Arabians in matters pertaining to the stars: this task was committed to Alfazari. An abridgment of these tables was made in the succeeding age by Mohammed Ben Musa, under the patronage of Almamun before his accession to the Khalifat. (Colebrooke). The same Mohammed Ben Musa is recognized by the Arabians as the first who made known the Indian Arithmetic and Algebra: his Treatise on Algebra, the earliest written in Arabic, is still extant: a MS. copy is preserved in the Bodleian Library at Oxford, which was translated into English by the late Dr Rosen, and published at the expense of the Oriental Translation Fund. In this treatise the rules of the science are given in prose, and their accuracy is established by geometrical illustrations. In the Sanscrit treatises on Arithmetic and Algebra, the rules are given in verse. Almansur ascended the throne of the Khalifs A.D. 813, and it was the glory of his reign, that he invited learned men from various countries for the introduction of science and literature into his dominions. He founded a college at Bagdad, and appointed Mesuc of Damascus, a famous Christian physician, its president. It was here, under the auspices and encouragement of Almamun that Arabic translations of Indian and Greek science commenced, which were continued in succeeding reigns. The few manuscripts of the mathematical and philosophical writings of the Greeks which had escaped the general ruin, were diligently sought for and translated into Arabic. lations were made of the writings of Euclid, Archimedes, Apollonius, and others: besides which, Arabic commentaries were written to elucidate and explain these writings. To the Arabians of Bagdad is due the merit of preserving many writings, which, at present, are not known to be extant in the original Greek. Almamun died at about forty-eight years of age, after a reign of more than twenty years, A. D. 833. He is reported to have uttered the following ejaculation just before his death, "O Thou who never diest, have mercy on me, a dying man!" Trans The celebrated Alkindi is mentioned among the mathematicians and astronomers of the age of Almamun: his medical writings, which are still extant, prove that he sustained a very honourable rank among Arabian physicians. Alfragan was a celebrated astronomer, who flourished at the latter part of the eighth century; he was a native of Fargan, in Samarcand. In his Elements of Astronomy, a work which consists of thirty chapters, he adopts Ptolemy's hypothesis, and frequently quotes from his writings. Professor Golius, of Leyden, translated this treatise into Latin, with notes on the first nine chapters, which were published with the original Arabic, in 1669, after his death. Albategni was an Arabian astronomer of the ninth century: Dr Halley describes him as a man of great acuteness. His work, entitled "The Science of the Stars," was founded on his own observations, combined with those of Ptolemy. On his observations were founded the famous Alphonsine Tables. He died A.D. 888; his work was first printed in 1537. Albumazar was a physician and astronomer of the ninth century. His Introductio ad Astronomiam was printed in 1489, and his work "De magnis conjunctionibus, annorum revolutionibus ac eorum perfectionibus," in 1526, at Venice. Rhazes was a most distinguished physician, and received the appel lation of the experimenter. He is also said to have been profoundly skilled in astronomy and other sciences: he had the reputation of being a skilful alchemist, and of having been the first to use chemical preparations in medicine. Many of his numerous works have come down to us, and some of them have been translated and printed. Honain was an Arabian physician and a Christian, who lived in the ninth century. He is reported to have travelled into Greece and Persia, and afterwards to have settled at Bagdad, where he translated the Elements of Euclid, and the writings of Hippocrates, into Arabic. Thabet Ben Korrah lived during the latter part of the ninth and the early part of the tenth century. Ebn Khallikan relates, in his Biographical Dictionary, which has been translated into English, that Thabet Ben Korrah left Harran, and established himself at Kafratutha, where he remained, till Abu Jafar Mohammed Ben Musa arrived there, on his return from the Greek dominions, to Bagdad. He became acquainted with Thabet, and on seeing his skill and sagacity, invited him to Bagdad, made him lodge at his own house there, introduced him to the Khalif Almotaded, and procured him an appointment amongst the astronomers. Thabet became secretary to the Khalif, and was distinguished for his skill in the mathematics and astronomy. To him is attributed a translation of the Conics of Apollonius, and the Almagest of Ptolemy. In the tenth century several treatises on Geometry are ascribed to Mohammed Bagdedin, among which is one "On the Division of Surfaces;" it was translated into Latin, by Commandine, and published in 1570; it was also translated into English, by John Dee. This treatise on the Division of Surfaces is by some attributed to Euclid. Avicenna, who lived in the tenth century, has been accounted the prince of Arabian physicians and philosophers. He was a most voluminous writer; his greatest work was an Encyclopædia, in twenty volumes, with the title of "Utility of Utilities." He is reported to have written on almost every subject of physics, metaphysics, and the mathematical sciences. Among his mathematical works was an abridgment of Euclid's Elements of Geometry. Many of his writings are extant, and some of them have been printed at Venice. About the middle of the eleventh