Abraham bar Ḥiyya ha-Nasi (;
– 1136 or 1145), also known as Abraham Savasorda, Abraham Albargeloni, and Abraham Judaeus, was a Catalan Jewish
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
,
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
and
philosopher
A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...
who resided in
Barcelona
Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...
.
Bar Ḥiyya was active in translating the works of
Islamic science
Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Umayyads of Córdoba, the Abbadids of Seville, the Samanids, the Ziyarids, the Buyids in Persia, the Abbasid Caliphate and ...
into
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
, and was likely the earliest to introduce Arabic algebra into
Christian Europe
Christendom historically refers to the Christian states, Christian-majority countries and the countries in which Christianity dominates, prevails,SeMerriam-Webster.com : dictionary, "Christendom"/ref> or is culturally or historically intertwine ...
. He also wrote several original works on
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
,
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
,
Jewish philosophy
Jewish philosophy () includes all philosophy carried out by Jews, or in relation to the religion of Judaism. Until modern ''Haskalah'' (Jewish Enlightenment) and Jewish emancipation, Jewish philosophy was preoccupied with attempts to reconcile ...
,
chronology
Chronology (from Latin ''chronologia'', from Ancient Greek , ''chrónos'', "time"; and , '' -logia'') is the science of arranging events in their order of occurrence in time. Consider, for example, the use of a timeline or sequence of events. I ...
, and
land surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ca ...
. His most influential work is his ''Ḥibbur ha-Meshiḥah ve-ha-Tishboret'', translated in 1145 into Latin as ''Liber embadorum''. A Hebrew treatise on
practical
Pragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. ...
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
and Islamic algebra, the book contains the first known complete solution of the
quadratic equation
In algebra, a quadratic equation () is any equation that can be rearranged in standard form as
ax^2 + bx + c = 0\,,
where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equati ...
, and influenced the work of
Leonardo Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western ...
.
Biography
Abraham bar Ḥiyya was the great-grandson of the
Hezekiah Gaon Hezekiah Gaon or Hezekiah ben David ( he, חזקיה בן דוד) was the last Gaon of the Talmudic academy in Pumbedita from 1038–40.
Hezekiah ben David was a member of the House of Exilarchs, his father David was the son of Zakkai. Some scho ...
. Bar Ḥiyya occupied a high position in the royal court, serving as minister of police, and bore the title of governor (). Scholars assume that Bar Hiyya would have obtained this title in the court of
Banu Hud
The Banu Hud ( ar, بنو هود ', the Hudid dynasty) were an Arab dynasty that ruled the ' of Zaragoza from 1039 until 1110.
In 1039, under the leadership of Al-Mustain I, Sulayman ibn Hud al-Judhami, the Bani Hud seized control of Zaragoza f ...
of Saragossa-Lerida; there is even a record of a Jewish Savasorda there in the beginning of the 12th century. In his travelogues,
Benjamin of Tudela
Benjamin of Tudela ( he, בִּנְיָמִין מִטּוּדֶלָה, ; ar, بنيامين التطيلي ''Binyamin al-Tutayli''; Tudela, Kingdom of Navarre, 1130 Castile, 1173) was a medieval Jewish traveler who visited Europe, Asia, an ...
mentions bar Ḥiyya living in Barcelona in the 1160s.
According to Adolph Drechsler, bar Ḥiyya was a pupil of Rabbi
Moshe haDarshan
Moshe haDarshan (circa early 11th century) ( he, משה הדרשן, trans. "Moses the preacher") was chief of the yeshiva of Narbonne, and perhaps the founder of Jewish exegetical studies in France. Along with Rashi, his writings are often cited ...
and teacher of Abraham Ibn Ezra. 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. 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. Other works included papers on astrology, trigonometry, and music.
Some scholars think that the Magister Abraham who dictated ''De Astrolabio'' (probably at
Toulouse
Toulouse ( , ; oc, Tolosa ) is the prefecture of the French department of Haute-Garonne and of the larger region of Occitania. The city is on the banks of the River Garonne, from the Mediterranean Sea, from the Atlantic Ocean and from Par ...
