Abraham bar Hiyya
Abraham bar Hiyya Ha-Nasi
|Died||1136 or 1145|
|Known for||Quadratic equation |
|Influenced||Abraham ibn Ezra |
Abraham bar Ḥiyya ha-Nasi (1070 Barcelona, Catalonia – 1136 or 1145 Narbonne, France) was a Jewish mathematician, astronomer and philosopher, also known as Savasorda (from the Arabic صاحب الشرطة Ṣāḥib al-Shurṭa "Chief of the Police") or Abraham Judaeus. He was born in Barcelona and scholars suspect he travelled to Narbonne where he is thought to have died.
Abraham bar Ḥiyya's most influential work is his Ḥibbūr ha-meshīḥah we-ha-tishboret ("Treatise on Measurement and Calculation"), a Hebrew treatise on Islamic algebra and practical geometry. It was translated in 1145 into Latin by Plato of Tivoli as Liber Embadorum (the same year Robert of Chester translated al-Khwārizmī's Algebra.) It contains the first complete solution of the quadratic equation x2 − ax + b = 0 known in Europe, and influenced the work of Leonardo Fibonacci.
Abraham bar Hiyya, great-grandson of Hezekiah Gaon is remembered in the world of mathematics for his role in the dissemination of the quadratic equation. Bar Hiyya wrote several scientific works in the fields of astronomy, mathematics, land surveying and calendar calculations. Abraham ben Chiya Albargeloni (b. 1065, d. 1136), also occupied a high position under another Mahometan prince al-Hud. He was a sort of minister of police (Zachib al-Shorta, hence Savasorda which literally means something like 'chief of police' but probably indicates a position of a courtier), and bore the title of prince. Savasorda is a Latinized degeneration of the Arabic title  and scholars assume that Bar Hiyya would have obtained this title in the court of Banu Hud of Saragossa-Lerida; there is even a record of a Jewish Savasorda there in the beginning of the 12th century. Zachib al-Shorta, meaning " Chief of the Police" is a large landed proprietor was then named, "Governor" or " Nasi" as he was called in Hebrew. By his name Savasorda he is known through the works of the Middle Ages. He was held in high consideration by the ruler he served on account of his astronomical knowledge, and had disputes with learned priests, to whom he demonstrated the accuracy of the Jewish calendar. He also praised astrology and drew a horoscope of favourable and unfavourable days. Abraham Albargeloni reckoned that the Messiah would appear in the year after the Creation 5118 (1358 CE).
Benjamin of Tudela, in the 1160s, starting his famous journey to the East, traveled first from Tudela, which is to the northeast of Soria (his birthplace), along the river Ebro to Saragossa and then further to Tortosa on the coast of the Mediterranean, before turning northwards along the coast, through Tarragona to Barcelona and Provence. He says of Barcelona: " Where there is a holy congregation, including sages, wise and illustrious men, such as R. Sheshet, R. Shealtiel, R. Solomon and R. Abraham, son of Chisdai".
According to Adolph Drechsler, he was a pupil of Rabbi Moshe haDarshan and teacher of Abraham Ibn Ezra. Abraham bar Hiyya is said to have been a great astronomer and wrote some works on Astronomy and Geography. One tells about the form of the earth, the elements and the structure of the spheres (Manuscripts may be in the Vatican, in Vienna and Paris); this work was printed in Basel by Oswald Schreckenfuchs, including a Latin translation. Other works included papers on astrology, trigonometry and music.
He also wrote two religious works in the field of Judaism and the Hebrew Bible: Hegyon ha-Nefesh ("Contemplation of [the] Soul") on repentance and Megillat ha-Megalleh on the redemption of the Jewish people. Even these religious works contain scientific and philosophical speculation. His Megillat ha-Megalleh ("Scroll of the Revealer") was also astrological in nature. It claimed to forecast the messianic future 
Bar Hiyya wrote all his works in Hebrew, not in Judaeo-Arabic of the earlier Jewish scientific literature, which made him a pioneer in the use of the Hebrew language for scientific purposes. He also cooperated with Plato of Tivoli in the translation of scientific works from Arabic into Latin, particularly the translation of Ptolemy's Tetrabiblos in 1138 at Barcelona.
