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BY JAMES RYAN,
The Differential and Integral Calculus, &c.
44 NORTH FOURTH STREET.
ENTERED according io the Act of Congress, in the year 1833 by KINDER & SHARPLESS, in the Clerk's Office of the District Court of lie Eastern District of Pennsylvania.
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TO THE LONDON EDITION.
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THE ART OF MEASURING, like all other useful inven. tions, appears to have been the offspring of want and necessity; and to have had its origin in those remote ages of antiquity, which are far beyond the reach of credible and authentic history. Egypt, the fruitful mother of almost all the liberal sciences, is imagined likewise to have given birth to GEOMETRY or MENSURATION; it being to the inundations of the Nile that we are said to be indebted for this most perfect and delightful branch of human knowledge.
After the overflowings of the river had deluged the country, and all artificial boundaries and land-marks were destroyed, there could have been no other method of ascertaining individual property, than by a previous knowledge of its figure and dimensions. From this circumstance, it appears highly probable, that Geometry was first known and cultivated by the ancient Egyptians; as being the only science which could administer to their wants, and furnish them with the assistance they required. The name itself signifies properly the art of measuring the earth; which serves still further to confirm this opinion, especially as it is well known that many of the ancient mathematicians applied their geometrical knowledge entirely to that purpose, and that even the Elements of Euclid, as they now stand, are only the theory from whence we obtain the rules and precepts of our present more mechanical practice.
But to trace the sciences to their first rude beginnings, is a matter of learned curiosity, which could afford but little gratification to readers in general. It is of much more consequence to the rising generation to be informed that, in their present improved state, they are