) to Rudolf de Bruges (a work that the latter finished in 1143) was identical with Abraham bar Ḥiyya. Although the title "
Sephardi
Sephardic (or Sephardi) Jews (, ; lad, Djudíos Sefardíes), also ''Sepharadim'' , Modern Hebrew: ''Sfaradim'', Tiberian Hebrew, Tiberian: Səp̄āraddîm, also , ''Ye'hude Sepharad'', lit. "The Jews of Spain", es, Judíos sefardíes (or ), ...
" 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
Jews of Catalonia
Jews of Catalonia (Catalonian Jewry, Catalonian Judaism, in Hebrew: יהדות קטלוניה) is the Jewish community that lived in the Iberian Peninsula, in the Lands of Catalonia, Valencia and Mallorca until the expulsion of 1492. Its splendor ...
. Catalonia joined
Provence
Provence (, , , , ; oc, Provença or ''Prouvènço'' , ) is a geographical region and historical province of southeastern France, which extends from the left bank of the lower Rhône to the west to the Italian border to the east; it is bor ...
in 1112 and
Aragon
Aragon ( , ; Spanish and an, Aragón ; ca, Aragó ) is an autonomous community in Spain, coextensive with the medieval Kingdom of Aragon. In northeastern Spain, the Aragonese autonomous community comprises three provinces (from north to sou ...
in 1137, and thus the
County of Barcelona
The County of Barcelona ( la, Comitatus Barcinonensis, ca, Comtat de Barcelona) was originally a frontier region under the rule of the Carolingian dynasty. In the 10th century, the Counts of Barcelona became progressively independent, heredi ...
became the capital of the Catalan-Aragonese Confederation called the
Crown of Aragon
The Crown of Aragon ( , ) an, Corona d'Aragón ; ca, Corona d'Aragó, , , ; es, Corona de Aragón ; la, Corona Aragonum . was a composite monarchy ruled by one king, originated by the dynastic union of the Kingdom of Aragon and the County of B ...
. The kings of the Crown of Aragon extended their domains to the
Occitan Occitan may refer to:
* Something of, from, or related to the Occitania territory in parts of France, Italy, Monaco and Spain.
* Something of, from, or related to the Occitania administrative region of France.
* Occitan language
Occitan (; o ...
countries in what is now
southern France
Southern France, also known as the South of France or colloquially in French language, French as , is a defined geographical area consisting of the regions of France that border the Atlantic Ocean south of the Marais Poitevin,Louis Papy, ''Le midi ...
. Abraham Albargeloni spent some time in Narbonne where he composed some works for the
Jews of Provence
The history of the Jews in France deals with Jews and Jewish communities in France since at least the Early Middle Ages. France was a centre of Jewish learning in the Middle Ages, but persecution increased over time, including multiple expulsio ...
, in which he complains of their Provençal Jewry's ignorance of mathematics.
Work
Abraham bar Ḥiyya was one of the most important figures in the scientific movement which made the
Jews of Provence
The history of the Jews in France deals with Jews and Jewish communities in France since at least the Early Middle Ages. France was a centre of Jewish learning in the Middle Ages, but persecution increased over time, including multiple expulsio ...
, the
Jews of Catalonia
Jews of Catalonia (Catalonian Jewry, Catalonian Judaism, in Hebrew: יהדות קטלוניה) is the Jewish community that lived in the Iberian Peninsula, in the Lands of Catalonia, Valencia and Mallorca until the expulsion of 1492. Its splendor ...
,
Spain
, image_flag = Bandera de España.svg
, image_coat = Escudo de España (mazonado).svg
, national_motto = ''Plus ultra'' (Latin)(English: "Further Beyond")
, national_anthem = (English: "Royal March")
, i ...
