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

复杂性在广野中扩展了自己， 算术比率对于任何追求准确性尝试都是无用。

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可能性，但它却完全破坏了他急于为算术命题证明确定性和普遍性。

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.

在真理中，包括那仅仅陈述在意义上给出东西真理，也包括某抽象逻辑和算术原则，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那部分，在工场手工业各个不同阶段，只会按算术比例与工资增长成比例增长。

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，就是生活本质——令人眼花缭乱胜利让所有人眼花缭乱，吉普赛女妖让他们满足于微薄工资和他们最终成功算术上不可能。

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?

朱佩依附于安慰可怜无知，拒绝了知道优越安慰，在可靠算术基础上，她父亲是一个不自然流浪者，让葛雷格林德先生充满了怜悯。然而，该怎么办？