NUMBER.

Was Euclid right in defining number to be a collection of unities¹ of the same kind? When Newton says that number is an abstract relation of one quantity to another of the same kind, does he not understand by that the use of numbers in arithmetic and geometry? Wolfe says, number is that which has the same relation with unity² as one right line has with another. Is not this rather a property attributed to a number, than a definition? If I dared, I would simply define numbers the idea of several unities.

I see white — I have a sensation, an idea of white. It signifies not whether these two things are or are not of the same species; I can reckon two ideas. I see four men and four horses — I have the idea of eight; in like manner, three stones and six trees will give me the idea of nine.

That I add, multiply, subtract, and divide these, are operations of the faculty³ of thought which I have received from the master of nature; but they are not properties inherent to number. I can square three and cube it, but there is not certainly in nature any number which can be squared or cubed. I very well conceive what an odd or even number is, but I can never conceive either a perfect or an imperfect one.

Numbers can have nothing by themselves. What properties, what virtue⁴, can ten flints, ten trees, ten ideas, possess because they are ten? What superiority will one number divisible in three even parts have over another divisible in two?

Pythagoras was the first, it is said, who discovered divine virtue in numbers. I doubt whether he was the first; for he had travelled in Egypt, Babylon, and India, and must have related much of their arts and knowledge. The Indians particularly, the inventors of the combined and complicated game of chess, and of ciphers⁵, so convenient that the Arabs learned of them, through whom they have been communicated to us after so many ages — these same Indians, I say, joined strange chimeras⁶ to their sciences. The Chald?ans had still more, and the Egyptians more still. We know that self-delusion is in our nature. Happy is he who can preserve himself from it! Happy is he who, after having some access of this fever of the mind, can recover tolerable health.

Porphyrius, in the “Life of Pythagoras,” says that the number 2 is fatal. We might say, on the contrary, that it is the most favorable of all. Woe⁷ to him that is always single! Woe to nature, if the human species and that of animals were not often two and two!

If 2 was of bad augury⁸, 3, by way of recompense, was admirable, and 4 was divine; but the Pythagoreans and their imitators forgot that this mysterious 4, so divine, was composed of twice that diabolical⁹ number 2! Six had its merit, because the first statuaries divided their figures into six modules¹⁰. We have seen that, according to the Chald?ans, God created the world in six gahambars; but 7 was the most marvellous number; for there were at first but seven planets, each planet had its heaven, and that made seven heavens, without anyone knowing what was meant by the word heaven. All Asia reckoned seven days for a week. We divide the life of man into seven ages. How many reasons have we in favor of this number!

The Jews in time collected some scraps¹¹ of this philosophy. It passed among the first Christians¹² of Alexandria with the dogmas of Plato. It is principally displayed in the “Apocalypse of Cerinthus,” attributed to John the Apostle.

We see a striking example of it in the number of the beast: “That no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name. Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is six hundred three score and six.”

We know what great pains all the great scholars have taken to divine the solution of this enigma¹³. This number, composed of three times two at each figure, does it signify three times fatal to the third power? There were two beasts, and we know not yet of which the author would speak.

We have seen that Bossuet, less happy in arithmetic than in funeral orations¹⁴, has demonstrated that Diocletian is the beast, because we find the Roman figures 666 in the letters of his name, by cutting off those which would spoil this operation. But in making use of Roman figures, he does not remember that the Apocalypse was written in Greek. An eloquent¹⁵ man may fall into this mistake. The power of numbers was much more respected among us when we knew nothing about them.

You may observe, my dear reader, in the article on “Figure,” some fine allegories that Augustine, bishop¹⁶ of Hippo, extracted from numbers.

This taste subsisted¹⁷ so long, that it triumphed at the Council of Trent. We preserve its mysteries, called “Sacraments” in the Latin church, because the Dominicans, with Soto at their head, allege¹⁸ that there are seven things which contribute to life, seven planets, seven virtues¹⁹, seven mortal sins, six days of creation and one of repose²⁰, which make seven; further, seven plagues of Egypt, seven beatitudes; but unfortunately the fathers forget that Exodus²¹ reckons ten plagues, and that the beatitudes are to the number of eight in St. Matthew and four in St. Luke. But scholars have overcome this difficulty; by retrenching²² from St. Matthew the four beatitudes of St. Luke, there remain six, and add unity to these six, and you will have seven. Consult Fra Paolo Sarpi, in the second book of his history of the County of Trent.

1 unities   

n.统一体( unity的名词复数 )；（艺术等） 完整；（文学、戏剧） （情节、时间和地点的）统一性；团结一致

参考例句：

• Aristotle's Poetics advocates the "dramatic unities'', the unities of action, place and time. 亚里士多德在《诗学》一书中提倡“戏剧的统一性”，即事件、事件发生的时间和地点的统一。 来自英汉非文学 - 文明史
• All compounds are unities of opposites differing in nature. 化合物都是不同性质的东西的对立统一。 来自互联网

2 unity   

n.团结，联合，统一；和睦，协调

参考例句：

• When we speak of unity,we do not mean unprincipled peace.所谓团结，并非一团和气。
• We must strengthen our unity in the face of powerful enemies.大敌当前，我们必须加强团结。

3 faculty   

n.才能；学院，系；(学院或系的)全体教学人员

参考例句：

• He has a great faculty for learning foreign languages.他有学习外语的天赋。
• He has the faculty of saying the right thing at the right time.他有在恰当的时候说恰当的话的才智。

4 virtue   

n.德行，美德；贞操；优点；功效，效力

参考例句：

• He was considered to be a paragon of virtue.他被认为是品德尽善尽美的典范。
• You need to decorate your mind with virtue.你应该用德行美化心灵。