, and
Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...
the intermediaries between
Arabic science
Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Umayyads of Córdoba, the Abbadids of Seville, the Samanids, the Ziyarids, the Buyids in Persia, the Abbasid Caliphate and ...
and the
Christian
Christians () are people who follow or adhere to Christianity, a monotheistic Abrahamic religion based on the life and teachings of Jesus Christ. The words ''Christ'' and ''Christian'' derive from the Koine Greek title ''Christós'' (Χρι ...
world, in both his original works and his translations.
Bar Ḥiyya's ''Yesode ha-Tebunah u-Migdal ha-Emunah'' (, usually referred to as the ''Encyclopedia'', 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
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
,
mathematical operations
In mathematics, an operation is a function which takes zero or more input values (also called "''operands''" or "arguments") to a well-defined output value. The number of operands is the arity of the operation.
The most commonly studied operat ...
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
,
optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
, and
music
Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...
. The book draws from a number of Greek sources then available in Arabic, as well as the works of al-Khwarizmi and
Al-Karaji
( fa, ابو بکر محمد بن الحسن الکرجی; c. 953 – c. 1029) was a 10th-century Persian people, Persian mathematician and engineer who flourished at Baghdad. He was born in Karaj, a city near Tehran. His three principal sur ...
. Only a few short fragments of this work have been preserved.
Bar Ḥiyya's most notable work is his ''Ḥibbur ha-Meshiḥah ve-ha-Tishboret'' (), probably intended to be a part of the preceding work. This is the celebrated geometry translated in 1145 by
Plato of Tivoli Plato Tiburtinus ( la, Plato Tiburtinus, "Plato of Tivoli"; fl. 12th century) was a 12th-century Italian mathematician, astronomer and translator who lived in Barcelona from 1116 to 1138. He is best known for translating Hebrew and Arabic document ...
, under the title ''Liber embadorum a Savasordo in hebraico compositus''.
Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western ...
made the Latin translation of the ''Ḥibbūr'' the basis of his ''Practica Geometriae'', following it even to the sameness of some of the examples.
Bar Ḥiyya also wrote two religious works in the field of
Judaism
Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in the ...
repentance
Repentance is reviewing one's actions and feeling contrition or regret for past wrongs, which is accompanied by commitment to and actual actions that show and prove a change for the better.
In modern times, it is generally seen as involving a co ...
, and ''Megillat ha-Megalleh'' ("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 ''Liber de redemptione Israhel''. Even these religious works contain scientific and philosophical speculation. His ''Megillat ha-Megalleh'' was also
astrological
Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Dif ...
in nature, and drew a horoscope of favourable and unfavourable days. Bar Ḥiyya forecasted that the
Messiah
In Abrahamic religions, a messiah or messias (; ,
; ,
; ) is a saviour or liberator of a group of people. The concepts of ''mashiach'', messianism, and of a Messianic Age originated in Judaism, and in the Hebrew Bible, in which a ''mashiach'' ...
would appear in AM 5118 (1358 CE).
Abraham bar Ḥiyya wrote all his works in
Hebrew
Hebrew (; ; ) is a Northwest Semitic language of the Afroasiatic language family. Historically, it is one of the spoken languages of the Israelites and their longest-surviving descendants, the Jews and Samaritans. It was largely preserved ...
, not in
Judaeo-Arabic
Judeo-Arabic dialects (, ; ; ) are ethnolects formerly spoken by Jews throughout the Arabic-speaking world. Under the ISO 639 international standard for language codes, Judeo-Arabic is classified as a macrolanguage under the code jrb, encomp ...
of the earlier Jewish scientific literature, which made him a pioneer in the use of the Hebrew language for scientific purposes.
Other notable works
* "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. A portion was translated into
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
by
Sebastian Münster
Sebastian Münster (20 January 1488 – 26 May 1552) was a German cartographer and cosmographer. He also was a Christian Hebraist scholar who taught as a professor at the University of Basel. His well-known work, the highly accurate world map, '' ...
Bodleian Library
The Bodleian Library () is the main research library of the University of Oxford, and is one of the oldest libraries in Europe. It derives its name from its founder, Sir Thomas Bodley. With over 13 million printed items, it is the second- ...
contains a copy with a commentary, apparently by Ḥayyim Lisker.
