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Abraham bar Hiyya

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1655:"; and out of pure matter the celestial bodies, and out of impure matter the four elements, were evolved. But while the first formed into an inseparable combination and the mixture of the latter is one which constantly changes, a third form exists which mixes with matter for a certain time, to live again in a disembodied state after its separation, and this is the human soul. According to its wisdom—which makes it seek the upper world, the pure lasting form—or its folly—which makes it follow the impure matter of the perishable world below—the soul of man partakes of the nature of either the one or the other but, his destination being to live forever like the angels, man has been appointed by God to be the ruler of all beings on earth; and in the same measure in which he fulfills or deviates from his destination, does he rise or fall in dignity above or below his fellow creatures. 866: 1753:, when the evil spirit shall have vanished altogether, when the sensual man shall have become a spiritual one, and the passions that created hatred and strife shall have given way to love of man and to faithful obedience to the will of God, no other laws than those given to the God-devoted one in the Decalogue—the law written upon the heart of man—will be necessary. Men, imbued solely with love for their fellows, free from sin, will rise to the standard of the God-devoted man, and, like him, share in the eternal bliss of God. 1622:. In it, he exhorts the reader to lead a life of purity and devotion. At the same time he does not hesitate to borrow ideas from non-Jewish philosophers, and he pays homage to the ancient Greek philosophers who, without knowledge of the Torah, arrived at certain fundamental truths regarding the beginning of things, though in an imperfect way, because both the end and the divine source of wisdom remained hidden to them. In his opinion the non-Jew may attain to as high a degree of godliness as the Jew. 2837: 2002: 841:, bar Ḥiyya modestly states that, because none of the scientific works such as those which exist in Arabic were accessible to his brethren in France, he felt called upon to compose books which, though containing no research of his own, would help to popularize knowledge among Hebrew readers. His Hebrew terminology, therefore, occasionally lacks the clearness and precision of later writers and translators. 2210: 1651:
two different elements. There is pure and there is impure matter. So also there is form too sublime to mingle with matter, such as that of the angelic or the upper world; and form which, being receptive and hollow, is susceptible to mixture with matter. The upper world, while gazing upon the lower and radiating its higher light, causes the mixture of matter with receptive form, the "
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that the soul in this world of flesh is imprisoned, while the animal soul craves for worldly pleasures, and experiences pain in foregoing them. Still, only the sensual man requires corrections of the flesh to liberate the soul from its bondage; the truly pious need not, or rather should not, undergo
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Matter, being void of all reality, requires form to give it existence. Now the union of these two by the will of God, which brings them from a state of potentiality into one of actuality, is creation, time itself being simultaneously produced with the created things. Both matter and form consist of
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would appear in the year AM 5118 (AD 1358). Its fifth and last chapter, the largest part of the work, may be read as an independent treatise providing an astrological explanation of Jewish and universal history based on an analysis of the periodical conjunctions of
372:. Abraham bar Hiyya is said to have been a great astronomer and wrote some works on astronomy and geography. One talks about the form of the earth, the elements, and the structure of the spheres. Other works included papers on astrology, trigonometry, and music. 787:. There remains doubt as to the particulars: a number of Jewish translators named Abraham existed during the 12th century, and it is not always possible to identify the one in question. Known translations of bar Ḥiyya include: 1703:
such as take part in the world's affairs, but are, as regards their conduct, ruled only by the divine laws and statutes without concerning themselves with the rest of men (these form the "holy congregation" or the "faithful
1731:; the other nine present the various laws in relation to God, to domestic life, and to society at large. Each of these three classes again refers either to the heart or sentiment, to the speech or to the action of man. 1707:
such as lead righteous lives, but take care also that the wrong done outside of their sphere is punished and the good of all the people promoted (these form the "kingdom of justice" or the "righteous nation").
391:" is always appended to his name, Barcelona was at the time no longer under Muslim rule, and therefore not part of Sepharad. Abraham Albargeloni (i.e., from Barcelona) thus belonged to the community of the 1965:
Also Ḥayya. Other variants include Abraham ben Chija, Abraham ben Hiyya al-Bargeloni, Avraham ben Chiya Hanasi mi'Barcelona, Abraham ben Chiva, Abraham ben Chaja, and Rabbi Abrahamo Hispano filio Rabbi
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such as lead a life altogether apart from worldly pursuits and devoted only to God ("these are but few in number and may in their sovereignty over the world be regarded as one individuality").
