The Calcutta Review/Series 1/Number 4/Article 5
Art. V.—1. Lilawati, or a Treatise on Arithmetic and Geometry, by Bhascara Acharja. Translated from the original Sanscrit, by John Taylor, M.D., of the Hon’ble East India Company’s Bombay Medical Establishment. Bombay, 1816.
2. Algebra, with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bhascara. Translated by Henry Thomas Colebrooke, Esq. F.R.S., &c. London, 1817.
3. History of Algebra in all Nations, by Charles Hutton, LL D., (Mathematical and Philosophical Tracts, vol. ii.) London, 1812.
4. Lectures on the Principles of Demonstrative Mathematics, by the Rev. Philip Kelland, A.M., F.R.S.S.L. and E., Professor of Mathematics in the University of Edinburgh. Late Fellow and Tutor of Queen’s College, Cambridge. Edinburgh, 1843.
Herodotus informs us that Geometry took its origin in Egypt, and supposes that necessity was the mother of the invention;—that the purpose of it was to delineate the boundaries of the fields on their emerging from the waters of the Nile. We see no reason to reject the venerable historian’s statement of the fact, nor to accept his theory in regard to it. As to the fact, it seems to be incontrovertible that Geometry as a Science was unknown in Greece before the time of Thales the Milesian, and there seems no reason to question the uniform tradition that he imported the knowledge of it from Egypt. But as to the theory of Herodotus regarding the necessity that gave rise to the invention,[1] we can suppose no foundation on which it can rest, except the etymology of the Greek name of the Science ((Greek characters), or measure of the earth) and this is useless as a foundation for the hypothesis, unless it can be shown that this name is an exact rendering of the Egyptian name of the Science. Moreover, we should suppose that (Greek characters) is not the term that would have been employed to signify the mensuration of land, since we know of no instance in which the term (Greek characters) or (Greek characters) is employed in such a sense. If we might be allowed to conjecture, we would venture to suggest that this name was given to the Science only when it reached such a stage of advancement that mathematicians began to apply it to the determination of the size of the earth. In fact the whole amount of Geometry that would be required for the purpose indicated by Herodotus, (the rather that he tells us the Egyptian estates were all squares) would be the problem to draw a straight line between two points, and this problem we presume it was not left to the Egyptians to be the first to solve.
This consideration suggests to us a fact that seems to have been strangely overlooked by writers on the history of the Mathematical Sciences;—viz. that, speaking strictly, the mathematical sciences could have no beginning apart from the original creation of the human race, for their first elements are bound up in the very constitution of the mind of man. We believe there has never been a man capable of exercising his faculties, who did not know that things which are equal to the same thing are equal to one another, yet no one who knows this can properly be said to be wholly ignorant of mathematical science. From this initial point a line continuous and unbroken stretches upwards and onwards to all that modern mathematicians know of the properties and relation of space and figure, and is destined to be prolonged to all that their successors shall ever know. And what is true of Geometry is equally true in regard to Algebra—the other great branch of mathematical science. An utter ignorance of number and quantity seems to be scarce compatible with rationality. We scarcely know how thought can be exercised apart from a knowledge that there is a difference between one and two. Yet this is the foundation of Algebra, the first step on the ladder that stretches continuously upward to that lofty eminence from which Lagrange looked down. If in this statement we be in error at all, it is, we apprehend, in speaking of the ascent from the lowest degree of knowledge that is compatible with rationality to the highest attainment in this department that is permitted to man in his present state of being, as accomplished by a series of successive steps: it is rather by a continuous plane of the gentlest and scarcely perceptible elevation, so that of those engaged in the ascent it is often difficult to determine who has attained the greatest height. There is no break in the whole ascent; and this, we may state in passing, is one of the grand advantages of mathematical study as a mental exercise. There is no man who is incapable of the study, neither is there any man who does not find in it full employment for all his faculties. No man is incapable of taking his place on the bottom of the plane, and beginning the ascent; no man, on the other hand, has ever reached, or will ever reach, the summit.
This too it is that renders the history of mathematical discovery often a work of great difficulty. Of this the most notable example is furnished by the long-agitated, and still unPage:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/543 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/544 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/545 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/546 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/547 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/548 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/549 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/550 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/551 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/552 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/553 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/554 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/555 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/556 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/557 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/558 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/559 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/560 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/561 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/562 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/563 Page:Calcutta Review Vol. II (Oct. - Dec. 1844).pdf/564 Among the Hindus, six hundred, and even twelve hundred years ago, there were men who were as profoundly versed in this branch of mathematical science, as were our fathers a hundred years ago. Their representatives in these days are the miserable drivellers, whose whole knowledge amounts to a few scraps of “tank arithmetic,” and that generally known only by rote. Shall it be then that the successors of Peacock and Airy, and Whewell and De Morgan shall ever become such pigmies in intellect? The history of Hindu science very clearly points out to us that there is nothing in the nature of man to prevent such a degeneracy. Yet we are not without hope, though it comes from another quarter. Since European science is not the property of a man but of the community, its continuance is not dependent on the accident of individual talents, (though its extension may be,) but is secured on a basis as broad and firm as any thing human can rest upon. It was with the Hindu science, as with the monstrous empires that rose by the prowess of a single hero and passed away along with him. But European science is now so deeply rooted and so widely spread, so amalgamated with all the institutions of government and all the arts of life, that nothing short of an entire revulsion of all that is human can ever eradicate it. This advantage, be it remembered, is one of the thousand unthought of blessings which we derive from that blessed book, which has taught us far more clearly than men were ever taught before, the duties and privileges of mankind. Little as some of our philosophers may dream of it, the Bible is the palladium of our science, as well as of those blessings and privileges which are more directly traceable to it. Its absence, and the prevalence of all those barriers to improvement which it alone can wholly banish, have reduced the science of India to its present despicable state; its suppression produced the dark ages in Europe, and its restoration to its due place gave the impulse to that vast movement which has for three centuries been going on; and its dissemination, with all attendant blessings, is the means appointed by the Lord and Ruler of all for introducing light and liberty and joy into all the dwellings of men.