幾何原本雜議几何原本杂议

下學工夫，有理有事。此書爲益，能令學理者袪其浮氣，練其精心；學事者資其定法，發其巧思，故舉世無一人不當學。聞西國古有大學，師門生常數百千人，來學者先問能通此書，乃聽入。何故？欲其心思細密而已。其門下所出名士極多。

下学工夫，有理有事。此书为益，能令学理者袪其浮气，练其精心；学事者资其定法，发其巧思，故举世无一人不当学。闻西国古有大学，师门生常数百千人，来学者先问能通此书，乃听入。何故？欲其心思细密而已。其门下所出名士极多。

The work of learning from below has two sides, principles and practice. What this book gives is this: it makes those who study principles shed their restless airs and train a careful mind, and it gives those who work at practical things fixed methods and wakes their ingenuity. So there is no one in the world who ought not to learn it. I have heard that in the West there was in ancient times a great academy, where a master's pupils often numbered hundreds or thousands, and anyone who came to study was first asked whether he understood this book; only then was he admitted. Why? Because they wanted his thinking to be fine and exact, nothing more. A great many distinguished men came out of that school.

凡他事，能作者能言之，不能作者亦能言之。獨此書爲用，能言者卽能作者；若不能作，自是不能言。何故？言時一毫未了，向後不能措一語，何由得妄言之？以故精心此學，不無知言之助。

凡他事，能作者能言之，不能作者亦能言之。独此书为用，能言者即能作者；若不能作，自是不能言。何故？言时一毫未了，向后不能措一语，何由得妄言之？以故精心此学，不无知言之助。

In every other matter, those who can do a thing can talk about it, and those who cannot do it can talk about it too. With this book alone, those who can speak of it are the ones who can do it; if you cannot do it, you simply cannot speak of it. Why? Because if, while speaking, a single hair's breadth is left unclear, you cannot say one more word after it; how could anyone talk nonsense here? So to give one's mind to this study is no small help in knowing what words are worth.

凡人學問，有解得一半者，有解得十九或十一者。獨幾何之學，通卽全通，蔽卽全蔽，更無高下分數可論。

凡人学问，有解得一半者，有解得十九或十一者。独几何之学，通即全通，蔽即全蔽，更无高下分数可论。

In learning, people may understand half of a thing, or nine parts in ten, or one part in ten. Only in geometry, to understand is to understand wholly, and not to understand is not to understand at all; there are no grades or fractions to speak of.

人具上資而意理疎莽，卽上資無用；人具中材而心思縝密，卽中材有用。能通幾何之學，縝密甚矣！故率天下之人而歸於實用者，是或其所由之道也。

人具上资而意理疏莽，即上资无用；人具中材而心思缜密，即中材有用。能通几何之学，缜密甚矣！故率天下之人而归于实用者，是或其所由之道也。

A person of the highest gifts whose thinking is loose and careless will find those gifts of no use; a person of middling talent whose thinking is close and exact will find that talent useful. To understand geometry is to be exact in the highest degree. So if all the people under heaven are to be led back to what is of real use, this may well be the road they take.

此書有四不必：不必疑，不必揣，不必試，不必改。有四不可得：欲脫之不可得，欲駁之不可得，欲減之不可得，欲前後更置之不可得。有三至、三能：似至晦，實至明，故能以其明明他物之至晦；似至繁，實至簡，故能以其簡簡他物之至繁；似至難，實至易，故能以其易易他物之至難。易生於簡，簡生於明，綜其玅在明而已。

此书有四不必：不必疑，不必揣，不必试，不必改。有四不可得：欲脱之不可得，欲驳之不可得，欲减之不可得，欲前后更置之不可得。有三至、三能：似至晦，实至明，故能以其明明他物之至晦；似至繁，实至简，故能以其简简他物之至繁；似至难，实至易，故能以其易易他物之至难。易生于简，简生于明，综其妙在明而已。

This book has four things it does not need: it need not be doubted, need not be guessed at, need not be tested, need not be changed. It has four things that cannot be done: you cannot take anything away from it, you cannot refute it, you cannot shorten it, you cannot rearrange its order. It has three extremes and three powers. It seems most obscure and is in truth most clear, so that with its clearness it can make clear what is most obscure in other things. It seems most complicated and is in truth most simple, so that with its simplicity it can simplify what is most complicated in other things. It seems most difficult and is in truth most easy, so that with its ease it can make easy what is most difficult in other things. Ease is born of simplicity, simplicity is born of clearness; taken all together, its wonder lies in clearness, and that is all.

此書爲用至廣，在此時尤所急須。余譯竟，隨偕同好者梓傳之。利先生作敘，亦最喜其亟傳也，意皆欲公諸人人，令當世亟習焉，而習者葢寡。竊意百年之後，必人人習之，卽又以爲習之晚也。而謬謂余先識，余何先識之有？

此书为用至广，在此时尤所急须。余译竟，随偕同好者梓传之。利先生作叙，亦最喜其亟传也，意皆欲公诸人人，令当世亟习焉，而习者盖寡。窃意百年之后，必人人习之，即又以为习之晚也。而谬谓余先识，余何先识之有？

The uses of this book are very wide, and in these times it is especially needed. When I had finished the translation, I went with friends of the same mind to have it cut on blocks and passed on. Master Ricci wrote the preface, and he was the most eager of all that it should be spread quickly; both of us wanted it given to everyone, so that people now might study it at once. Yet those who study it are few. My own thought is that a hundred years from now everyone will study it, and will then think they came to it late. And then they will mistakenly say that I saw it first; but what foresight is there in me?

有初覽此書者，疑奧深難通，仍謂余當顯其文句。余對之：「度數之理，本無隱奧，至於文句，則爾日推敲再四，顯明極矣。倘未及留意，望之似奧深焉，譬行重山中，四望無路，及行到彼，蹊徑厯然。請假旬日之功，一究其旨，卽知諸篇自首迄尾，悉皆顯明文句。」

有初览此书者，疑奥深难通，仍谓余当显其文句。余对之：「度数之理，本无隐奥，至于文句，则尔日推敲再四，显明极矣。倘未及留意，望之似奥深焉，譬行重山中，四望无路，及行到彼，蹊径历然。请假旬日之功，一究其旨，即知诸篇自首迄尾，悉皆显明文句。」

There are those who, looking at this book for the first time, suspect it of being deep and hard to penetrate, and say I ought to make its sentences plainer. My answer is this: “In the principles of measure and number there was never anything hidden. As for the sentences, we weighed and turned them over again and again at the time, and they are as plain as they can be. If you have not yet given them your attention, they look deep from a distance. It is like walking among layered mountains: looking around, you see no road; when you get there, the paths are all distinct. Give it ten days of work, look into what it means, and you will see that every chapter, from beginning to end, is written in plain sentences.”

吳淞徐光啟記。

吴淞徐光启记。

Recorded by Xu Guangqi of Wusong.