Entering upon our subject, and beginning at the root of the tree of science, we make the pleasing discovery that to the Arab-Moors of Spain belongs the honor of having been the first to generally introduce in Europe, for scientific and industrial and commercial purposes, the science of arithmetic. Had they achieved nothing else, the introduction of this most needful of all the branches of mathematics alone, would have entitled them to a distinguished place among the world's benefactors. That introduction was the starting point of a new progress. Its use and development made possible the higher mathematics and analytical mechanics and astronomy, and every other science discovered since, and hailed with delight. Little do we think to-day when we pride ourselves on the startling achievements of our astronomers and meteorologists and other scientists, when we speak of the miracles they work in space and time, of the ascensions they make to the remotest of the nebulæ, and of their holding communion there with stars and worlds and solar systems whose light has not yet reached the earth, little do we think when we speak of electricity obeying our every wish, and of steam yoked in our service, and of the countless other wonders of modern science, little do we think that for all these blessings we are lastingly indebted to the Arab-Moors, and to their assistants, the Jews, for their faithful labors in mathematics. Little do we think that we are pronouncing Arabic words when we speak of the "zero" or the "cipher", the "naught,"--that most important of all figures, upon which the most needful of all arithmetical contrivances is based--the decimal system. And when we remember that the prosperity and progress of every country in Europe dates from the introduction of the Arabian figures[22] and when we realize the clumsiness and uselessness of the Hebrew and Greek and Latin alphabet figures, in vogue in Europe before the entrance of the Arab-Moors into Spain, and when we try to work out a problem of multiplication, say ninety-nine multiplied by ninety-nine, in accordance with the notation of the Arabic nine digits and cipher, and then, in accordance with the Roman alphabet figures, XCIX times XCIX, then, perhaps, will we most readily give thankful praise to those to whom Europe owes so magnificent a boon--to those who, with so simple an invention, opened the avenues of prosperity and loosened the fetters that had shackled the advance of science. [22] In Germany and England not until the fifteenth century, and hence their backwardness till then.