Discovery. In general this name can be given to everything that is newly found in the Arts and the Sciences; however, it is scarcely applied, and ought not to be applied, except to that which is not only new, but also curious, useful, and difficult to find, and which, consequently has a certain degree of importance. The less important discoveries are simply called inventions . See Discover.

For the rest, it is not necessary for a discovery that its object be at the same time useful, curious, and difficult; discoveries that bring these three qualities together are, truly, of the first order; there are others which do not have all three advantages; but it is necessary that they have at least one of them. For example, the discovery of the compass was a very useful thing, but one which could have been made by chance, and which consequently does not suppose any difficulty overcome. The discovery of the electric shock ( see Electric shock) is a very curious discovery, but one which was also made by chance, and which consequently did not require great effort, and which from another perspective has also not yet proved very useful. The discovery of the squaring of the circle would suppose overcoming great difficulty; but this discovery would not be rigorously useful in practice because approximations suffice, and because there are methods of approximation that are sufficiently exact. See Squaring.

Let us observe, however, that in a discovery for which the principal merit is the difficulty overcome, there must be at least some utility, or at least singularity: the squaring of the circle of which we have just spoken would be of the latter type; it would be a difficult and unique discovery because it has been sought for a long time.

Discoveries , following what we have just said, are thus the fruit of chance or of genius: they are often the fruit of chance in practical things, as in the Arts and Trades; it is doubtless for this reason that the inventors of the most useful things in the Arts are unknown to us, because most often these things present themselves to people who do not seek them, and thus the merit of having found them not having occurred to them, the invention has remained without our knowing the inventor. To this reason another could be added; that the majority of things that have been found in the Arts, have only been found little by little; that a discovery has been the result of the successive efforts of several artists, each of whom has added something to that which had been found before him, in such a way that one does not know how to attribute it properly. Finally, add to these two reasons that normally Artists do not write at all, and that the majority of men of letters who write, occupied by their own concerns, do not take a very lively interest in recording the discoveries of others.

The discoveries made by genius have taken place principally in the reasoning Sciences: by this I do not mean to say that genius does not discover also in the Arts, I mean only that chance, in the matter of the Sciences, normally discovers less than genius does. However, the Sciences have also had discoveries of pure chance: for example, the attraction of iron by the magnet could not have been figured out, either by itself, or by any analogy; it must have been that by chance a magnetic stone was brought close to a piece of iron, in order to see that it attracted it. In general it can be said in the matter of Physics, that we owe to chance the knowledge of many facts. There are also discoveries in the sciences which are at the same time the fruit of genius and chance; it is while seeking one thing, and employing to that end different means suggested by genius, that one finds something else that one was not looking for. Thus many chemists in seeking to make certain discoveries , and imagining to that end different compound and subtle processes, have found singular truths that they did not anticipate at all. There is no science where this does not happen. Many geometers, for example, in seeking the squaring of the circle, which they have not found, have found by chance beautiful theorems, and of great utility. Discoveries such as these are a form of luck; but luck which comes only to those who deserve it; and if it has been said that a fine and fitting retort is the good fortune of a man of wit, one can call a discovery of this sort the good fortune of a man of genius : we shall recall on this occasion what King William said of the Marshall of Luxembourg who was so often the victor over him: He is too lucky not to be .

