility seems never to have occurred to him, yet it is one which utterly destroys the certainty and universality which he is anxious to vindicate for arithmetical propositions.

他似乎从来没有想到过这种可能性，但它却完全破坏他急于为命题证明的确定性和普遍性。

Among such truths are included those which merely state what is given in sense, and also certain abstract logical and arithmetical principles, and (though with less certainty) some ethical propositions.

在这真理中，包括那仅仅陈述在意义上给出的东西的真理，也包括某抽象的逻辑和原则，以及（尽管不太确定）一伦理命题。

That part of the price of the commodity which resolved itself into the wages, would, through all the different stages of the manufacture, rise only in arithmetical proportion to this rise of wages.

商品价格中体现为工资的那部分，在工场手工业的各个不同阶段，只会按例与工资的这种增长成例增长。

Such, obviously, was the stuff of life—a dizzy triumph dazzling the eyes of all of them, a gypsy siren to content them with meagre wage and with the arithmetical improbability of their eventual success.

显然，这就是生活的本质——令人眼花缭乱的胜利让所有人眼花缭乱，吉普赛女妖让他们满足于微薄的工资和他们最终成功的上的不可能。

The wretched ignorance with which Jupe clung to this consolation, rejecting the superior comfort of knowing, on a sound arithmetical basis, that her father was an unnatural vagabond, filled Mr. Gradgrind with pity. Yet, what was to be done?

朱佩依附于这种安慰的可怜的无知，拒绝知道的优越安慰，在可靠的基础上，她的父亲是一个不然的流浪者，让葛雷格林德先生充满怜悯。然而，该怎么办？