Plutarch, however, states the method in a form requiring the knowledge of Euclid vi.
Allman, " Greek Geometry from Thales to Euclid," Hermathena, No.
He also studied the first six books of Euclid and some algebra, besides reading a considerable quantity of Hebrew and learning the Odes of Horace by heart.
If there were such a thing as a triangle contained by absolutely straight lines, its three angles would no doubt measure what Euclid says; but straight lines and true triangles nowhere exist in reruns natura.
No doubt we are informed by Proclus, on the authority of Eudemus, that the theorem Euclid i.
His introduction to Euclid took place accidentally in 1629 (Aubrey's Lives, p. 604).
Agnes (Catholic), Euclid Avenue Temple (Jewish), and the Amasa Stone memorial chapel of Adelbert College.
At the age of eight he began Latin, Euclid, and algebra, and was appointed schoolmaster to the younger children of the family.
In 1548 Tartaglia accepted a situation as professor of Euclid at Brescia, but returned to Venice at the end of eighteen months.
He published the first Italian translation of Euclid (1543), and the earliest version from the Greek of some of the principal works of Archimedes (1543).
Leonardo, making use of fractions of the sexagesimal scale, gives X = I° 221 7 42" i 33 iv 4v 40 vi, after having demonstrated, by a discussion founded on the 10th book of Euclid, that a solution by square roots is impossible.
Lower Euclid Avenue (the old country road to Euclid, 0., and Erie, Pa.) is given up to commercial uses; the eastern part of the avenue has handsome houses with spacious and beautifully ornamented grounds, and is famous as one of the finest residence streets in the country.
The Arcade, between Euclid and Superior avenues, and the Colonial Arcade, between Euclid and Prospect avenues, are office and retail store buildings worthy of mention.
Dodgson periodically published mathematical works - An Elementary Treatise on Determinants (1867); Euclid, Book V., proved Algebraically (1874); Euclid and his Modern Rivals (1879), the work on which his reputation as a mathematician largely rests; and Curiosa Mathematica (1888).
Copied at his own expense, amongst them the Codex Clarkianus of Plato (brought to England from the monastery of St John in Patmos), and the Dorvillian MS. of Euclid (now at Oxford).
Another work was a commentary on Euclid (referred to by the Arabs as" the book of the resolution of doubts in Euclid ") from which quotations have survived in an-Nairizi's commentary.
The founder of the mathematical school was the celebrated Euclid (Eucleides); among its scholars were Archimedes; Apollonius of Perga, author of a treatise on Conic Sections; Eratosthenes, to whom we owe the first measurement of the earth; and Hipparchus, the founder of the epicyclical theory of the heavens, afterwards called the Ptolemaic system, from its most famous expositor, Claudius Ptolemaeus.
- Legendre's name is most widely known on account of his Elements de geometrie, the most successful of the numerous attempts that have been made to supersede Euclid as a text-book on geometry.
Still extant that were copied at his expense are the Bodleian Euclid (888) and the Bodleian Plato (895).
He is said to have written before Euclid and Ptolemy; and Cassiodorus arranges his Introduction to Music between those of Nicomachus and Gaudentius.
Euclid defines it (Book I.
Then by Euclid iii.
John Casey, professor of mathematics at the Catholic university of Dublin, has given elementary demonstrations founded on the theory of similitude and coaxal circles which are reproduced in his Sequel to Euclid; an analytical solution by Gergonne is given in Salmon's Conic Sections.
Each of these was divided into two books, and, with the Data, the Porisms and Surface-Loci of Euclid and the Conics of Apollonius were, according to Pappus, included in the body of the ancient analysis.
French and Euclid were taught by Rowbotham.
Pappus then enumerates works of Euclid, Apollonius, Aristaeus and Eratosthenes, thirty-three books in all, the substance of which he intends to give, with the lemmas necessary for their elucidation.
With the mention of the Porisms of Euclid we have an account of the relation of porism to theorem and problem.
According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was utilized by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
Following Euclid, a right angle is formed by a straight line standing upon another straight line so as to make the adjacent angles equal; any angle less than a right angle is termed an acute angle, and any angle greater than a right angle an obtuse angle.
This work, which contained only the first six and the eleventh and twelfth books, and to which in its English version he added the Data in 1762, was for long the standard text of Euclid in England.