Some scholars think that the Magister Abraham who dictated De Astrolabio (probably at Toulouse) to Rudolf de Bruges (a work that the latter finished in 1143) was identical with Abraham bar Ḥiyya. As the title "Sephardi" is always appended to his name, it is certain that he was Spanish. Nevertheless, he must have passed several years in what is now southern France, likely Narbonne, as he composed some works for the Jews of Provence, in which he complains of their Provençal Jewry's ignorance of mathematics.
Abraham bar Ḥiyya, together with Abraham ibn Ezra, occupies an important place in the history of Jewish science. He was, indeed, one of the most important figures in the scientific movement which made the Jews of Provence, Jews of Spain, and Italy the intermediaries between Mohammedan science and the Christian world. He aided this movement not only by original works, but also by translations and by acting as interpreter for another great translator, the celebrated Plato of Tivoli. Steinschneider has also shown that his original works were written in Hebrew and not, as some have thought, in Arabic. These original works are:
- יסודי התבונה ומגדל האמונה ("The Foundations of Understanding and the Tower of Faith"), an encyclopedic work, which is said to treat of arithmetic, geometry, optics, astronomy, and music. Unfortunately only a few short fragments of this work have been preserved (MSS. De Rossi Library, No. 1170; Berlin Library, No. 244; Munich Library, No. 36; and, under a false title, MSS. Bodleian, 1268, No. 7).
- חבור המשיחה והתשבורת ("Treatise on Geometry"), probably intended to be a part of the preceding work. This is the celebrated geometry translated in 1145 by Plato of Tivoli, under the title Liber Embadorum (see Boncompagni in Atti dell' Accademia dei Lincei, 1851, iv. 275; Hebr. Bibl. vii. 84; Serapeum, 1858, p. 34; it was edited by Steinschneider in the Publications of the Meḳiẓe Nirdamim, 1895, vol. xi.).
- צורת הארץ ("Form of the Earth"), 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 (see No. 4). A portion was translated into Latin by Sebastian Münster and by Erasmus Oswald Schreckenfuchs. It appears also that complete translations into Latin and French were made (Steinschneider, Abraham Judæus, 12). MS. 2033 in the Bodleian Library at Oxford contains a copy with a commentary, apparently by Ḥayyim Lisker.
- חשבון מהלכות הכוכבים ("Calculation of the Courses of the Stars"), the sequel to the preceding work, which is found sometimes in manuscripts with the notes of Abraham ibn Ezra (MS. 37 of Leyden, according to the catalogue of Steinschneider, p. 147; MS. 203 of Rome, Bibl. Casanatense, according to the catalogue of Gustavo Sacerdote.
- לוחות or לוחות הנשיא ("Tables" or "Tables of the Prince"), astronomical tables, called also Tables of Al-Battani, because the author followed the Arabic astronomer of that name (see Battani). Several manuscripts of this work contain notes by Abraham ibn Ezra, and this fact has occasioned some confusion between the "Tables" of these two authors.
- ספר העבור ("Book of Intercalation"). This work was published in 1851, in London, by Filipowski. It is the oldest Hebrew work treating of the calculation of the Hebrew calendar.
- הגיון הנפש ("Meditation of the Soul"), an ethical work upon a rationalistic religious basis. It was published in 1860 by Freimann, with a biography of the author (by the editor), a list of his works, and a learned introduction by Rapoport.
- מגלת המגלה ("Scroll of the Revealer"), a controversial work, in defense of the theory that the Messiah would appear in the year 5118 (1358; MS. Munich, 103, ).
- An apologetic epistle addressed to Judah ben Barzilai al-Barzeloni.
