幾何原本雜議几何原本杂议

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.

Whoever masters this book can master anything; whoever loves to study this book can study anything.

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.

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.

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.

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.

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?

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.”

Recorded by Xu Guangqi of Wusong.