William Gibson was born in the year 1720, at the village of Bolton, in Westmoreland, England. On the death of his father, he put himself to a farmer to learn his business. When he was about eighteen or nineteen, he rented a small farm of his own, at a place called Hollins, where he applied himself assiduously to study.

A short time previous to this, he had admired the operation of figures, but labored under every disadvantage, for want of education. As he had not yet been taught to read, he got a few lessons in English, and was soon enabled to comprehend a plain author. He then purchased a treatise on arithmetic; and though he could not write, he soon became so expert a calculator, from mental operations only, that he could tell, without setting down a figure, the product of any two numbers multiplied together, although the multiplier and the multiplicand each of them consisted of nine figures. It was equally astonishing that he could answer, in the same manner, questions in division, in decimal fractions, or in the extraction of the square or cube roots, where such a multiplicity[Pg 73] of figures is often required in the operation. Yet at this time he did not know that any merit was due to himself, conceiving that the capacity of other people was like his own.

Finding himself still laboring under farther difficulties for want of a knowledge of writing, he taught himself to write a tolerable hand. As he had not heard of mathematics, he had no idea of anything, in regard to numbers, beyond what he had learned. He thought himself a master of figures, and challenged all his companions and the members of a society he attended, to a trial. Something, however, was proposed to him concerning Euclid. As he did not understand the meaning of the word, he was silent; but afterwards found it meant a book, containing the elements of geometry; this he purchased, and applied himself very diligently to the study of it, and against the next meeting he was prepared with an answer in this new science.

He now found himself launching out into a field, of which before he had no conception. He continued his geometrical studies; and as the demonstration of the different propositions in Euclid depend entirely upon a recollection of some of those preceding, his memory was of the utmost service to him. Besides, it was a study exactly adapted to his mind; and while he was attending to the business of his farm, and humming over some tune or other, his attention was often engaged with some of his geometrical propositions. A few figures with a piece of chalk, upon the knee of his breeches, or any other convenient spot, were all[Pg 74] he needed to clear up the most difficult parts of the science.

He now began to be struck with the works of nature, and paid particular attention to the theory of the earth, the moon, ............