As has already been stated, Abraham bar Ḥiyya assisted a number of scholars in their translations of scientific works. But there is still a great deal of 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. It is only possible, therefore, to give the titles of the works thus translated, without touching upon the question of authorship, or inquiring into the language of the originals, as follows:
- De Horarum Electionibus, the well-known treatise of Ali ben Aḥmad al-Imrani.
- Capitula Centiloquium, astrological aphorisms.
- A commentary of Aḥmad ibn Yusuf on the Centiloquium, attributed to Ptolemy.
- De Astrolabio of Rudolph de Bruges.
- Liber Augmenti et Diminutionis, a treatise on mathematics; a manuscript in the Bibliothèque Nationale of Paris (7377 A).
Abraham b. Ḥiyya or (as Rapoport in his introduction to the Hegyon ha-Nefesh, p. 63, suggests) Ḥayya, so as to rime with "Zakkaya", was a pioneer in his field of work. In the preface to his book, Ẓurat ha-Areẓ he modestly states that, because none of the scientific works such as exist in Arabic was 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.
As a moral philosopher
Not only as mathematician and astronomer, but also as moral philosopher, the author of the profoundly religious work, Hegyon ha-Nefesh (Meditation of the Soul) deserves special notice. In this field of philosophy he had also pioneer work to do; for, as is shown by Guttmann (Monatsschrift, 1900, p. 195), in refutation of Kaufmann's assumption that the Hegyon ha-Nefesh was originally written in Arabic (Z. D. M. G. xxx. 364; Die Spuren Al-Baṭlajûsis, p. 28, and Bacher, Die Bibelexegese der Jüdischen Religionsphilosophen des Mittelalters, p. 82), Abraham b. Ḥiyya had to wrestle with the difficulties of a language not yet adapted to philosophic terminology.
Whether composed especially for the Ten Days of Repentance, as Rapoport (ibid.) and Rosin (Ethik des Maimonides, p. 15) 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 Hafṭarot of the Day of Atonement and Shabbat Shuvah. In it, with the fervor of a holy preacher, 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 sages of the heathen world 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 (Hegyon, pp. 1, 2). In his opinion the non-Jew may attain to as high a degree of godliness as the Jew (Hegyon, p. 8a).
Matter and Form
- 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 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 "tohu va-bohu"; 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.
Says Abraham b. Ḥiyya, in common with Aristotle (Ethics, vii. 11), and others:
Greater is he who has succeeded in training himself to abandon every thought of worldly passion and longs only for the service and adoration of the Most High, than he who has still to wrestle with the appetites of the flesh, though he overcome them in the end.
For after all, says he with Plato (Phædo, p. 64), the soul in this world of flesh is, as it were, 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 fasting or other forms of asceticism except such as the law has prescribed (Hegyon, p. 16a). But, precisely as man has been set apart among his fellow creatures as God's servant, so Israel is separate from the nations (Hegyon, p. 7), the same three terms (bara, yaẓar, 'asah) being used by the prophet for Israel's creation (Isa. xliii. 7) as for that of man in Genesis.
Three Classes of Pious Men
Like Baḥya (Ḥobot ha-Lebabot, ix. 3) Abraham b. Ḥiyya distinguishes three classes of pious men:
- 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"; Alfarabi, Model State; see Guttmann, ib. p. 212, note)
- 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 city")
- 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").
In accordance with these three classes of servants of God, he finds the laws of the Torah to be divided into three groups:
- The Decalogue, containing the fundamental laws with especial reference to the God-devoted man who, like Moses, 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 Ten Commandments, which he considers merely as an introductory word, accentuates the divine origin and the eternal goal of the Law; 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.
- The group of laws contained in the second, third, and fourth books of Moses, intended for the people of Israel during their wandering in the desert or during the Exile, to render them a holy congregation relying solely upon the special protection of God without resorting to warfare.