century, Diophantus was translated into Arabic, by Abulwafa Buzjani. In the twelfth century, Nassir Eddin, a Mahommedan, acquired the highest reputation in all branches of literature and science. He translated the Elements of Euclid into Arabic, which, with his commentary, was printed at Rome, in 1594, under the patronage of the Medici. He is also reported to have written commentaries on the Spherics of Theodosius and Menelaus. The Kholasat al Hisab, is a compendium of Arithmetic and Geometry, composed by Baha Eddin, who died A.D. 1575. The Arabic text, and a Persian commentary written by Roshan Ali, were printed at Calcutta, in 1812. In this treatise, Baha Eddin remarks, that "Learned Hindus have invented the well-known nine figures for them;" meaning the Arabians. The Arabian mathematicians are not noted for any very important discoveries or improvements in Geometry. There is, however, one improvement in Trigonometry of considerable importance, to which they have an undoubted claim. The Greeks in their astronomical cal culations employed the chords of arcs; but the Arabians introduced the sines, or half the chord of the whole arc, which led to greater simplicity in calculation. During the middle ages but few names have come down to us of men who were skilled in the mathematical sciences. Beda, commonly called the Venerable Bede, was born A. D. 672, near Wearmouth, in the bishopric of Durham; he was the first of the Anglo-Saxon historians. His Ecclesiastical History was completed in A. D. 731: his writings are numerous, and the first collection of them was printed at Paris, in 1544. Athelard or Adelard, was a monk of Bath, and the first who made known in England, Euclid's Elements of Geometry. This he did by making a translation from the Arabic into Latin, long before any Greek copies of Euclid were known. He is said to have travelled into France, Germany, Italy, Spain, Egypt and Arabia, to increase his knowledge. He also wrote numerous works; some MS. copies of which are said by Vossius to be in some of the College Libraries, at Oxford. The works of Ptolemy, the astronomer of Alexandria, became known to the learned of these times through the same language as the works of Euclid. A Treatise on the Sphere, by John de Sacro Bosco, or John of Holywood, was first put forth in the early part of the thirteenth century. It is asserted by Montucla (1. p. 506), to be only an abridgment of Ptolemy. MS. copies of it exist, and it has been printed several times; there is also a commentary on this treatise, written by Clavius. Roger Bacon, an English monk of the Franciscan order, was born near Ilchester, in Somersetshire, in 1214. He studied first at Oxford, and afterwards at Paris, and became the most celebrated philosopher of his age. Of his writings, which are numerous, some only have been printed; his tract on Chronology has not been printed. By his great skill in astronomy, he discovered the error which gave occasion for the reformation of the Calendar, and his plan was afterwards followed by Pope Gregory XIII, with this variation, that Bacon would have had the correction to begin from the birth of our Saviour; whereas Gregory's amendment reached no higher than the Nicene Council. His great knowledge of the sciences in an ignorant age, no doubt gave rise to the story of his having dealings with the devil. John de Basingstoke, who died A.D. 1252, is reported to have introduced into England the knowledge of the Greek numerals. His merits and learning recommended him to the favour of Robert Grossetete, then bishop of Lincoln, who is reported by Roger Bacon to have excelled in Geometry and the other mathematical sciences, and to have spent many years in the study of them. Grossetete wrote on many subjects, and some of his pieces are still extant. He is reported to have studied first at Cambridge, afterwards at Oxford, and lastly at Paris; he was made Bishop of Lincoln in 1235. About the year 1261 another translation of Euclid's Elements of Geometry from the Arabic was made into Latin, by Campanus of Novara, who also wrote a Commentary on Euclid. It was printed at Venice, in 1482, without a title-page, by Erhardus Ratdolt, and was the first printed edition of the Elements in Latin. The translation of Campanus has been supposed by some to be only a revision of the translation which had been made by Adelard. It is possible he might have revised and improved Adelard's translation, and annexed his Commentary; but this could only be determined by a collation of early MS. copies of the two versions. Campanus was the author of a treatise on the Quadrature of the Circle, which has been printed, in the Appendix to the Margarita Filosofica. In the thirteenth century, Vitello, a native of Poland, displayed an intimate knowledge of the geometrical writings of the Arabians and Greeks. He is chiefly celebrated for the treatise on Optics, which he composed from the writings of the Greeks and Arabians on that science. It was printed in 1572: he also translated the Spherics of Theodosius. As geometers in the fourteenth century, Chaucer and Wallingfort may be mentioned. Chaucer, the father of English poetry, was born in London, A.D. 1328, and died at the age of seventy-two. He is said to have been learned in all the sciences. He was the author of a treatise on the Astrolabe, in which he describes the methods of astronomical observation known in his day: it has been printed. Richard Suisset or Swineshead wrote a work called "the Calculator." It is highly commended by Cardan, and has been printed. Thomas Bradwardine, Archbishop of Canterbury, in the time of Edward III. was the