1735-10-30 Benjamin Franklin.ON THE USEFULNESS OF THE MATHEMATICS.

Mathematics originally signified any kind of discipline or learning, but now it is taken for that science which teaches or contemplates whatever is capable of being numbered or measured. That part of the mathematics which relates to numbers only, is called arithmetic; and that which is concerned about measure in general, whether length, breadth, motion, force, &c., is called geometry.

数学最初指的是任何类型的学科或学习，但现在它指的是教授或思考所有可以被计数或测量的事物的科学。数学中只涉及数字的部分叫做算术；而涉及度量的部分，无论是长度、宽度、运动、力量等，称为几何学。

As to the usefulness of arithmetic, it is well known that no business, commerce, trade, or employment whatsoever, even from the merchant to the shopkeeper, &c., can be managed and carried on without the assistance of numbers; for by these the trader computes the value of all sorts of goods that he dealeth in, does his business with ease and certainty, and informs himself how matters stand at any time with respect to men, money, and merchandise, to profit and loss, whether he goes forward or backward, grows richer or poorer.

至于算术的有用性，大家都知道，没有数字的帮助，任何生意、商业、贸易或工作都无法管理和进行，从商人到店主等都不例外；通过数字，商人可以计算他所交易的各种商品的价值，轻松且确定地做生意，并随时了解有关人、金钱和商品的情况，盈亏、前进或后退、富裕或贫穷。

Neither is this science only useful to the merchant, but is reckoned the primum mobile (or first mover) of all mundane affairs in general, and is useful for all sorts and degrees of men, from the highest to the lowest.

这门科学不仅对商人有用，而且被认为是所有世俗事务的“原动力”（或第一推动力），对各类各阶层的人都有用，从最高层到最低层。

As to the usefulness of geometry, it is as certain that no curious art or mechanic work can either be invented, improved, or performed without its assisting principles.

至于几何学的有用性，毫无疑问，任何精巧的艺术或机械工作都无法在没有几何学原理的帮助下发明、改进或完成。

It is owing to this that astronomers are put into a way of making their observations, coming at the knowledge of the extent of the heavens, the duration of time, the motions, magnitudes, and distances of the heavenly bodies, their situations, positions, risings, settings, aspects, and eclipses; also the measure of seasons, of years, and of ages.

正因为此，天文学家才能进行观测，掌握天体的广度、时间的持续、天体的运动、大小和距离，它们的位置、状态、升起、落下、方位和日食等；还包括季节、年份和时代的衡量。

It is by the assistance of this science that geographers present to our view at once the magnitude and form of the whole earth, the vast extent of the seas, the divisions of empires, kingdoms, and provinces.

正是借助这门科学，地理学家向我们展示了整个地球的大小和形状、广阔的海洋、帝国、王国和省份的划分。

It is by the help of geometry the ingenious mariner is instructed how to guide a ship through the vast ocean, from one part of the earth to another, the nearest and safest way, and in the shortest time.

借助几何学，巧妙的航海者得以学习如何在广阔的海洋中引导船只，从地球的一部分到另一部分，选择最近且最安全的航道，并在最短的时间内完成。

By help of this science the architects take their just measures for the structure of buildings, as private houses, churches, palaces, ships, fortifications, &c.

借助这门科学，建筑师可以准确地测量建筑结构，如私人住宅、教堂、宫殿、船只、堡垒等。

By its help engineers conduct all their works, take the situation and plan of towns, forts, and castles, measure their distances from one another, and carry their measures into places that are only accessible to the eye.

通过它的帮助，工程师进行所有工作，测量城市、堡垒和城堡的位置和规划，测量它们之间的距离，并将这些测量带入肉眼无法到达的地方。

From hence also is deduced that admirable art of drawing sundials on any place, howsoever situate, and for any part of the world, to point out the exact time of the day, the sun's declination, altitude, amplitude, azimuth, and other astronomical matters.

由此也推导出在任何地方、无论如何安置的日晷绘制艺术，适用于世界任何地方，准确指出白天的时间、太阳的偏角、高度、振幅、方位角及其他天文学相关事项。

By geometry the surveyor is directed how to draw a map of any country, to divide his lands, and to lay down and plot any piece of ground, and thereby discover the area in acres, rods, and perches; the gauger is instructed how to find the capacities or solid contents of all kinds of vessels, in barrels, gallons, bushels, &c.; and the measurer is furnished with rules for finding the areas and contents of superfices and solids, and casting up all manner of workmanship.

通过几何学，测量师能指导如何绘制任何国家的地图，划分土地，绘制并标出任何一块地，从而计算出土地的面积，单位如英亩、杆和英尺；而计量员也能学会如何测量各种容器的容量或实心内容，例如桶、加仑、蒲式耳等；而测量师也配备了规则，用于计算表面和固体的面积及内容，并计算各种工艺品。

All these, and many more useful arts, too many to be enumerated here, wholly depend upon the aforesaid sciences, namely, arithmetic and geometry.