- The Deuteronomic legislation intended for the people living in an agricultural state and forming a "kingdom of justice." However, in the time of the Messianic redemption, 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.
Against Rapoport, Guttmann has shown (Monatsschrift, p. 201, note 2) that Naḥmanides read and used the Hegyon ha-Nefesh, though occasionally differing from it; but while Saadia is elsewhere quoted by Abraham b. Ḥiyya, he never refers to him in Hegyon (Guttmann, in Monatsschrift, pp. 199, 200). Characteristic of the age is the fact that while Abraham b. Ḥiyya contended against every superstition, against the teḳufah (Sefer ha-'Ibbur, p. 8), against prayers for the dead (Hegyon, p. 32a), and similar practises (ib. p. 40a), he was, nevertheless, like Ibn Ezra, a firm believer in astrology. In his Megillat ha-Megalleh he calculated from Scripture the exact time for the advent of the Messiah to be the year of the world 5118 (see Ben Chananja, 1869, iv. 7, 8). He wrote also a work on redemption, from which Isaac Abravanel appropriated many ideas. It is in defense of Judaism against Christian arguments, and also discusses Mohammed, "the Insane"; announcing the downfall of Islam, according to astrological calculation, for the year 4946 A.M.
Avraam proved by geometro-mechanical method of indivisibles the following equation for any circle: S = LxR/2, where S is the surface area, L is the circumference length and R is radius.
The same proof as appears in the commentary of the Tosafists (12th century) on the Babylonian Talmud, tractate Sukkah, 8a in the Vilna edition:
- Langermann, Y. Tzvi (2007). "Bar Ḥiyya: Abraham Bar Ḥiyya Savasorda". In Thomas Hockey; et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 95–6. ISBN 978-0-387-31022-0. (PDF version)
- Hebrew: אברהם בר חייא הנשיא Abraham son of [Rabbi] Hiyya "the Prince". Also Abraham ben Chija, "Abraham ben Hiyya alBargeloni"(The Jewish Encyclopedia Volume 1, Page 322), "Abraham ben Chiya albargeloni Ha'Nasi" (Hegion Ha'Nefesh by Abraham ben Chiya Ha'Nsi in, Printed in Leipzig, 1860, Page 40), "Rabeinu Avraham Bar Chiya HaNasi" (Sefer Yisodei HaTevuna uMigdal HaEmunah, by Rabeinu Avraham Bar Chiya HaNasi), "R' Avraham ben Chiya Hanasi mi'Barcelona" (Hamaayan / The Torah Spring, Edited by Shlomo Katz, Volume XII, Number 18, 16 Adar 5758, March 14, 1998, Page 4), Avraham ben Chiya Hanasi medinat Bartselona, Abraham ben Chiva (Judaism and its history: in two parts By Abraham Geiger and Charles Newburgh, Page 172), Abraham Ben Chaja (Allgemeine Enzyklopädie der Wissenschaften und der Künste, Part 1, Vol. 1, p. 157; Illustr. Lexikon der Astronomie, by Adolph Drechsler, Verlag J.J. Weber, Leipzig 1881, p. 5; Poggendorff’s Handwörterbuch, Volume I, A-L, 1863 Leipzig), Abraham ben Chaja ben Rabbi Chiya, or Chaja or Haija (The Biographical Dictionary of the Society for the Diffusion of Useful Knowledge--, Volume 1, part 1, by Society for the Diffusion of Useful Knowledge , Page 139), Rabbi Abrahamo Hispano filio Rabbi Haijae (Kepler and Hebrew astronomical tables, Journal for the History of Astronomy (ISSN 0021-8286), Vol. 32, Part 2, No. 107, p. 130 - 136 (2001), by B. R. Goldstein)
- Encyclopedia of the Middle Ages, Volume 1, By André Vauchez, Richard Barrie Dobson, Michael Lapidge, Page 8
- La obra Sefer Hesbon mahlekot ha-kokabim de Abraham bar Hiyya ha-Bargeloni, by Jose M. Millas Vallicrosa, Barcelona, 1959, pp. 13-14
- Judaism and its history, by Abraham Geiger, Page 290
- History of the Jews: from the earliest times to the present day. BY Prof Heinrich Graetz, 1892, Page 320.
