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of the other. Generalization gives us a command over our ideas more complete than we can ever derive from the mere efforts of memory: It holds in its hand the clue by which this latter faculty must be guided through the labyrinth of things; and there is room to doubt, whether die power thus given to the mind is not the main source of the delight arising from abstract and philosophic speculation. Were the memory in.itself to become so perfect, as to be independent of connecting principles, generalization would not be necessary, and perhaps would rarely be attempted.
Two minds, both disposed to the acquisition of knowledge, could hardly be constituted with less conformity to one another, than those of Le Sage and his son. When the young man was labouring to classify his ideas, and to reduce them under general heads, the father was perpetually starting objections to his rules, and bringing forward the instances most difficult to be reduced to any general principle of arrangement. This seemed to proceed, not from any desire to embarrass or distress his son, but from a dislike which he had conceived (singular, doubtless, in a mathematician) to general methods, and to all systems whatsoever. The education, therefore, which he gave his son, was truly antiphilosophic, and certainly had no tendency to produce that love of order, system and method which characterized him through his whole life. But the mind may be constituted with some powers so weak, that discipline cannot improve them; and with others so strong, that discipline, when most perverse, cannot destroy them. Nothing could give to young le Sage a memory neariv equal to that of ordinary men; and nothing could take from him a delight and 'Skill in generalization, which were vastly superior.
We must not imagine from this, that the whole plan of the old man in the education of his son, was as perverse as in the case here mentioned: the information he communicated, even with so little of method and arrangement to connect the parts together, was of great value to his son, who, through his whole life, used to speak with much gratitude of his father's attention to his instruction, and of the pleasure and advantage he derived from his conversation.
The inquisitive turn of Le Sage soon displayed itself in questions, to which he did not always receive the kindest or most satisfactory answers, especially from his mother, who appears to have had none of the gentleness and patience necessary for the instruction of children. This led him to think of having recourse to trial and experience, and to interrogate nature rather than any other instructor. One of his first attempts of this sort
has has been recorded in his notes, and, from the singularity of it, deserves to be remembered.
At the time we are now speaking of, the Sabbath was observed at Geneva, with a gloom and austerity of which we in Scotland can probably form a more correct notion than the inhabitants of any other country in Christendom. Le Sage felt some curiosity to know whether the Author of Nature still continued to impose on himself the same law that originally marked the institution of the day of rest. It would have puzzled the first philosopher in Europe to think of any method by which this question could be brought to the decision of experiment; but the ingenuity of our young inquirer soon suggested an expedient. He measured, with great care, the increase of a plant, day after day, in order to discover whether it would cease growing on the Sabbath. The result could not fail to solve the difficulty, and to convince the young man, that though the work of creation might terminate, the work of Providence is never interrupted.
The pensive and contemplative turn of Le Sage was increased by the circumstance of his health being delicate, and his temperament too weak, to allow him to join in the fatiguing exercises which amused and occupied his companions. Great modesty, sensibility, and reserve, added, as far as his mother was concerned, to the want of comfortable society at home, condemned him almost to continual solitude, and rendered the acquisition of knowledge his only enjoyment. Thus, from circumstances apparently unfortunate, much of his intellectual excellence may be supposed to have arisen.
It is material to observe every circumstance that gave a determination to a mind that has in any thing attained celebrity; but it is very rarely that this can be done so well as in the instance we have now before us. . The father of our young philosopher had but few books; and almost the only entire work on physics, which he possessed, was that of Bernard Palissy. The writings of a man who was self-instructed,—who had paid no regard to authority, when not supported by experience,—who had made valuable discoveries, and reached some very sublime and just notions concerning the structure" and the revolutions of the globe, could not fail to make a strong impression on a young mind already inspired by the love of knowledge. However, though Le Sage became a great cosmologist, it does not appear that geology, of which Palissy was in some measure the founder, ever attracted much of his attention.
When he was not much more than thirteen, his father put into his hands the Antiquite Expliquee of Montfaucon, in order to excite in him a curiosity about researches into antiquity. It was the
fate fate of this young man, however, to derive, from the means used for his instruction, advantages very different from those that were intended, and often of far greater value. The weakness of Montfaucon's conjectures, concerning the use of many of the instruments he has described, did not escape the observation of Le Sage; and he began even then to try to establish some general and certain rules for discovering the end of a workman from the inspection of his work. Such extent of view, at so early a period of life, has rarely occurred, and must be considered as a decided mark of genius and originality. Some years after this period, connecting the pursuit just mentioned with one closely allied to it, namely, the rules that must guide us when, in the works of nature, we would trace the marks of the wise design of the Creator, he formed the idea of a treatise, entitled Teleology, and of which an account will afterwards be given.
The perusal of Lucretius is one of the events that did most determine the objects of Le Sage's researches, and indeed the whole colour and complexion of his future speculations. The precise time when this happened does not appear, though it was certainly very early, and before he had attained the age of twenty. It was then that he conceived the notion of a mechanical explanation of gravity, and of the reduction of all the motions observed in nature, to the principle of impulsion. This was suggested by the atoms of Lucretius; and the invention of a system by which such an explanation could be given, even with tolerable plausibility, must be considered as a work of great merit by all who know the difficulty with which it is attended, and its importance to philosophy. The system by which Le Sage proposed to effect this great object will be by and by considered.