author of a work entitled "Geometria Speculativa cum Arithmetica Speculativa." He also wrote "de Proportionibus," and "de Quadratura Circuli." Bradwardine was the most distinguished geometrician of his time. He died A.D. 1348: his work on Geometry was printed in 1495. George of Purbach, commonly called Purbach, was born in 1423, at a town of that name on the confines of Bavaria and Austria, and became the most eminent astronomer and mathematician of his time. He amended the Latin translation of Ptolemy's Almagest, which had been made, not from the Greek original, but from the Arabic translation. He also corrected, by means of the Greek text, the translation of Archimedes, made by Gerrard of Cremona, and wrote commentaries on those books of Archimedes which Eutocius had omitted. He translated the Conics of Apollonius, and made a Latin version of the Spherics of Theodosius and Menelaus; and of the book of Serenus on Cylinders. He composed an introduction to Arithmetic, and a treatise on Dialling and Gnomonics. He also made very great improvements in Trigonometry by introducing the table of Sines, and a new division of the radius into 600,000 instead of 60 equal parts. He thus completely changed the appearance of that science, so important in Astronomy. John Muller, or, as he was called, Regiomontanus, from the Latinized name of his native town, Konigsberg, died at Rome, in 1476, at the early age of forty years: he had been invited thither by Pope Sixtus IV. to assist in rectifying the Calendar. Muller was the disciple and friend of Purbach; after whose premature death, he revised and completed, at Rome, the Latin version of Ptolemy, which Purbach had left unfinished; he also further improved Purbach's division of the radius. He rejected the sexagesimal subdivision of the radius, and made it to consist of 1,000,000 equal parts. With this new division, he computed the sines of arcs, to every minute of the quadrant, to seven places of figures; he also annexed a table of secants. His celebrated treatise on Triangles, in five books, was not published in his lifetime, and did not appear till 1533, when it was edited and published by Schener. The solutions of the more difficult cases of plane and spherical triangles are to be found in his work; and, with the exception of what Spherical Trigonometry owes to Napier, that science may be said to have made but small advances for more than two centuries after the age of Muller. In his work on Triangles he gave a table for finding the angle of a right-angled triangle, from the base and perpendicular, without knowing the hypothenuse. This table, which he styled "Canon Fœcundus," was calculated for every degree of the quadrant, and was, in reality, a table of tangents, which he was the first to introduce into the science of Trigonometry. He added also many new theorems to that science; and after him few improvements were made in it till the time of Euler. His fifth book contains numerous problems concerning rectilinear triangles, of which some are solved by Algebra. The tables of Regiomontanus were printed in 1490. The revival of ancient literature in Europe, about the middle of the fifteenth century, contributed to bring the mathematical writings of the Greeks into notice; and the discovery of the art of printing, about the same time, was the commencement of a new era in literature and science. The writings of the ancients were now no longer confined in MS. to the religious houses, and to the few who had the means of purchasing copies of the manuscripts. The fall of the Eastern empire, and the capture of Constantinople by the Turks, in 1458, drove many Greeks to seek their safety and subsistence in Italy and other parts of Europe. These became living instructors in the Greek language, and very much facilitated its revival in Italy. As the literature of the Greeks became known, their mathematical writings also attracted notice they were printed and translated, and published with commentaries. Restorations also of lost treatises were attempted by mathematicians of that and following centuries. Mr Hallam in a note, p. 157, Vol. 1. of his History of the Middle Ages, remarks, "It may be considered a proof of the attention paid to Geometry in England, that two books of Euclid were read at Oxford, about the middle of the fifteenth century." With respect to the mathematical science of the middle ages, though we do not find any original writers who made additions to it by their discoveries; there must, in justice, be conceded to the men of those times, the possession of no mean or scanty knowledge of Geometry. The splendid ecclesiastical buildings of the middle ages, which are still standing both in Great Britain and in the south and west of Europe, evince in their structure a practical knowledge, at least, of some of the most difficult problems of Geometry and the science of Equilibrium. Lucas de Burgo's work, entitled "Summa de Arithmetica, Geometriâ, &c." was published in 1494. Fifteen years later he published the Latin translation of Euclid, which had been made from the Arabic by Campanus. Copernik, or (as he is commonly called) Copernicus, was born at Thorn in Prussia, in 1473, and his name is immortalized by his discovery of the true Solar system. The motion of the sphere, of the fixed stars with the sun and moon round the earth, in twenty-four hours, appeared to him too complex; and he felt persuaded that such could not be the system of nature. The Pythagoreans and some later philosophers had held the rotation of the earth round its own axis, and its revolution round the sun. Copernicus collected the writings of pre |