480:, was the first European attempt to synthesize Greek and Arabic mathematics. Likely written in the first quarter of the 12th century, the book is said to elaborate on the interdependence of 1806: 1867: 621:), an astronomical work on the formation of the heavens and the earth, which was to have been followed by a second part on the course of the stars. A portion was translated into 1610:, as Rapoport and Rosin think, or not, the object of the work was a practical, rather than a theoretical, one. It was to be a homily in four chapters on repentance based on the 278: 1664:
fasting or other forms of asceticism except such as the law has prescribed. But, precisely as man has been set apart among his fellow creatures as God's servant, so
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religious basis. It was published in 1860 by Freimann, with a biography of the author (by the editor), a list of his works, and learned introduction by Rapoport.
1927: 1907: 1887: 530:'Treatise on Measurement and Calculation'), probably intended to be a part of the preceding work. This is the celebrated geometry translated in 1145 by 2850: 2015: 1785:
he calculated from Scripture the exact time for the advent of the Messiah to be the year of the world 5118. He wrote also a work on redemption, from which
1538: 642: 573:("Scroll of the Revealer") on the redemption of the Jewish people. The latter was partly translated into Latin in the 14th century under the title 2697:
Sela, Shlomo (2001). "The Fuzzy Borders between Astronomy and Astrology in the Thought and Work of Three Twelfth-Century Jewish Intellectuals".
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Allgemeine Enzyklopädie der Wissenschaften und der Künste, Part 1, Vol. 1, p. 157; Poggendorff’s Handwörterbuch, Volume I, A-L, 1863 Leipzig.
1723:, lives solely in the service of God (the singular being used because only Moses or the one who emulates him is addressed). The first of the 1574: 1164: 186: 1749:
legislation intended for the people living in an agricultural state and forming a "kingdom of justice." However, in the time of the
3165: 364:. He was held in high consideration by the ruler he served on account of his astronomical knowledge and had disputes with learned 3048: 604:
of the earlier Jewish scientific literature, which made him a pioneer in the use of the Hebrew language for scientific purposes.
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In accordance with these three classes of servants of God, he finds the laws of the Torah to be divided into three groups:
3160: 2969: 2755: 865: 3140: 2041: 1769:. Characteristic of the age is the fact that while Abraham bar Ḥiyya contended against every superstition, against the 3110: 3105: 1742:, to render them a holy congregation relying solely upon the special protection of God without resorting to warfare. 1603:, Abraham bar Ḥiyya had to wrestle with the difficulties of a language not yet adapted to philosophic terminology. 504:. The book draws from a number of Greek sources then available in Arabic, as well as the works of al-Khwarizmi and 2419:
Levey, Martin (September 1952). "The Encyclopedia of Abraham Savasorda: A Departure in Mathematical Methodology".
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in 1137, and thus the County of Barcelona became the capital of a new Catalan-Aragonese confederation called the
301: 3170: 1831: 1727:, which he considers merely as an introductory word, accentuates the divine origin and the eternal goal of the 349:; there is even a record of a Jewish Savasorda there in the beginning of the 12th century. In his travelogues, 1341: 630: 1346: 1159: 3175: 2220: 2046: 1560: 1508: 1461: 1240: 1789:
appropriated many ideas. It is in defense of Judaism against Christian arguments, and also discusses
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Abraham bar Ḥiyya co-operated with a number of scholars in the translation of scientific works from
387:(a work that the latter finished in 1143) was identical with Abraham bar Ḥiyya. Although the title " 3053: 1336: 585:
in nature, and drew a horoscope of favourable and unfavourable days. Bar Ḥiyya forecasted that the
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Abraham bar Ḥiyya was one of the most important figures in the scientific movement which made the
235: 3043: 2855: 2229: 2083: 2020: 1426: 945: 485: 337:'prince'). Scholars assume that Bar Hiyya would have obtained this title in the court of 2556:
Levey, Martin (1954). "Abraham Savasorda and His Algorism: A Study in Early European Logistic".
2078: 1825: 1607: 1456: 1396: 1366: 1126: 1063: 656:), the sequel to the preceding work, which is found sometimes in manuscripts with the notes of 476:'The Foundations of Understanding and the Tower of Faith'), usually referred to as the 318: 2599:
Schub, Pincus (1932). "A Mathematical Text by Mordecai Comtino (Constantinople, XV Century)".
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The group of laws contained in the second, third, and fourth books of Moses, intended for the
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This work was printed in Basel by Oswald Schreckenfuchs, including a Latin translation. See
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Kaunzner, Wolfgang (1987). "On the Transmission of mathematical Knowledge to Europe".
