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 can be found. Another mode of trying for solutions is a combination of the preceding with the cuttaca (pulveriser)." These calculations were used in astronomy.

Doubtless this "cyclic method" constitutes the greatest invention in the theory of numbers before the time of Lagrange. The perversity of fate has willed it, that the equation $$\scriptstyle{y^2=ax^2+1}$$ should now be called Pell's problem, while in recognition of Brahmin scholarship it ought to be called the "Hindoo problem." It is a problem that has exercised the highest faculties of some of our greatest modern analysts. By them the work of the Hindoos was done over again; for, unfortunately, the Arabs transmitted to Europe only a small part of Indian algebra and the original Hindoo manuscripts, which we now possess, were unknown in the Occident.

Hindoo geometry is far inferior to the Greek. In it are found no definitions, no postulates, no axioms, no logical chain of reasoning or rigid form of demonstration, as with Euclid. Each theorem stands by itself as an independent truth. Like the early Egyptian, it is empirical. Thus, in the proof of the theorem of the right triangle, Bhaskara draws the right triangle four times in the square of the hypotenuse, so that in the middle there remains a square whose side equals the difference between the two sides of the right triangle. Arranging this square and the four triangles in a different way, they are seen, together, to make up the sum of the square of the two sides. "Behold!" says Bhaskara, without adding another word of explanation. Bretschneider conjectures that the Pythagorean proof was substantially the same as this. In another place, Bhaskara gives a second demonstration of this theorem by drawing from the vertex of