The discoveries which are the fruit of genius (and it is these above all that should be our concern), are made in three ways: either by finding one or several entirely new ideas, or by joining a new idea to a known idea, or by bringing together two known ideas. The discovery of Arithmetic seems to have been of the first type; because the idea of representing all the numbers by nine digits, and above all to add to them the zero which determines their value and creates the means of doing in a condensed way the operations of calculation; this idea, I say, would seem to have been absolutely new and original, and could not have been occasioned by any other; it was a stroke of genius that produced as it were suddenly and at once an entire science. The discovery of Algebra seems to have been of the second type: in fact, it was an absolutely new idea to represent all possible quantities by general characters, and to imagine the means of calculating these quantities, or rather to represent them through the simplest expression that would comport with their state of generalization. See Universal arithmetic and the Preliminary Discourse in volume 1. But to complete absolutely this idea, it was necessary to join it to the calculation of numbers already known, or Arithmetic; because this calculation is almost always necessary in algebraic operations to reduce the quantities to their simplest expression. Finally, the discovery of the application of Algebra to Geometry is of the third type; because this application has as its principal foundation the method of representing curves by equations with two variables. Now, what kind of reasoning was it necessary to make to find this way of representing curves? Here it is: a curve, it has been said, following the idea that has always been had of it, is the site of an infinite number of points that satisfy the same problem. See Curve. Now, a problem which has an infinite number of solutions is an indeterminate problem; and we know that an indeterminate problem in Algebra is represented by an equation with two variables. See Equation. Therefore one can use an equation with two variables to represent a curve. Voilà a line of reasoning of which the two premises, as we see, were known; it seems that the consequence was easy to draw: however, Descartes was the first to have drawn this consequence: when it comes to discoveries of the last type, however easy they appear to be, they are often the ones that are made last. The discovery of the differential calculus is more or less of the same sort as that of the application of Algebra to Geometry. See Differential, Application, and Geometry.

For the rest, the discoveries which consist in bringing together two ideas of which neither one is new, should not be regarded as discoveries except when something important results from them, or when this union was difficult to achieve. It could be noted also that often a discovery consists in bringing together two or several ideas, of which each one by itself was or seemed to be sterile, even though they were very costly to their inventors. These people [the inventors] could say in that case of the author of the discovery , sic vos non nobis [you do not labor for yourselves]; but they would not always have the right to add, tulit alter honores [to another the praise]: because true glory belongs to him who achieves, although the suffering often is by those who begin. [1] The Sciences are a great edifice on which many people work in concert; some with the sweat of their bodies pull the stone from the quarry; others haul it with great effort to the foot of the building; others raise it with the strength of their arms and machines; but the architect who gets things started and puts it in place gets all the credit for the construction.

As far as erudition is concerned, discoveries properly speaking are rare because the facts which are the object of erudition are neither figured out nor invented, and consequently the facts must already have been written by some author. However, one can give the name discovery , for example, to the solid and ingenious explanation of some ancient monument that until then had taxed scholars fruitlessly; to the proof and the discussion of a singular or important fact until then unknown or disputed; and so forth. See Decipher.

It seems that the only two sciences which are not susceptible to discoveries of any sort are Theology and Metaphysics: the first because the subjects of revelation have been established since the birth of Christianity, and all that Theologians have added since then can be reduced to pure systems that are more or less satisfying, but about which one is free to be divided, such as systems to explain the action of grace, and so many other subjects; the perpetual subject of disputes and sometimes of unrest. With regard to Metaphysics, if we set aside a small number of truths known and demonstrated for a long time, all the rest is also purely contentious. Moreover, men having always had the same core beliefs and basic ideas, the combinations of them must soon be exhausted. In Metaphysics the facts are as it were within each person; a little bit of attention is all it takes to see them: in Physics, by contrast, since they are outside of us, it normally requires more sagacity to discover them; and sometimes even by combining bodies in a new way one can create as it were entirely new facts: such are, for example, several experiments with electricity, several manipulations in Chemistry, etc. I do not claim to conclude from this that there is little merit in writing clearly about Metaphysics; Locke and the author of the traité des systèmes would suffice to prove the contrary. [2] And one could apply to them the passage from Horace, difficile est propriè communia dicere : it is difficult to make one’s own [or render properly] that which seems to belong to everyone. [3]

1. The Latin phrases come from Virgil’s Aeneid :

This translation by John Richardson, Emeritus Professor of Classics, University of Edinburgh is available with an interesting gloss at http://www.raglanjunior.org/index.php/about/info/sic_vos_non_vobis_-_the_school_motto/.

2. The references are to John Locke (presumably his Essay Concerning Human Understanding , 1690) and Etienne Bonnot de Condillac, Traité des Systèmes (1749).

3. The meaning of this Latin phrase, drawn from Horace’s Ars poetica was apparently hotly debated in both France and England in the eighteenth century. See the very long footnote in James Boswell’s Life of Johnson, vol. 3. Does it refer to rendering properly, politely, or own’s own? In a recent translation, A.S. Kline gives a very different translation: “It’s hard to make the universal specific.” See Horace, Ars Poetica, Or: Epistle To The Pisos, line 128.