Le Sage had the good fortune to study mathematics under Cramer, and philosophy under Calendrini, two eminent professors, who then adorned the University of Geneva. When it became necessary for him to make choice of a profession, he gave the preference to that of medicine. The pursuit of this study led him first to Basle, and afterwards to Paris. At the former place, he became acquainted with Daniel Bernoulli, from whom, however, his merit seems to have been completely con.T cealed, by his awkwardness and diffidence. He says of himself, when he entered at this University—' 111 dressed, timid, and expressing myself with difficulty, I was quite neglected in the first months of my stay at Basle; insomuch, that they did not even think it worth while to speak French before me.' He undertook the study of the German, but the weakness of his, memory did not permit him to succeed.
The same awkwardness could not fail to have effects at Paris yet more unfavourable, as the narrowness of his income must likewise have had; yet he persevered not only in pursuing medicine, but in applying to his favourite objects in philosophy. At last he returned to Geneva; but not having the freedom of a burgess of the city, he was refused the privilege of practising as a physician; and saw himself, in the end, forced to relinquish every other view of fixing himself in life, but that of following the business of his father, and giving lessons in mathematics and natural philosophy.
For this he appears to have been well qualified. He says of himself, that the structure of his mind was such, as had fitted him for understanding the mathematics well, but not extensively. 'Propre a bien savoir les mathematiques, mais non a en savoir beaucoup.' The first part of this assertion, we imagine, may be understood more literally than the last; though it is probably true that he was not quite master of all the modern improvements of the calculus. Some of his remarks on the state of the mathematical sciences in France, are worth attending to. In a letter to the Duke de Rochefoucault, whom he had had the honour to instruct in the mathematics, dated in 1778, he has this observation.
'In their elementary treatifes of mathematics and phyfics, the French writers take fo little trouble about the foundations of thofe calculations which they accumulate without end, that it feems as if they wanted to make all their pupils mere cferks in a banking houfc, or affiftants in an obfervatory. They treat geometry the leafl geometrically poSible, under the pretence that algebraic demonftrations are the (horteft: as if the only object. were to get to the end, and as if the road leading to it were of no importance. They are in hafte to give a few notions, rather grammatical than intellectual, of the fublimer parts, before they have fufficiently developed the elements. They feem deiirous of reducing aftronomy, the fcience of motion, and chemiftry, to be nothing but the humble attendants on navigation, gunnery, and the arts; as if all the world was deftined for infpectors of the marine, of artillery, or manur failures; and as if the cultivation of reafon was nothing in comparifon with the art of getting wealth. This was not the proceeding of Defcartes or Newton.' p. 272.
This chara£ter of the French elementary writers, though, incertain refpe&s, juft, evidently has fomething of the air of latire, and muft not be received %s perfectly correct. Of too little regard to the methods of pure geometry, and too much hafte to reach the more profound parts of the calculus* they may certainly be accufed. But a general preference of the methods of algebra and analyfis, cannot be regarded as an error, if the foundations of thofe insthods are carefully and accurately
explained-, explained. Analytical reafonings are fo much preferable to fynthetical, and the art of investigation is fo much more eafily learned in the fchool of algebra than in any other, that, in a fyftem of mathematical inftruftion, this latter fcience is undoubtedly of the firft confideration. It is true, on the other hand, that the methods of analyfis are not confined to algebra. Geometry has its analytical reafonings, not fo extenfive, nor fo general, as thofe of algebra, but pofleffing a degree of fimplicity and beauty that is not excelled, or rather, we think, not equalled in any other branch of fcience. It is a ftrongcr proof of the neglect of geometry, among the French mathematicians, than any thing that Le Sage has alleged, that in the Encyclopedic, intended to exhibit a complete picture of the knowledge of the eighteenth century,. the article geometrical analyfts is not to be found.
The love of accurate and precife knowledge, which Le Sage poffefTed eminently, probably qualified him well for a teacher of the mathematical fciences. lie had feveral illustrious pupils, and none, certainly, who does him more credit than the prelent proftflbrof mathematics in the univerfity of Geneva. M. S. L'Huilier was his relation, and was inftrufted by him in the fcience which he now profeffes with fo much credit both to his mafter and himfelf. He is one of the few mathematicians equally verfed in the fimple and elegant methods of the ancient geometry, and in the profound refearches of the modern analyfis.
Le Sage, through his whole life, had to Struggle with a feeble constitution, as well as the mental defects which have been already mentioned. He was particularly afflicted with fleeplcfsnefs, which, at times, ufed greatly to affect his intellectual powers, and reduce them to a ftate of extreme debility. NotTvithftanding this, by employing every moment when his mind was clear and active, preferving fuch order and regularity as fupplied the want of memory, committing every thing to writing., and having his papers in a ftate of the moft complete arrangement, he was able to accomplifh a great deal, and to devote much time to philofophical purfuits.
IJis ftudies, however, were rendered lefs ufeful than they might have been with the originality of his turn of thinking, the precifion of his knowledge and the extent of his views, by the number of objects to which he directed his attention, and by his frequent changes from one purfuit to another. Though he came back eafily to the fame object, yet this did not entirely make up for the want of the continued application neceffary in all great undertakings.
Accordingly, though few men wrote fo much, and fo accurately, he publifhed nothing in his lifetime but mere opufcula, and