所有这些，及更多无法一一列举的有用技艺，完全依赖于前述的科学，即算术和几何学。

This science is descended from the infancy of the world, the inventors of which were the first propagators of human kind, as Adam, Noah, Abraham, Moses, and divers others.

这门科学自世界的初期便传承下来，其发明者是人类最早的传播者，如亚当、诺亚、亚伯拉罕、摩西等。

There has not been any science so much esteemed and honoured as this of the mathematics, nor with so much industry and vigilance become the care of great men, and laboured in by the potentates of the world, namely, emperors, kings, princes, &c.

没有任何一门科学像数学一样被如此尊崇和重视，也没有哪门科学能像它那样，成为伟人们如此辛勤和警觉的关注焦点，且为世界的强权人物，如皇帝、国王、王子等所操劳。

Mathematical demonstrations are a logic of as much or more use than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even subjects not mathematical.

数学证明是一种比学校里常学的逻辑更为有用的逻辑，它有助于公正地塑造心智，扩展思维的容量，并增强思维能力，使其能够进行精确的推理，并辨别所有事件中的真伪，即使是非数学领域的内容。

For which reason it is said the Egyptians, Persians, and Lacedæmonians seldom elected any new kings but such as had some knowledge in the mathematics; imagining those who had not men of imperfect judgments, and unfit to rule and govern.

正因为如此，人们常说，埃及人、波斯人和斯巴达人很少选举没有数学知识的人作为新国王，因为他们认为没有数学知识的人判断力不完备，不适合治理国家。

Though Plato's censure, that those who did not understand the 117th proposition of the 13th book of Euclid's Elements ought not to be ranked among rational creatures, was unreasonable and unjust, yet to give a man the character of universal learning, who is destitute of a competent knowledge in the mathematics, is no less so.

尽管柏拉图的批评认为，那些不理解欧几里得《几何原本》第13卷第117命题的人不应被列为理性生物，这是不合理和不公正的，但如果给一个人贴上博学的标签，而他缺乏足够的数学知识，同样也是不合理的。

The usefulness of some particular parts of the mathematics, in the common affairs of human life, has rendered some knowledge of them very necessary to a great part of mankind, and very convenient to all the rest, that are any way conversant beyond the limits of their own particular callings.

数学的某些特定部分在日常生活中的有用性，使得对它们的一些知识对大多数人来说非常必要，对其他任何超出自己特定职业范围的人来说也非常方便。

Those whom necessity has obliged to get their bread by manual industry, where some degree of art is required to go along with it, and who have had some insight into these studies, have very often found advantages from them sufficient to reward the pains they were at in acquiring them.

那些因生计而必须依靠手工劳动的人，需要一定的技艺配合，他们如果曾涉足这些学问，常常会发现从中获得的好处足以回报他们在学习过程中付出的努力。

And whatever may have been imputed to some other studies, under the notion of insignificance and loss of time, yet these, I believe, never caused repentance in any, except it was for their remissness in the prosecution of them.

无论其他学科曾被认为微不足道或浪费时间，我相信这些学问从未让任何人感到后悔，除非是因为他们在学习过程中懈怠。

Philosophers do generally affirm that human knowledge to be most excellent which is conversant among the most excellent things. What science, then, can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of the mathematics?

哲学家们普遍认为，人类的知识中最卓越的是那些涉及最优秀事物的知识。那么，哪门科学比数学更高贵、更卓越、更有用、更令人赞叹和更具证明性呢？

I shall conclude with what Plato says, in the seventh book of his Republic, with regard to the excellence and usefulness of geometry, being to this purpose:

我将以柏拉图在《理想国》第七卷中关于几何学卓越性和有用性的言论作为结尾，内容如下：

"Dear friend—You see, then, that mathematics are necessary, because, by the exactness of the method, we get a habit of using our minds to the best advantage. And it is remarkable that, all men being capable by nature to reason and understand the sciences, the less acute, by studying this, though useless to them in every other respect, will gain this advantage, that their minds will be improved in reasoning aright; for no study employs it more, nor makes it susceptible of attention so much; and those who we find have a mind worth cultivating, ought to apply themselves to this study."

“亲爱的朋友——你看，数学是必要的，因为通过方法的精确性，我们养成了最有效利用思维的习惯。值得注意的是，所有人天生都能够推理和理解科学，虽然对某些人而言，学习数学在其他方面可能没有用处，但通过学习这门学科，他们的思维能力将得到提高，能够正确推理；没有其他学科能像它一样如此有效地训练思维，也没有其他学科能如此吸引注意力；那些我们认为有培养价值的心智，应该致力于这项学习。”

1735-10-30 Benjamin Franklin.ON THE USEFULNESS OF THE MATHEMATICS.

1735-10-30 Benjamin Franklin.ON THE USEFULNESS OF THE MATHEMATICS.

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