, an Arabic name for the label, index, or ruler, which is moveable about the centre of an astrolabe, quadrant, &c, and carrying the sights or telescope, and by which are shewn the degrees cut off the limb or arch of the instrument.

ALIQUANT part, is that part which will not exactly measure or divide the whole, without leaving some remainder. Or the aliquant part is such, as being taken or repeated any number of times, does not make up the whole exactly, but is either greater or less than it. Thus 4 is an aliquant part of 10; for 4 twice taken makes 8 which is less than 10, and three times taken makes 12 which is greater than 10. |

ALIQUOT part, is such a part of any whole, as will exactly measure it without any remainder. Or the aliquot part is such, as being taken or repeated a certain number of times, exactly makes up, or is equal to the whole. So 1 is an aliquot part of 6, or of any other whole number; 2 is also an aliquot part of 6, being contained just 3 times in 6; and 3 is also an aliquot part of 6, being contained just 2 times: so that all the aliquot parts of 6 are 1, 2, 3.

All the aliquot parts of any number may be thus found: Divide the given number by its least divisor; then divide the quotient also by its least divisor; and so on always dividing the last quotient by its least divisor, till the quotient 1 is obtained; and all the divisors, thus taken, are the prime aliquot parts of the given number. Then multiply continually together these prime divisors, viz. every two of them, every three of them, every four of them, &c; and the products will be the other or compound aliquot parts of the given number. So if the aliquot parts of 60 be required; first divide it by 2, and the quotient is 30: then 30 divided by 2 also, gives 15, and 15 divided by 3 gives 5, and 5 divided by 5 gives 1: so that all the prime divisors or aliquot parts are 1, 2, 2, 3, 5. Then the compound ones, by multiplying every two, are 4, 6, 10, 15; and every three 10, 20, 30. So that all the aliquot parts of the given number 60, are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30.—In like manner it will be found that all the aliquot parts of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 180.

ALLEN (Thomas) a celebrated mathematician of the 16th century. He was born at Uttoxeter in Staffordshire, in 1542; was admitted a scholar of Trinity college, Oxford, in 1561; where he took his degree of master of arts in 1567. In 1570 he quitted his college and fellowship, and retired to Glocester hall, where he studied very closely, and became famous for his knowledge in antiquity, philosophy and mathematics. He received an invitation from Henry earl of Northumberland, a great friend and patron of the mathematicians, and he spent some time at the earl's house; where he became acquainted with those celebrated mathematicians Thomas Harriot, John Dee, Walter Warner, and Nathaniel Torporley. Robert earl of Leicester, too, had a great esteem for Allen, and would have conferred a bishopric upon him; but his love for solitude and retirement made him decline the offer. His great skill in the mathematics gave occasion to the ignorant and vulgar to look upon him as a magician or conjurer. Allen was very curious and indefatigable in collecting scattered manuscripts relating to history, antiquity, astronomy, philosophy, and mathematics: which collections have been quoted by several learned authors, and mentioned as in the Bibliotheca Alleniana. He published in Latin the second and third books of Ptolemy, Concerning the Judgment of the Stars, or, as it is usually called, of the quadripartite construction, with an exposition. He wrote also notes on many of Lilly's books, and some on John Bale's work, De scriptoribus Maj. Britanniæ. He died at Glocester hall in 1632, being 90 years of age.

Mr. Burton, the author of his funeral oration, calls him the very soul and sun of all the mathematicians of his age. And Selden mentions him as a person of the most extensive learning and consummate judgment, the bright- est ornament of the university of Oxford. Also Camden says he was skilled in most of the best arts and sciences. A. Wood has also transcribed part of his character from a manuscript in the library of Trinity college, in these words: “He studied polite literature with great application; he was strictly tenacious of academic discipline, always highly esteemed both by foreigners and those of the university, and by all of the highest stations in the church of England, and the university of Oxford. He was a sagacious observer, an agreeable companion, &c.”

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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