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To assist and encourage a critical exanıination of these

Elements, as the most effectual means of establishing
a juster taste upon mathematical subjects, than that
which at present prevails.

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T would be a very entertaining speculation, and well

calculated to thew the importance of geometry, to enquire into the probable state of human affairs at prefent, upon a supposition that the mathematical sciences had been generally known and cultivated in the early ages of the world.

If they had only understood how to make a map or an almanack, a great deal of rational curiosity would have been gratified, which we now endeavour in vain to fatisfy. For mankind have Nept on, from age to age, without taking notice of time or occurences ; and as to what concerns geography they have been equally remiss. The human race have migrated from one country to another, until they have covered the face of the whole Earth, without gaining the least information by their travels; having rather strayed like cattle, than changed their habitation like rational creatures.

However the happy effects of a proper cultivation of this fcience, 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 superiour to every obftaele, for

our efforts keep pace with all our rational imaginations : and thus


(ii) it rises 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 single individual. And what this might have produced through a length of ages, operating in every quarter of the globe is not so easily to be conceived.

It has indeed been alledged, that the improvements ascribed to the cultivation of this science, 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 beasts of the field are as likely to make a proper use of them, as illiterate savages. And the little attention paid by ignorant men to those very circumstances which inform and enlarge the understanding, shew us better than any thing else, what human nature can rise and fall to.

Both you and I are fufficiently sensible 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, sufficiently attentive to it. And we only used to regret that the world is ignorant, how successfully this science might be employed for making us rational creatures.

It has often been the subject of our conversation and surprize to run over the various methods contrived for making mathematicians, without imposing upon them the necessity of being rational creatures. And such difcourses 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 sufficient marks of your friendship to be sensible that you will be much more sollicitous about its success 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 answer 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 expressing geometrical ideas in common language.

But whatever your opinion of the work may be, I beg of you to accept of this address, as a testimony of the high esteem 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 person of master and scholar; but rather in the character of two friends who had taken a somewhat different view of the same subject.

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