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Levy, Raphael (October 1942). "The Authorship of a Latin Treatise on the Astrolabe".
2448: 2355: 2343: 2291: 2167: 2118: 2050: 1421: 1411: 1401: 1316: 1250: 1245: 1078: 1053: 857: 824: 435: 392: 206: 152: 2706: 2608: 2565: 2522: 2428: 2335: 2159: 1774: 1735: 1724: 1716: 1693: 1488: 1436: 1131: 1073: 1038: 1028: 1018: 985: 680: 657: 638: 577:. Even these religious works contain scientific and philosophical speculation. His 431: 422:, in which he complained about the Provençal community's ignorance of mathematics. 419: 384: 361: 357: 1773:, against prayers for the dead, and similar practises, he was, nevertheless, like 2993: 2216: 1983: 1786: 1681: 1600: 1446: 1295: 1187: 1103: 1093: 770: 762: 725: 710: 703: 687: 664: 649: 634: 614: 597: 531: 516: 462: 415: 407: 369: 365: 309: 210: 125: 88: 679:" and the "Jerusalem Tables". Several manuscripts of this work contain notes by 2846: 2339: 2244:
Katz, Shlomo, ed. (14 March 1998). "R' Avraham ben Chiya Hanasi mi'Barcelona".
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Lévy, Tony (2002). "Encyclopedia of the Middle Ages". In Vauchez, André (ed.).
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La obra Séfer hešbón mahlekot ha-kokabim de R. Abraham bar Hiyya ha-Bargeloní
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and algebra, the book contains the first known complete solution of the
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Goldstein, Bernard R. (2001). "Kepler and Hebrew Astronomical Tables".
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Die Bibelexegese der Jüdischen Religionsphilosophen des Mittelalters,
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is elsewhere quoted by Abraham bar Ḥiyya, he never refers to him in
304:. Bar Ḥiyya occupied a high position in the royal court, serving as 16:
Catalan Jewish mathematician, astronomer and philosopher (1070-1136)
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Bar Ḥiyya was a pioneer in the field of philosophy: as shown by
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History of the Jews: from the Earliest Times to the Present Day
1979: 1934: 1543: 738: 695: 508:. Only a few short fragments of this work have been preserved. 497: 403: 346: 305: 1696:, Abraham bar Ḥiyya distinguishes three classes of pious men: 1794: 1739: 1720: 1660: 927: 550:, following it even to the sameness of some of the examples. 182: 2214: 633:. It appears also that complete translations into Latin and 1929:
is radius. The same proof appears in the commentary of the
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Some scholars think that the Magister Abraham who dictated
732:), a controversial work in defense of the theory that the 2503:
Poggendorff’s Handwörterbuch, Volume I, A-L, 1863 Leipzig
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Allgemeine Enzyklopädie der Wissenschaften und der Künste
553:
Bar Ḥiyya also wrote two religious works in the field of
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world, in both his original works and his translations.
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According to Adolph Drechsler, bar Ḥiyya was a pupil of
1848: 2373:. Barcelona: Instituto Arias Montano. pp. 13–14. 1915: 1895: 1875: 1834: 1757:
Guttmann has shown that Naḥmanides read and used the
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mentions bar Ḥiyya living in Barcelona in the 1160s.
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is separate from the nations, the same three terms (
323: 2967: 2744:. New York: Frederick Ungar Publishing. p. 11. 1761:, though occasionally differing from it; but while 1738:during their wandering in the desert or during the 794:
the well-known treatise of Ali ben Aḥmad al-Imrani.