- The Itinerary of Benjamin of Tudela, by Marcus Nathan Adler, New York, 1907, Page 2
- Allgemeine Enzyklopädie der Wissenschaften und der Künste, Part 1, Vol. 1, p. 157
- Illustr. Lexikon der Astronomie, by Adolph Drechsler, Verlag J.J. Weber, Leipzig 1881, p. 5
- Poggendorff’s Handwörterbuch, Volume I, A-L, 1863 Leipzig
- The Messiah idea in Jewish historyBy Julius Hillel Greenstone, Page 134
- Haskins, Charles Homer. (1967) Studies in the History of Mediaeval Science. New York: Frederick Ungar Publishing Co., p. 11.
- The Authorship of a Latin Treatise on the Astrolabe, by Raphael Levy © 1942 Medieval Academy of America
- Boaz Tsaban & David Garber. "The proof of Rabbi Abraham Bar Hiya Hanasi". Archived from the original on 2011-08-25. Retrieved 2011-03-28.
- Levey, Martin (1970). "Abraham bar Hiyya Ha-Nasi". Dictionary of Scientific Biography. 1. New York: Charles Scribner's Sons. pp. 22–23. ISBN 0-684-10114-9.
- This article incorporates text from a publication now in the public domain: Singer, Isidore; et al., eds. (1901–1906). "Abraham bar Hiyya ha-Nasi". Jewish Encyclopedia. New York: Funk & Wagnalls Company.. The JE cites the following works:
- Moritz Steinschneider, Z. D. M. G. 1876, p. 633;
- Steinschneider, Abraham Judœus, in Zeitschrift für Mathematik und Physik, 1867, xii. 1 et seq.;
- idem, Abraham ibn Ezra, ibid. 1880, xxv. 119, 125;
- idem, Hebr. Bibl. vii. 84;
- idem, Hebr. Uebers. pp. 502, 525, 529, 532, 550, 572, 585, 594, 972;
- idem, Cat. of Hebr. Manuscripts in the Library of Leyden, p. 148;
- idem, Hebr. Bibl. 1861, iv. 108-109 (where Rapoport's reading of the name "Ḥayyah," instead of "Ḥiyyah," is adopted); 1876, xvi. 90 (where the name "Albargeloni" is declared to be a pure invention).
- See also Brüll's Jahrb. ii. 189.
- Wolf, Bibliotheca Hebrœa, i. 51. iv. 761;
- Rapoport, preface to Hegyon ha-Nefesh;
- Boncompagni, in Atti dell' Accademia dei Lincei, 1863, p. 935;
- Woepke, Mémoire sur la Propagande des Chiffres, p. 80;
- Kerem Ḥemed, vii. 77;
- Geiger, Mosheh ben Maimon, p. 70;
- Henri Gross, Gallia Judaica, p. 369;
- Bacher, Die Bibelexegese der Jüdischen Religionsphilosophen vor Maimuni, ch. iv.G. Sa.
- Langermann, Y. Tzvi (2007). "Bar Ḥiyya: Abraham Bar Ḥiyya Savasorda". In Thomas Hockey; et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 95–6. ISBN 978-0-387-31022-0. (PDF version)
- O'Connor, John J.; Robertson, Edmund F., "Abraham bar Hiyya", MacTutor History of Mathematics archive, University of St Andrews.
- Jewish Encyclopedia article for Abraham bar Hiyyah[permanent dead link], by G. Sacerdote and J. Guttmann and Kaufmann Kohler.
- PDF biography
- musicologie.org Abraham bar Hiyya and music. Sources, editions, bibliography, comments. (In French)