EUCLID [EUCLEIDES], of Megara, founder of the Megarian (also called the eristic or dialectic) school of philosophy, was born c. 450 B.C., probably at Megara, though Gela in Sicily has also been named as his birthplace (Diogenes Lacrtius ii.
(5) the theorem Euclid i.
Proclus, too, in his summary of the history of geometry before Euclid, which he probably derived from Eudemus of Rhodes, says that Thales, having visited Egypt, first brought the knowledge of geometry into Greece, Assyrian Discoveries, p. 409.
In the part omitted, at p. 154 of the original edition, Hobbes refers to his first introduction to Euclid, in a way that confirms the story in Aubrey quoted in an earlier paragraph.
Of Euclid is known as the Pons Asinorum, bridge of asses.
370-415) mathematician and philosopher, born in Alexandria, was the daughter of Theon, also a mathematician and philosopher, author of scholia on Euclid and a commentary on the Almagest, in which it is suggested that he was assisted by Hypatia (on the 3rd book).
At Pavia in 1494 we find him taking up literary and grammatical studies, both in Latin and the vernacular; the former, no doubt, in order the more easily to read those among the ancients who had laboured in the fields that were his own, as Euclid, Galen, Celsus, Ptolemy, Pliny, Vitruvius and, above all, Archimedes; the latter with a growing hope of some day getting into proper form and order the mass of materials he was daily accumulating for treatises on all his manifold subjects of enquiry.
But, two years before, he had accidentally fallen in with a Latin copy of Euclid, which he eagerly devoured; and at twelve he attacked Newton's Arithmetica universalis.
He therefore bought an English edition of Euclid with an index of propositions at the end of it, and, having turned to two or three which he thought likely to remove his difficulties, he found them so selfevident that he put aside Euclid " as a trifling book," and applied himself to the study of Descartes's Geometry.
Thomas Taylor, the "Platonist," translated the commentaries on the Timaeus and Euclid, The Theology of Plato, the Elements of Theology, and the three Latin treatises.
Part of Euclid Avenue, and Ontario St.
The geometry of the sphere was studied by the Greeks; Euclid, in book xii.
Euclid devotes his third book entirely to theorems and problems relating to the circle, and certain lines and angles, which he defines in introducing the propositions.
Right angled at C, semicircles are described on the three sides, thus forming two lunes Afcda and Cgbec. The sum of the areas of these lunes equals the area of the triangle ABC.] As for Euclid, it is sufficient to recall the facts that the original author of prop. 8 of book iv.
It is reported that in his examination for a scholarship at Trinity, to which he was elected on the 28th of April 1664, he was examined in Euclid by Dr Isaac Barrow, who formed a poor opinion of his knowledge, and that in consequence Newton was led to read the Elements again with care, and thereby to form a more favourable estimate of Euclid's merits.
She received a rather desultory education, and mastered algebra and Euclid in secret after she had left school, and without any extraneous help. In 1804 she married her cousin, Captain Samuel Greig, who died in 1806; and in 1812 she married another cousin, Dr William Somerville (1771-1860), inspector of the army medical board, who encouraged and greatly aided her in the study of the physical sciences.
Even Socrates, in spite of his aversion to physics, was led by pious reflection to expound a teleological view of the physical world, as ordered in all its parts by divine wisdom for the realization of some divine end; and, in the metaphysical turn which Plato gave to this view, he was probably anticipated by Euclid of Megara, who held that the one real being is " that which we call by many names, Good, Wisdom, Reason or God," to which Plato, raising to a loftier significance the Socratic identification of the beautiful with the useful, added the further name of Absolute Beauty, explaining how man's love of the beautiful finally reveals itself as the yearning for the end and essence of being.
With Ricci's assistance, he rapidly mastered the elements of the science, and eventually extorted his father's reluctant permission to exchange Hippocrates and Galen for Euclid and Archimedes.
On the authority of the two great commentators Pappus and Proclus, Euclid wrote four books on conics, but the originals are now lost, and all we have is chiefly to be found in the works of Apollonius of Perga.
The first four books, of which the first three are dedicated to Eudemus, a pupil of Aristotle and author of the original Eudemian Summary, contain little that is original, and are principally based on the earlier works of Menaechmus, Aristaeus (probably a senior contemporary of Euclid, flourishing about a century later than Menaechmus), Euclid and Archimedes.
Allman, Greek Geometry from Thales to Euclid (1889); Florian Cajori, History of Mathematics (New York, 1894); M.
Ludwich (1895); commentary on Euclid by G.