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pleased bim, and to every. seed bis own body. That is, in every grain of corn, is contained a minute seminal principle, which is itself the entire blade, and ear; and in due season expands itself when all the rest of the grain is corrupted, and dead, that is, the lobe, which being single in corn, is almost peculiar to it. For most seeds have two or more lobes, which sometimes rise in dissimilar leaves; but in corn, the single lobe dies, and the seminal principle containing the plume and radical, evolves and unfolds itself, into the visible form of both, so our present mortal and corruptible body may be but the extraordinary expanfion, of some minute; hidden, and at present insensible principle, which at the resurrection shall discover. itself in its proper form.
Thus you see a confiderable use may be made of these kinds of studies even in matters of Rea ligion, to which in the opinion of the ignorant they seem to have no relation,
And as natural philosophy assists you in dem fending Religion, so will mathematics also. From this science you may answer many of the objections to the mysteries of faith. For if it be required to assent to religious propositions, though we have not always clear and adequate ideas of things fignified by the terms, this is no more unreasonable, than the assent required to all the propositions relating to infinity, with which the mathematical science does abound; and which no man conversant in those kind of studies ever prefumed to deny. For infinity is equally incomprehensible to the mind of man See part 2. and Grew's anatome of plants. ..
whether it be applied to quantity or to spiritual substance. And therefore the use of this and other incomprehensible terms, which are the foundation of many glorious and useful truths; ought not to be objected to, except by those, who, out of fondness to ignorance, error and vice, are endeavouring to render the road to knowledge impaffable. · Does not the science of geometry begin with a trinity of mysteries ? For is there any such thing as a point without dimensions, a line without breadth, or a surface without profundity? Does not this science demonstrate, that the minutest portion of matter has every dimension of the greatest, and is therefore still capable of divifion? And does not this contradict the first definition ? A point is that which in magnitude is indivisible even in thought. Yet this is a noble science, and there is no way of coming at truth in it, except by means of these fuppofi. tions, which are seemingly contrary to truth, but absolutely necessary to the weak compres hension of man, who cannot even conceive things by halves; but must be satisfied at the first setting out, with the unnatural presumed conception of the third part of the dimensions of quantity at once. .
From this science also you may reply very justly to all those, who refuse their assent to truths upon account of some difficulties, which seem to follow from them; which difficulties do not arise from the uncertainty of reason, buť very often from a subtilty of mind disposed to embarrass things, rather than to clear them up: But supposing that they may arise from the things themselves; are there not many examples of the demonstrative kind, from which there follow such absurdities, that, if the same spirit of dispute had always prevailed in the world, which is now so remarkable; they would have stopped the progress of reasoning even in mathematics i
A remarkable instance of this we have in the science of geometry. The nature of this science, you know, is to have every thing fairly and incontestably demonstrated ; and what is so, cannot possibly have any demonstrations to the contrary; nor any absurdities demonstrably con, nected with it ; and every demonstration depends upon the undoubted truth of every demonstration previous to it. Yet is there one proposi. tion, which, although fairly demonstrated, has seemingly as fair demonstration of several abfurd and contradictory things annext to it, which our writers chuse to call paradoxes . Of the third book of Euclid it is the 16th proposition : · Aright line perpendicular to the diameter of a Circle, through the extremity, falls entirely without the Circle, and touches it in the extreme point of the diameter ; nor can any right line be drawn between it and the Circle to the point of contact, that shall not cut the Circle. :
® In the edition of Euclid by Whiston upon Tacquet, you may read • Demonftratur et folvitur fallacia paradoxorum, quæ ex angu
lo contactus deduci folent quæ omnem captum humanæ mentis excedunt.
Hæc et plura ex hac propofitione deduci folent, quæ profecto, f ita, ut proponuntur fefe habeant, merito incomprehenfibilia videri poffunt. .
This proposition is as fairly demonstrated, as any propofition belonging to the sciences, and yet several impossible things seem to be demonstrable consequences of it, and which the Geometricians endeavour to solve by a distinction; an angle, say they, is not quantitas but modus quantitatis: and even this solution (if it be one) was not given till it passed through a great number of hands, and all Geometricians, notwithstanding this, reited satisfied of the truth of the proposition fairly demonstrated, and were not at all staggered with those many absurdities, which had too much appearance of fair reasoning, to admit of any solution for many hundred years.
In this case you might ask a sceptick what was to be done? Should mankind quit the pure suit of geometrical knowledge, which is exceedingly beneficial to the world, inasmuch as without it, land could never be measured; neis ther a house could be built, nor a ship made, nor a town fortified, nor various utensils effected for the improvement of manufactures > What! must all these useful, nay necessary arts; without which human life is barbarous and ignorant, be thrown aside, as being without foun. dation of truth; since one proposition belonging to the principles, upon which they all de pend, is attended with insuperable difficulties? Perhaps the sceptick will say, they are all to be thrown afide ; for what is there too absurd for the mind of man, when prejudice and error rule in it, instead of reason and impartiality. But however absurdly the sceptick may speak, the bulk of mankind are not so sottilh, as not to
purfue reasonable things that are extremely úseful, tho' greit difficulties sometimes attend them. Hence it is, that the study of Geometry and the practice of the arts depending upon it, is not in the least retarded by thofe difficulties attending one proposition, which lie in the road of that science. Land is surveyed upon principles of Geometry; houses and ships and mills are built, towns are fortified, and numberless machines for manufactures contrived, all apon the principles of that science. And in this, mankind act wisely, and so they thould in religion : The plain realoning, upon which religious truths depend, should convince; and the difficul ties sometimes attending them should not stagger their faith; but only make them modest and humble. They should be thankful for the light, which God has given them, and not perversely extinguish it, thereby to bring all things into chaos, and darkness, and confusion.
To this geometrical difficulty may be added a similar case in optics. The ingenuous Doctor Barrow in the conclusion of his optic Lectures says, 6 before I quit this subject for good
and all, the fair dealing that I owe both to “ you and to truth, obligeth me to acquaint « you, with a certain untoward difficulty, which « seems directly opposite to the doctrine I have « been hitherto inculcating, at least admits of « no solution from it. Then he proposes the difficulty, and further remarks. “Nor is our « tenet alone struck at by this experiment, but " likewise all others, that ever came to my “ knowledge are, every whit as much, endan
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