, the first principles, of which all bodies and things are composed. These are supposed few in number, unchangeable, and by their combinations producing that extensive variety of objects to be met with in the works of nature.

Democritus stands at the head of the Elementary Philosophers, in which he is followed by Epicurus, and many others after them, of the Epicurean and corpuscular philosophers.

Among those who hold the Elements corruptible, some will have only one, and some several. Of the former, the principal are Heraclitus, who held fire; Anaximenes, air; Thales Milesius, water; and Hesiod, | earth; as the only Element. Hesiod is followed by Bernardin, Telesius; and Thales by many of the chemists.

Among those who admit several corruptible Elements, the principal are the Peripatetics; who, after their leader Aristotle, contend for four Elements, viz, fire, air, water, and earth. Aristotle took the notion from Hippocrates; Hippocrates from Pythagoras; and Pythagoras from Ocellus Lucanus, who it seems was the first author of it.

The Cartesians admit only three Elements, fire, air, and earth. See Cartesian Philosophy.

Newton observes, that it seems probable that God, in the beginning, formed matter in solid, massive, hard, impenetrable, moveable particles, of such sizes and sigures, &c, as most conduced to the end for which he formed them; and that these primitive particles, being solids, are incomparably harder than any porous body compounded of them; even so hard as never to wear out; no ordinary power being able to divide what God made one in the first creation. While the particles remain entire, they may compose bodies of one and the same nature and texture in all ages; but should they wear away, or break in pieces, the nature of things, depending on them, would be changed; water and earth, composed of old worn particles, and fragments of particles, would not be of the same nature and texture now, with water and earth composed of entire particles in the beginning. And therefore, that things may be lasting, the changes of corporeal things are to be placed only in the various separations, and new associations and motions of those permanent particles; compound bodies being apt to break, not in the midst of solid particles, but where those particles are laid together, and only touch in a few points. It seems to him likewise, that these particles have not only a vis inertiæ, with the passive laws of motion thence resulting, but are also moved by certain active principles; such as gravity, and the cause of fermentation, and the cohesion of bodies.


, a term also used for the first grounds and principles of arts and sciences; as the Elements of geometry, Elements of mathematics, &c. So Euclid's Elements, or simply the Elements, as they were anciently and peculiarly named, denotes the treatise on the chief properties of geometrical figures by that author.

The Elements of Mathematics have been delivered by several authors in their courses, systems, &c. The first work of this kind is that of Herigon, in Latin and French, and published in 1664, in 10 tomes; which contains Euclid's Elements and Data, Apollonius, Theodosius, &c; with the modern Elements of arithmetic, algebra, trigonometry, architecture, geography, navigation, optics, spherics, astronomy, music, perspective, &c. The work is remarkable for this, that a kind of real and universal characters are used throughout; so that the demonstrations may be understood by such as only remember the characters, without any dependence on language or words at all.

Since Herigon, the Elements of the several parts of mathematics have been also delivered by others; particularly the Jesuit Schottus, in his Cursus Mathematicus, in 1674; De Chales, in his Cursus, 1674; Sir Jonas Moore, in his New System of Mathematics, in 1681; Ozanam, in his Cours de Mathematique, in 1699; Jones, in his Synopsis Palmariorum Matheseos, in 1706; and many others, but above all, Christ. Wolfius, or Wolf, in his Elementa Matheseos Universæ, in 2 vols 4to, the 1st published in 1713, and the 2d in 1715; a very excellent work of the kind. Another edition of the work was published at Geneva, in 5 vols 4to, of the several dates 1732, 1733, 1735, 1738, and 1741.

The Elements of Euclid, as they were the first, so they continue still the best system of geometry, are in 15 books. There have been numerous editions and commentaries of this work. Proclus wrote a commentary on it. Orontius Fineus first gave a printed edition of the sirst 6 books, in 1530, with notes, to explain Euclid's sense. Peletarius did the same in 1557. Nic. Tartaglia, about the same time, made a comment on all the 15 books, with the addition of many things of his own. And the same was also done by Billingsley in 1570; and by Flussates Candalla, a noble Frenchman, in the year 1578, with considerable additions as to the comparison and inscriptions of solid bodies; which work was afterwards republished with a prolix commentary, by Clavius. Commandine gave also a good edition of it. In 1703, Dr. Gregory published an edition of the whole works of Euclid, in Greek and Latin, including his Elements. But it would be endless to relate all the other editions of these Elements, either the whole, or in part, that have been given; some of the best of which are those of De Chales, Tacquet, Ozanam, Whiston, Stone, and most especially that of Dr. Rob. Simson, of Glasgow.

Other writers on the Elements of Geometry are almost out of number, in all nations.


, in the Higher or Sublime Geometry, are the insinitely small parts, or differentials, of a right line, curve, surface, or solid.


, in Astronomy, are those principles deduced from astronomical observations and calculations, and those fundamental numbers, which are employed in the construction of tables of the planetary motions. Thus, the Elements of the theory of the sun, or rather of the earth, are his mean motion and eccentricity, with the motion of the aphelia. And the Elements of the theory of the moon, are her mean motion, that of the node and apogee, the eccentricity, the inclination of her orbit to the plane of the ecliptic; &c.

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

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