675:), astronomical tables, called also the "Tables of 1921: 1901: 1881: 1861: 536:Liber embadorum a Savasordo in hebraico compositus 272: 3037: 2368: 641:contains a copy with a commentary, apparently by 177:Bar Ḥiyya was active in translating the works of 3087: 410:. The kings of Aragon extended their domains to 2671: 2665: 2265: 368:, to whom he demonstrated the accuracy of the 2272:. Thalmessinger & Cahn; Trübner & Co. 1687: 1568: 3016:The Biographical Encyclopedia of Astronomers 2970:"The proof of Rabbi Abraham Bar Hiya Hanasi" 2115:The Biographical Encyclopedia of Astronomers 1988: 1809:Bar Ḥiyya's theorem in a copy of the Talmud. 1630:Abraham bar Ḥiyya's philosophical system is 292:Abraham bar Ḥiyya was the great-grandson of 30: 3062:"Abraham bar Hiyya [dit Savasorda]" 2961: 2845: 2742:Studies in the History of Mediaeval Science 2382: 2380: 2281: 2279: 2266:Geiger, Abraham; Newburgh, Charles (1866). 2073: 2010: 648:"Calculation of the Courses of the Stars" ( 3059: 3009: 2476:: CS1 maint: location missing publisher ( 2108: 1575: 1561: 197:. He also wrote several original works on 2317: 2285: 1862:{\displaystyle A=C\times {\tfrac {R}{2}}} 1793:"the Insane", announcing the downfall of 596:Abraham bar Ḥiyya wrote all his works in 185:and was likely the earliest to introduce 3014:. In Thomas Hockey; et al. (eds.). 3012:"Bar Ḥiyya: Abraham Bar Ḥiyya Savasorda" 2414: 2412: 2410: 2386: 2377: 2276: 2261: 2259: 2113:. In Thomas Hockey; et al. (eds.). 2111:"Bar Ḥiyya: Abraham Bar Ḥiyya Savasorda" 1804: 3049:MacTutor History of Mathematics Archive 2739: 2692: 2690: 2143: 2141: 2139: 1828:the following equation for any circle: 1188:Maimonidean / Anti-Maimonidean 694:). This work was published in 1851, in 3088: 2656: 2641: 2549: 607: 3018:. New York: Springer. pp. 95–6. 2677:Zeitschrift für Mathematik und Physik 2598: 2555: 2461: 2418: 2407: 2256: 2117:. New York: Springer. pp. 95–6. 2104: 2102: 2034: 1947:Golden age of Jewish culture in Spain 511:Bar Ḥiyya's most notable work is his 2696: 2687: 2512: 2395:(2). Franz Steiner Verlag: 129–140. 2320:Journal for the History of Astronomy 2288:Illustriertes Lexikon der Astronomie 2243: 2204: 2202: 2200: 2198: 2196: 2164:10.1093/acref/9780227679319.001.0001 2147: 2136: 1606:Whether composed especially for the 663:"Tables" or "Tables of the Prince" ( 459:Yesode ha-Tebunah u-Migdal ha-Emunah 2464:The Itinerary of Benjamin of Tudela 2369:Millás Vallicrosa, José M. (1959). 2290:. Leipzig: J. J. Weber. p. 5. 1989: 748:An apologetic epistle addressed to 729: 714: 691: 668: 653: 618: 520: 466: 313: 221:, translated in 1145 into Latin as 217:. His most influential work is his 130:ר׳ אַבְרָהָם בַּר חִיָּיא הַנָשִׂיא 129: 31: 13: 2849:; et al., eds. (1901–1906). " 2659:The Messiah Idea in Jewish History 2099: 2042:Dictionary of Scientific Biography 2014:; et al., eds. (1901–1906). " 1815:Ḥibbur ha-meshīḥah ve-ha-tishboret 1625: 542:made the Latin translation of the 513:Ḥibbur ha-Meshiḥah ve-ha-Tishboret 308:, and bore the title of governor ( 219:Ḥibbur ha-Meshiḥah ve-ha-Tishboret 14: 3187: 3003: 2193: 2077:; et al., eds. (1901–1906). 1817:contains the first appearance of 565:("Contemplation of the Soul") on 2968:Boaz Tsaban & David Garber. 2859:. New York: Funk & Wagnalls. 2835: 2233:. New York: Funk & Wagnalls. 2208: 2087:. New York: Funk & Wagnalls. 2063: 2024:. New York: Funk & Wagnalls. 2000: 1909:is the circumference length and 864: 3166:Medieval Spanish mathematicians 2987: 2948: 2936: 2924: 2911: 2899: 2887: 2875: 2863: 2829: 2817: 2805: 2793: 2773: 2761: 2756:Bibliothèque Nationale of Paris 2748: 2740:Haskins, Charles Homer (1967). 