* "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.
* "Tables" or "Tables of the Prince" (, ''Luḥot ha-Nasi''), astronomical tables, called also the "Tables of
Al-Battani
Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī ( ar, محمد بن جابر بن سنان البتاني) ( Latinized as Albategnius, Albategni or Albatenius) (c. 858 – 929) was an astron ...
" and the "Jerusalem Tables". Several manuscripts of this work contain notes by Abraham ibn Ezra.
* "Book of Intercalation" (). This work was published in 1851, in
London
London is the capital and largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary down to the North Sea, and has been a majo ...
, by Filipowski. It is the oldest-known Hebrew work treating of the calculation of the
Hebrew calendar
The Hebrew calendar ( he, הַלּוּחַ הָעִבְרִי, translit=HaLuah HaIvri), also called the Jewish calendar, is a lunisolar calendar used today for Jewish religious observance, and as an official calendar of the state of Israel. I ...
.
* "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 learned introduction by Rapoport.
* "Scroll of the Revealer" (), a controversial work in defense of the theory that the
Messiah
In Abrahamic religions, a messiah or messias (; ,
; ,
; ) is a saviour or liberator of a group of people. The concepts of ''mashiach'', messianism, and of a Messianic Age originated in Judaism, and in the Hebrew Bible, in which a ''mashiach'' ...
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
Saturn
Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
and
Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...
Abraham bar Ḥiyya co-operated with a number of scholars in the translation of scientific works from
Arabic
Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...
into
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
, most notably
Plato of Tivoli Plato Tiburtinus ( la, Plato Tiburtinus, "Plato of Tivoli"; fl. 12th century) was a 12th-century Italian mathematician, astronomer and translator who lived in Barcelona from 1116 to 1138. He is best known for translating Hebrew and Arabic document ...
with their translation of
Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
's ''
Tetrabiblos
''Tetrabiblos'' () 'four books', also known in Greek as ''Apotelesmatiká'' () "Effects", and in Latin as ''Quadripartitum'' "Four Parts", is a text on the philosophy and practice of astrology, written in the 2nd century AD by the Alexandrian ...
'' in 1138 at
Barcelona
Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...
. 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:
* ''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
The ''Centiloquium'' (= "one hundred sayings"), also called ''Ptolemy's Centiloquium'', is a collection of one hundred aphorisms about astrology and astrological rules. It is first recorded at the start of the tenth century CE, when a commentary ...
'', attributed to
Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
.
* ''De Astrolabio'' of Rudolph de Bruges.
* ''Liber Augmenti et Diminutionis,'' a treatise on mathematics.
In the preface to ''Ẓurat ha-Areẓ'', 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.
Philosophy
Bar Ḥiyya was a pioneer in the field of philosophy: as shown by
Guttmann Guttmann is a surname. It may refer to the following people:
* Artur Guttmann (1891–1945), Austrian film score composer
* Béla Guttmann (1900–1981), Hungarian football (soccer) player and coach
* Jakob Guttmann (rabbi) (1845–1919), Germa ...
in refutation of
David Kaufmann
David Kaufmann (7 June 1852 – 6 July 1899) (Hebrew: דוד קויפמן) was a Jewish-Austrian scholar born at Kojetín, Moravia (now in the Czech Republic). From 1861 to 1867 he attended the gymnasium at Kroměříž, Moravia, where he studie ...
's assumption that the ''Hegyon ha-Nefesh'' was originally written in
Arabic
Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...
, Abraham bar 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
The Ten Days of Repentance ( he, עֲשֶׂרֶת יְמֵי תְּשׁוּבָה, ''ʿǍseret yəmēy təšūvā'') Hebrew aˈseʁet jeˈmeiː teʃuːˈvaːhare the first ten days of the Hebrew month of Tishrei, usually ...
