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To affift and encourage a critical examination of thefe
BY JAMES WILLIAMSON, M. A.
FELLOW OF HERTFORD COLLEGE.
Sed nil dulcius eft, bene quam munita tenere
PRINTED AT THE CLARENDON PRESS.
M DCC LXXXI.
RICHARD BURKE, Esq.
T would be a very entertaining speculation, and well calculated to fhew the importance of geometry, to enquire into the probable ftate of human affairs at prefent, upon a fuppofition that the mathematical fciences had been generally known and cultivated in the early ages of the world.
If they had only underfood how to make a map or an almanack, a great deal of rational curiofity would have been gratified, which we now endeavour in vain to fatisfy. For mankind have slept on, from age to age, without taking notice of time or occurences; and as to what concerns geography they have been equally remifs. The human race have migrated from one country to another, until they have covered the face of the whole Earth, without gaining the leaft information by their travels; having rather ftrayed like cattle, than changed their habitation like rational creatures.
However the happy effects of a proper cultivation of this science, are not confined to maps and almanaffs: for ck it is by the judicious application of mathematical knowledge, that human nature, notwithstanding its frailty, is rendered fuperiour to every obftacle, for our efforts keep pace with all our rational imaginations: and thus
it rifes greatly above all its imperfections, acquiring a dignity which must astonish every one, when he compares what has been done, with the weakness and imperfection of any fingle individual. And what this might have produced through a length of ages, operating in every quarter of the globe is not fo eafily to be conceived.
It has indeed been alledged, that the improvements afcribed to the cultivation of this fcience, have been often the effect of chance, and not produced by any rational scheme of improvement, conducted upon scientific principles. But the contrary appears from undoubted matter of fact; because we every where find that discoveries are made among the most enlightened nations, and never among barbarians. Events, no doubt, will happen, and natural appearances will keep their regular time; but the wild beafts of the field are as likely to make a proper use of them, as illiterate favages. And the little attention paid by ignorant men to those very circumstances which inform and enlarge the understanding, fhew us better than any thing else, what human nature can rise and fall to.
Both you and I are fufficiently fenfible of the great utility of mathematics in all the affairs of life; and that those whom it concerns are, to a certain degree at least, fufficiently attentive to it. And we only used to regret that the world is ignorant, how fuccessfully this fcience might be employed for making us rational creatures.
It has often been the subject of our conversation and furprize to run over the various methods contrived for making mathematicians, without impofing upon them the neceffity of being rational creatures. And fuch difcourfes have generally ended in your urging me to the execution of this plan; the first part of which I here beg
leave to present to you. I have had fufficient marks of your friendship to be fenfible that you will be much more follicitous about its fuccefs than I am myself: and from your partiality to me, I am also persuaded you will think that I have not done it justice in the execution.
It is true I could have improved the style very much; but it seems to anfwer my purpose better in its present form: for I write not to make people read, but to make them think. I have also affected a familiarity of phrase, to engage the attention of the reader by expreffing geometrical ideas in common language.
But whatever your opinion of the work may be, I beg of you to accept of this addrefs, as a teftimony of the high efteem which I have for your character and abilities. It is with the greatest pleasure that I recollect the share which I have had in your education, which was carried on, not in the perfon of mafter and scholar; but rather in the character of two friends who had taken a somewhat different view of the same subject.