2733: 2650: 2635: 2592: 2506: 2497: 2484: 2455: 2362: 2156:Encyclopedia of the Middle Ages 1969: 1959: 831:Liber Augmenti et Diminutionis, 756: 750:Judah ben Barzilai al-Barzeloni 302:Talmudic academies in Babylonia 139:– 1136 or 1145), also known as 3060:Warszawski, Jean-Marc (2006). 2311: 2302: 2237: 2180: 1800: 1132:Mansur ibn Sulayman al-Ghamari 1: 2462:Adler, Marcus Nathan (1907). 2215:Sacerdote, G.; Guttmann, J.; 2028: 1771:superstitions of the tequfoth 1642:"Reflections on the Soul" as 844: 631:Erasmus Oswald Schreckenfuchs 280:, and influenced the work of 133: 43: 3146:Medieval Catalan astronomers 3010:Langermann, Y. Tzvi (2007). 2109:Langermann, Y. Tzvi (2007). 2092: 1347:Eliezer ben Elijah Ashkenazi 575:Liber de redemptione Israhel 287: 273:{\displaystyle x^{2}-ax+b=c} 7: 3156:Medieval Jewish astronomers 3151:Medieval Jewish astrologers 3136:Philosophers from Catalonia 3126:12th-century Catalan rabbis 3121:12th-century mathematicians 3116:11th-century mathematicians 2675:(1867). "Abraham Judaeus". 2657:Greenstone, Julius Hillel. 2246:HaMaayan / The Torah Spring 2221:"Abraham bar Ḥiyya ha-Nasi" 2079:"Abraham bar Hiyya ha-Nasi" 2037:"Abraham bar Hiyya Ha-Nasi" 1940: 446:the intermediaries between 324: 10: 3192: 3161:Medieval Jewish scientists 2340:10.1177/002182860103200203 2286:Drechsler, Adolph (1881). 1688:Three Classes of Pious Men 1599:was originally written in 1462:Menachem Mendel Schneerson 1342:Elijah Ba'al Shem of Chelm 833:a treatise on mathematics. 773:with their translation of 724:"Scroll of the Revealer" ( 717:), an ethical work upon a 709:"Meditation of the Soul" ( 3141:Scientists from Catalonia 3131:Arabic–Hebrew translators 2996:, 8a in the Vilna edition 2851:ABRAHAM BAR ḤIYYA HA-NASI 2784:Die Spuren Al-Baṭlajûsis, 2642:Graetz, Heinrich (1892). 2494:, Part 1, Vol. 1, p. 157. 2158:. James Clarke & Co. 2045:. Vol. 1. New York: 2016:Abraham bar Ḥiyya ha-Nasi 1993:), 'Chief of the Police'. 1372:Simcha Bunim of Peshischa 1165:Hibat Allah Abu'l-Barakat 923:Aristobulus of Alexandria 686:"Book of Intercalation" ( 467:יסודי התבונה ומגדל האמונה 122:Abraham bar Ḥiyya ha-Nasi 115: 101: 94: 80: 62: 39: 28: 23:Abraham bar Ḥiyya ha-Nasi 21: 3111:12th-century astrologers 3106:11th-century astrologers 3054:University of St Andrews 2786:p. 28, and Bacher, 1952: 1824:Bar Ḥiyya proved by the 1337:Joseph Solomon Delmedigo 792:De Horarum Electionibus, 29: 2856:The Jewish Encyclopedia 2711:10.2979/ALE.2001.-.1.59 2269:Judaism and Its History 2230:The Jewish Encyclopedia 2084:The Jewish Encyclopedia 2047:Charles Scribner's Sons 2021:The Jewish Encyclopedia 1595:'s assumption that the 800:astrological aphorisms. 486:mathematical operations 425: 225:. A Hebrew treatise on 2673:Steinschneider, Moritz 2466:. New York. p. 2. 2227:; et al. (eds.). 2035:Levey, Martin (1970). 1933:(12th century) on the 1923: 1903: 1883: 1863: 1826:method of indivisibles 1810: 1657: 1608:Ten Days of Repentance 1397:Isaac Orobio de Castro 1367:Shneur Zalman of Liadi 1064:Shem-Tov ibn Falaquera 798:Capitula Centiloquium, 274: 3171:Rabbis from Barcelona 2800:Ethik des Maimonides, 1924: 1904: 1889:is the surface area, 1884: 1864: 1808: 1777:, a firm believer in 1648: 1638:and of the author of 1407:Samuel David Luzzatto 1377:Samson Raphael Hirsch 998:Spanish and European: 966:Ibn Bajjah (Avempace) 613:"Form of the Earth" ( 521:חיבור המשיחה והתשבורת 275: 3040:Robertson, Edmund F. 2908:p. 201, note 2. 