, 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 Hafṭarot of the
Day of Atonement
Yom Kippur (; he, יוֹם כִּפּוּר, , , ) is the holiest day in Judaism and Samaritanism. It occurs annually on the 10th of Tishrei, the first month of the Hebrew calendar. Primarily centered on atonement and repentance, the day's ...
and
Shabbat Shuvah
Special Shabbatot are Jewish Shabbat days on which special events are commemorated. Variations in the liturgy and special customs differentiate them from the regular Sabbaths and each one is referred to by a special name; many communities also a ...
. 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.
Matter and Form
Abraham bar Ḥiyya's philosophical system is
neoplatonic
Neoplatonism is a strand of Platonic philosophy that emerged in the 3rd century AD against the background of Hellenistic philosophy and religion. The term does not encapsulate a set of ideas as much as a chain of thinkers. But there are some ide ...
like that of
ibn Gabirol
Solomon ibn Gabirol or Solomon ben Judah ( he, ר׳ שְׁלֹמֹה בֶּן יְהוּדָה אִבְּן גָּבִּירוֹל, Shlomo Ben Yehuda ibn Gabirol, ; ar, أبو أيوب سليمان بن يحيى بن جبيرول, ’Abū ’Ayy ...
and of the author of ''Torot ha-Nefesh'' ('Reflections on the Soul'), as
Plotinus
Plotinus (; grc-gre, Πλωτῖνος, ''Plōtînos''; – 270 CE) was a philosopher in the Hellenistic philosophy, Hellenistic tradition, born and raised in Roman Egypt. Plotinus is regarded by modern scholarship as the founder of Neop ...
stated:
: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 bar Ḥiyya, in common with
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
, and others:
For after all, says he with
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
, 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. But, precisely as man has been set apart among his fellow creatures as God's servant, so
Israel
Israel (; he, יִשְׂרָאֵל, ; ar, إِسْرَائِيل, ), officially the State of Israel ( he, מְדִינַת יִשְׂרָאֵל, label=none, translit=Medīnat Yīsrāʾēl; ), is a country in Western Asia. It is situated ...
is separate from the nations, the same three terms (''bara'', ''yaẓar'', asah'') being used by the prophet for Israel's creation as for that of man in
Genesis
Genesis may refer to:
Bible
* Book of Genesis, the first book of the biblical scriptures of both Judaism and Christianity, describing the creation of the Earth and of mankind
* Genesis creation narrative, the first several chapters of the Book of ...
.
Three Classes of Pious Men
Like Baḥya, Abraham bar 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").
# 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
The Ten Commandments (Biblical Hebrew עשרת הדברים \ עֲשֶׂרֶת הַדְּבָרִים, ''aséret ha-dvarím'', lit. The Decalogue, The Ten Words, cf. Mishnaic Hebrew עשרת הדיברות \ עֲשֶׂרֶת הַדִּבְ ...
, containing the fundamental laws with especial reference to the God-devoted man who, like
Moses
Moses hbo, מֹשֶׁה, Mōše; also known as Moshe or Moshe Rabbeinu (Mishnaic Hebrew: מֹשֶׁה רַבֵּינוּ, ); syr, ܡܘܫܐ, Mūše; ar, موسى, Mūsā; grc, Mωϋσῆς, Mōÿsēs () is considered the most important pro ...
, 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
The Ten Commandments (Biblical Hebrew עשרת הדברים \ עֲשֶׂרֶת הַדְּבָרִים, ''aséret ha-dvarím'', lit. The Decalogue, The Ten Words, cf. Mishnaic Hebrew עשרת הדיברות \ עֲשֶׂרֶת הַדִּבְ ...
, which he considers merely as an introductory word, accentuates the divine origin and the eternal goal of the
Law
Law is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior,Robertson, ''Crimes against humanity'', 90. with its precise definition a matter of longstanding debate. It has been vario ...