5 ciphers   

n.密码( cipher的名词复数 )；零；不重要的人；无价值的东西

参考例句：

• The ciphers unlocked the whole letter. 解密码的方法使整封信的意义得到说明。 来自《现代英汉综合大词典》
• The writers often put their results in ciphers or anagrams. 写信人常常把成果写成密码或者搞成字谜。 来自辞典例句

6 chimeras   

n.（由几种动物的各部分构成的）假想的怪兽( chimera的名词复数 )；不可能实现的想法；幻想；妄想

参考例句：

• He was more interested in states of mind than in "puerile superstitions, Gothic castles, and chimeras." 他乐于描写心情，而不愿意描写“无聊的迷信，尖拱式的堡垒和妖魔鬼怪。” 来自辞典例句
• Dong Zhong's series, in its embryonic stage, had no blossoms, birds or surreal chimeras. 董重的这个系列的早年雏形并没有梅花、鸟和超现实的连体。 来自互联网

7 woe   

n.悲哀，苦痛，不幸，困难；int.用来表达悲伤或惊慌

参考例句：

• Our two peoples are brothers sharing weal and woe.我们两国人民是患难与共的兄弟。
• A man is well or woe as he thinks himself so.自认祸是祸，自认福是福。

8 augury   

n.预言，征兆，占卦

参考例句：

• Augury is the important part of Chinese traditional culture.占卜是中国传统文化中的一个重要组成部分。
• The maritime passage was a good augury for the aerial passage.顺利的航海仿佛也是航空的好预兆。

9 diabolical   

adj.恶魔似的，凶暴的

参考例句：

• This maneuver of his is a diabolical conspiracy.他这一手是一个居心叵测的大阴谋。
• One speaker today called the plan diabolical and sinister.今天一名发言人称该计划阴险恶毒。

10 modules   

n.模块( module的名词复数 )；单元；（宇宙飞船上各个独立的）舱；组件

参考例句：

• The course consists of ten core modules and five optional modules. 这门课程包括十个必修单元和五个选修单元。
• Our English course is divided into modules on poetry, drama, and novels. 我们的英语课分为诗歌、戏剧和小说等单元。 来自《简明英汉词典》

11 scraps   

油渣

参考例句：

• Don't litter up the floor with scraps of paper. 不要在地板上乱扔纸屑。
• A patchwork quilt is a good way of using up scraps of material. 做杂拼花布棉被是利用零碎布料的好办法。

12 Christians   

n.基督教徒( Christian的名词复数 )

参考例句：

• Christians of all denominations attended the conference. 基督教所有教派的人都出席了这次会议。
• His novel about Jesus caused a furore among Christians. 他关于耶稣的小说激起了基督教徒的公愤。

13 enigma   

n.谜，谜一样的人或事

参考例句：

• I've known him for many years,but he remains something of an enigma to me.我与他相识多年，他仍然难以捉摸。
• Even after all the testimonies,the murder remained a enigma.即使听完了所有的证词，这件谋杀案仍然是一个谜。

14 orations   

n.（正式仪式中的）演说，演讲( oration的名词复数 )

参考例句：

• The young official added a genuine note of emotion amid the pompous funeral orations. 这位年轻的高级官员，在冗长的葬礼演讲中加了一段充满感情的话。 来自辞典例句
• It has to go down as one of the great orations of all times. 它去作为一个伟大的演讲所有次。 来自互联网

15 eloquent   

adj.雄辩的，口才流利的；明白显示出的

参考例句：

• He was so eloquent that he cut down the finest orator.他能言善辩，胜过最好的演说家。
• These ruins are an eloquent reminder of the horrors of war.这些废墟形象地提醒人们不要忘记战争的恐怖。

16 bishop   

n.主教，（国际象棋）象

参考例句：

• He was a bishop who was held in reverence by all.他是一位被大家都尊敬的主教。
• Two years after his death the bishop was canonised.主教逝世两年后被正式封为圣者。

17 subsisted   

v.（靠很少的钱或食物）维持生活，生存下去( subsist的过去式和过去分词 )

参考例句：

• Before liberation he subsisted on wild potatoes. 解放前他靠吃野薯度日。 来自《现代汉英综合大词典》
• Survivors of the air crash subsisted on wild fruits. 空难事件的幸存者以野果维持生命。 来自辞典例句

18 allege   

vt.宣称，申述，主张，断言

参考例句：

• The newspaper reporters allege that the man was murdered but they have given no proof.新闻记者们宣称这个男人是被谋杀的，但他们没提出证据。
• Students occasionally allege illness as the reason for absence.学生时不时会称病缺课。

19 virtues   

美德( virtue的名词复数 )； 德行； 优点； 长处

参考例句：

• Doctors often extol the virtues of eating less fat. 医生常常宣扬少吃脂肪的好处。
• She delivered a homily on the virtues of family life. 她进行了一场家庭生活美德方面的说教。

20 repose   

v.(使)休息；n.安息

参考例句：

• Don't disturb her repose.不要打扰她休息。
• Her mouth seemed always to be smiling,even in repose.她的嘴角似乎总是挂着微笑，即使在睡眠时也是这样。

21 exodus   

v.大批离去，成群外出

参考例句：

• The medical system is facing collapse because of an exodus of doctors.由于医生大批离去，医疗系统面临崩溃。
• Man's great challenge at this moment is to prevent his exodus from this planet.人在当前所遇到的最大挑战，就是要防止人从这个星球上消失。

22 retrenching   

v.紧缩开支( retrench的现在分词 )；削减（费用）；节省

参考例句：