# Euclid Sentence Examples

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.Plutarch, however, states the method in a form requiring the knowledge of

**Euclid**vi.His introduction to

**Euclid**took place accidentally in 1629 (Aubrey's Lives, p. 604).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.At the age of eight he began Latin,

**Euclid**, and algebra, and was appointed schoolmaster to the younger children of the family.In 1756 appeared, both in Latin and in English, the first edition of his

**Euclid**'s Elements.No doubt we are informed by Proclus, on the authority of Eudemus, that the theorem

**Euclid**i.He translated into Hebrew a large number of Arabic books (including the Arabic form of

**Euclid**).**Euclid**'s manner of proof became the model for his own way of thinking upon all subjects.This, his second, sojourn abroad appears to have been spent chiefly in Paris, and the one important fact recorded of it is that he then first began to look into

**Euclid**.AdvertisementDeduction is synthesis when it is progressive from real ground to consequence, as when we start from these two results of analysis as principles and deduce synthetically the proposition that therefore the angles of a triangle are equal to two right angles, in the order familiar to the student of

**Euclid**.He has been credited with a knowledge of Greek, and it is said that his translation of

**Euclid**'s Elements was made from the original Greek.In addition to this, he translated various other treatises, to the number, it is said, of sixty-six; among these were the Tables of "Arzakhel," or Al Zarkala of Toledo, Al Farabi On the Sciences (De scientiis),

**Euclid**'s Geometry, Al Farghani's Elements of Astronomy, and treatises on algebra, arithmetic and astrology.In 1839 he produced a small work called First Notions of Logic, giving what he had found by experience to be much wanted by students commencing with [[

**Euclid**]].Alternative (a) was

**Euclid**'s parallel axiom.AdvertisementThe centre of retail trade moved steadily eastward, crowding out the large houses with spacious grounds which had made

**Euclid**avenue famous.That he made the fullest use of his predecessors' works, such as

**Euclid**'s four Books on Conics, is clear from his allusions to**Euclid**, Conon and Nicoteles.His principal works are - Propaedeumata aphoristica (London, 1 55 8); Monas hieroglyphica (Antwerp, 1564); Epistola ad Fredericum Commandinum (Pesaro, 1570); Preface Mathematical to the English

**Euclid**(1570); Divers Annotations and Inventions added after the tenth book of English**Euclid**(1570); Epistola praefixa Ephemeridibus Joannis Feldi, a.**Euclid**(Elements, book 1) defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other (see Geometry, Euclidean).The former treatise is historically interesting for the light it throws on the development which the geometry of the sphere had already reached even before Autolycus and

**Euclid**(see THEODOSrus OF Tripolis).AdvertisementThe more philosophic part of the circle, forming a group in which

**Euclid**of Megara (see Megarian School) seems at first to have taken the lead, regarded this Good as the object of a still unfulfilled guest, and were led to identify it with the hidden secret of the universe, and thus to pass from ethics to metaphysics.**Euclid**discusses them in the thirteenth book of his Elements, where he proves that no more regular bodies are possible, and shows how to inscribe them in a sphere.This phenomenon brought the mathematician,

**Euclid**(300 B.C.) to the conclusion that this ratio was divine.In his thirteen volume work Elements, the mathematician

**Euclid**, referred to a dividing line at the point of 0.6180399.**Euclid**wrote Elements in approximately 300 B.C.AdvertisementCalled the Divine Ratio by

**Euclid**, the Golden Ratio is found in nature, the arts and architecture.**Euclid**of Alexandria, a famed mathematician of the time, wrote the influential thirteen volume textbook Elements.In his book,

**Euclid**explains the proportion derived from dividing a line by the mean and extreme ratio.In literature Megara figures as the reputed home of the comedian Susarion, and in the 4th century gave its name to a school of philosophy founded by

**Euclid**.Under him Avicenna read the Isagoge of Porphyry and the first propositions of

**Euclid**.His son Moses, who died about the end of the 13th century, translated the rest of Maimonides, much of Averroes, the lesser Canon of Avicenna,

**Euclid**'s Elements (from the Arabic version), Ibn al-Jazzar's Viaticum, medical works of IIunain ben Isaac (Johannitius) and Razi (Rhazes), besides works of less-known Arabic authors.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).The second work of Leonardo, his Practica geometriae (1220) requires readers already acquainted with

**Euclid**'s planimetry, who are able to follow rigorous demonstrations and feel the necessity for them.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).**Euclid**'s Elements were first translated in the reign of Harun-al-Rashid (786-809), and revised by the order of Mamun.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.The geometry of the sphere was studied by the Greeks;

**Euclid**, in book xii.He is said to have written before

**Euclid**and Ptolemy; and Cassiodorus arranges his Introduction to Music between those of Nicomachus and Gaudentius.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.He went first to the university of Louvain, where he resided about two years, and then to the college of Rheims, where he had extraordinary success in his public lectures on

**Euclid**'s Elements.French and

**Euclid**were taught by Rowbotham.He also wrote commentaries on

**Euclid**'s Elements (of which fragments are preserved in Proclus and the Scholia, while that on the tenth Book has been found in an Arabic MS.), and on Ptolemy's `Ap/20vcKfi.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.After his death restorations of Apollonius's treatise De sectione determinata and of

**Euclid**'s treatise De porismatibus were printed for private circulation in xxv.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.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.In 1548 Tartaglia accepted a situation as professor of

**Euclid**at Brescia, but returned to Venice at the end of eighteen months.**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.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.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.