; 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
Israelis ( he, יִשְׂרָאֵלִים, translit=Yīśrāʾēlīm; ar, الإسرائيليين, translit=al-ʾIsrāʾīliyyin) are the citizens and nationals of the State of Israel. The country's populace is composed primarily of Je ...
during their wandering in the desert or during the
Exile
Exile is primarily penal expulsion from one's native country, and secondarily expatriation or prolonged absence from one's homeland under either the compulsion of circumstance or the rigors of some high purpose. Usually persons and peoples suf ...
, to render them a holy congregation relying solely upon the special protection of God without resorting to warfare.
# The
Deuteronomic
Deuteronomy ( grc, Δευτερονόμιον, Deuteronómion, second law) is the fifth and last book of the Torah (in Judaism), where it is called (Hebrew: hbo, , Dəḇārīm, hewords Moses.html"_;"title="f_Moses">f_Moseslabel=none)_and_th ...
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.
Guttmann has shown that Naḥmanides read and used the ''Hegyon ha-Nefesh'', though occasionally differing from it; but while
Saadia Gaon
Saʻadiah ben Yosef Gaon ( ar, سعيد بن يوسف الفيومي ''Saʻīd bin Yūsuf al-Fayyūmi''; he, סַעֲדְיָה בֶּן יוֹסֵף אַלְפַיּוּמִי גָּאוֹן ''Saʿăḏyāh ben Yōsēf al-Fayyūmī Gāʾōn''; ...
is elsewhere quoted by Abraham bar Ḥiyya, he never refers to him in ''Hegyon''. Characteristic of the age is the fact that while Abraham bar Ḥiyya contended against every superstition, against the teḳufah, against prayers for the dead, and similar practises, he was, nevertheless, like Ibn Ezra, a firm believer in
astrology
Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of Celestial o ...
. 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. He wrote also a work on redemption, from which
Isaac Abravanel
Isaac ben Judah Abarbanel ( he, יצחק בן יהודה אברבנאל; 1437–1508), commonly referred to as Abarbanel (), also spelled Abravanel, Avravanel, or Abrabanel, was a Portuguese Jewish statesman, philosopher, Bible commentator ...
appropriated many ideas. It is in defense of Judaism against Christian arguments, and also discusses
Mohammed
Muhammad ( ar, مُحَمَّد; 570 – 8 June 632 CE) was an Arab religious, social, and political leader and the founder of Islam. According to Islamic doctrine, he was a prophet divinely inspired to preach and confirm the monoth ...
, "the Insane"; announcing the downfall of
Islam
Islam (; ar, ۘالِإسلَام, , ) is an Abrahamic religions, Abrahamic Monotheism#Islam, monotheistic religion centred primarily around the Quran, a religious text considered by Muslims to be the direct word of God in Islam, God (or ...
, according to astrological calculation, for the year 4946 A.M.
Mathematics
Bar Ḥiyya's ''Ḥibbur ha-meshīḥah ve-ha-tishboret'' contains the first appearance of
quadratic equations
In algebra, a quadratic equation () is any equation that can be rearranged in standard form as
ax^2 + bx + c = 0\,,
where represents an unknown value, and , , and represent known numbers, where . (If and then the equation is linear, not quadr ...
in the West.
Bar Ḥiyya proved by geometro-mechanical
method of indivisibles
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows:
* 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that pl ...
the following equation for any circle: , where is the surface area, is the circumference length and is radius. The same proof as appears in the commentary of the
Tosafists
Tosafists were rabbis of France and Germany, who lived from the 12th to the mid-15th centuries, in the period of Rishonim. The Tosafists composed critical and explanatory glosses (questions, notes, interpretations, rulings and sources) on the Tal ...
(12th century) on the
Babylonian Talmud
The Talmud (; he, , Talmūḏ) is the central text of Rabbinic Judaism and the primary source of Jewish religious law (''halakha'') and Jewish theology. Until the advent of modernity, in nearly all Jewish communities, the Talmud was the cente ...
Golden age of Jewish culture in the Iberian Peninsula
The golden age of Jewish culture in Spain, which coincided with the Middle Ages in Europe, was a period of Muslim rule during which, intermittently, Jews were generally accepted in society and Jewish religious, cultural, and economic life flou ...