1913: 1893: 1873: 1832: 1783:Megillat ha-Megalleh 1751:Messianic redemption 1109:Judah Leon Abravanel 669:לוחות or לוחות הנשיא 654:חשבון מהלכות הכוכבים 579:Megillat ha-Megalleh 571:Megillat ha-Megalleh 236: 3044:"Abraham bar Hiyya" 3038:O'Connor, John J.; 2332:2001JHA....32..130G 1819:quadratic equations 1636:Solomon ibn Gabirol 1539:Microcosm–macrocosm 1457:Joseph Soloveitchik 1127:Natan'el al-Fayyumi 928:Philo of Alexandria 852:Part of a series on 608:Other notable works 548:Practica Geometriae 490:business arithmetic 172:County of Barcelona 145:Abraham Albargeloni 56:County of Barcelona 32:אברהם בר חייא הנשיא 3176:Jewish astronomers 2921:pp. 199, 200. 2770:1900, p. 195. 2754:Manuscript in the 2049:. pp. 22–23. 1919: 1899: 1879: 1859: 1857: 1811: 1452:Abraham Isaac Kook 1432:Monsieur Chouchani 1034:Joseph ibn Tzaddik 1004:Hasdai ibn Shaprut 971:Ismaili philosophy 961:Brethren of Purity 837:In the preface to 534:, under the title 351:Benjamin of Tudela 306:minister of police 294:Hezekiah ben David 270: 231:quadratic equation 227:practical geometry 85:Quadratic equation 3025:978-0-387-31022-0 2894:Ḥobot ha-Lebabot, 2188:Hegyon ha-Nefesh, 2173:978-0-19-518817-2 2151:Abraham Bar Hiyya 2124:978-0-387-31022-0 2056:978-0-684-10114-9 1935:Babylonian Talmud 1922:{\displaystyle R} 1902:{\displaystyle C} 1882:{\displaystyle A} 1856: 1591:in refutation of 1585: 1584: 1422:Eliezer Berkovits 1412:Elijah Benamozegh 1402:Moses Mendelssohn 1317:Francisco Sanches 1276:Reconstructionist 1079:Isaac ben Sheshet 1074:Moses of Narbonne 1054:Samuel ibn Tibbon 1014:Abraham bar Hiyya 858:Jewish philosophy 825:Rudolph de Bruges 627:Sebastian Münster 546:the basis of his 529: 475: 436:Jews of Catalonia 398:Catalonia joined 393:Jews of Catalonia 336: 322: 207:Jewish philosophy 141:Abraham Savasorda 119: 118: 96:Scientific career 3183: 3077: 3075: 3073: 3056: 3029: 2997: 2991: 2985: 2984: 2982: 2981: 2972:. 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The 610: 532:Plato of Tivoli 428: 416:southern France 414:in what is now 408:Crown of Aragon 370:Jewish calendar 360:and teacher of 290: 243: 239: 237: 234: 233: 223:Liber embadorum 179:Islamic science 166:who resided in 149:Abraham Judaeus 136: 108: 89:Hebrew calendar 87: 76: 67: 58: 49: 46: 35: 24: 17: 12: 11: 5: 3189: 3179: 3178: 3173: 3168: 3163: 3158: 3153: 3148: 3143: 3138: 3133: 3128: 3123: 3118: 3113: 3108: 3103: 3098: 3084: 3083: 3078: 3057: 3035: 3024: 3005: 3004:External links 3002: 2999: 2998: 2986: 2960: 2947: 2935: 2923: 2919:Monatsschrift, 2910: 2906:Monatsschrift, 2898: 2886: 2874: 2862: 2828: 2816: 2814:pp. 1, 2. 2804: 2792: 2772: 2768:Monatsschrift, 2760: 2747: 2732: 2686: 2664: 2661:. p. 134. 2649: 2646:. p. 320. 2634: 2613:10.1086/346637 2591: 2570:10.1086/368570 2548: 2521:(4): 566–569. 2505: 2496: 2483: 2454: 2433:10.1086/348115 2427:(3): 257–264. 2406: 2376: 2361: 2310: 2301: 2275: 2255: 2236: 2192: 2179: 2172: 2135: 2123: 2097: 2096: 2094: 2091: 2090: 2089: 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Index

Barcelona
County of Barcelona
Narbonne
Provence
Quadratic equation
Hebrew calendar
Astronomy
Mathematics
Hebrew
Catalan Jewish
mathematician
astronomer
philosopher
Barcelona
County of Barcelona
Islamic science
Latin
algebra
Muslim world
Christian Europe
mathematics
astronomy
Jewish philosophy
chronology
surveying
practical geometry
quadratic equation
Fibonacci
Hezekiah ben David
Gaon

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