The philosopher and astronomer Rabbi Abraham ibn Ezra ( c. 1140 ) established the symmetry of binomial coefficients, while a closed formula was obtained later by the talmudist and mathematician Levi ben Gerson ( better known as Gersonides ), in 1321.

: 1. the doctrine of the soul, in which Gersonides defends the theory of impersonal reason as mediating between God and man, and explains the formation of the higher reason ( or acquired intellect, as it was called ) in humanity — his view being thoroughly realist and resembling that of Avicebron ;

:" The view that God does not have foreknowledge of moral decisions which was advanced by ibn Daud and Gersonides ( Levi ben Gershom ) is not quite as isolated as Rabbi Bleich indicates, and it enjoys the support of two highly respected Achronim, Rabbi Yeshayahu Horowitz ( Shelah haKadosh ) and Rabbi Chaim ibn Attar ( Or haHayim haKadosh ).

Gersonides was also the earliest known mathematician to have used the technique of mathematical induction in a systematic and self-conscious fashion and anticipated Galileo ’ s error theory.

Gersonides believed that astrology was real, and developed a naturalistic, non-supernatural explanation of how it works.

Julius Guttman explained that for Gersonides, astrology was:

Gersonides concluded that the model was no good.

That challenge was finally answered, of course, by Copernicus three centuries later, but Gersonides was the only one to falsify the Alexandrian dogma-the first known instance of modern falsification philosophy.

This was the program of Jewish rationalist philosophers such as Saadia Gaon, Maimonides ( who was influenced by Ibn Sina aka Avicenna ), and Gersonides ( who was influenced by Ibn Roshd, aka Averroes ).

Thus instead there was a summary of the views of the most important medieval Jewish commentators, such as Abraham ibn Ezra, Rashi, Ramban, Radak, Sforno and Ralbag ( Gersonides ).

It is claimed that this is also the view expressed by some classical Jewish authorities, such as Abraham ibn Daud, Abraham ibn Ezra, and Gersonides.

* Jewish Science is sometimes also used in reference to the secular scholarship of some Jews in the Middle Ages, such as Abraham bar Hiyya, ibn Ezra, Gersonides, Abraham Zacuto, etc.

Gersonides on Providence, Covenant, and the Chosen People.

Whereas all other astronomers put the stars on a rotating sphere just beyond the outer planets, Gersonides estimated the distance to the stars to be ten billion times greater, of the order of 100 light-years ( in modern units ).

Unfortunately, there is no evidence that the findings had an impact on later generations of astronomers, even though Gersonides ' writings were translated and available.

Gersonides on Providence, Covenant, and the Chosen People: A Study in Medieval Jewish Philosophy and Biblical Commentary.

* Detailed bibliography of works on and by Gersonides

Isaac's responsa evidence a profound knowledge of the philosophical writings of his time ; in one of Responsa No. 118 he explains the difference between the opinion of Gersonides and that of Abraham ben David of Posquières on free will, and gives his own views on the subject.

Crescas rejects the theories of Maimonides and Gersonides on this point.

* “ Gersonides on Astrology, Divination, and Dreams ,” in Proceedings, Eighth World Congress of Jewish Studies, Division C, World Union of Jewish Studies, Jerusalem, 1982, pp. 47 – 52.

Jewish neo-Aristotelian philosophers, who are still influential today, include Maimonides, Samuel ben Judah ibn Tibbon, and Gersonides.

Key Jewish philosophers included Samuel Ibn Tibbon, Maimonides, and Gersonides, among many others.

Major Jewish philosophers include Solomon ibn Gabirol, Saadia Gaon, Judah Halevi, Maimonides, and Gersonides.

* 1288 – Gersonides, Jewish philosopher, mathematician, and astronomer ( d. 1344 )

** Gersonides, French rabbi and mathematician ( b. 1288 )

* Gersonides, Jewish philosopher, mathematician, and astronomer ( d. 1344 )

Louis Jacobs writes that modern Jewish thinkers such as Levi Olan, echoing some classical Jewish writers such as the 14th-century Talmudist Gersonides have " thought of God as limited by His own nature so that while He is infinite in some respects he is finite in others ," referencing the idea, present in classical sources, that " there is a primal formless material co-existent with God from all eternity upon which God has to work and that God only knows the future in a general sense but not how individual men will exercise their choice.

" On the topic of omniscience and free will, Jacobs writes that in the medieval period, three views were put forth: Maimonides, who wrote that God had foreknowledge and man is free ; Gersonides, who wrote that man is free and consequently God does not have complete knowledge, and Hasdai Crescas, who wrote in Or Adonai that God has complete foreknowledge and consequently God is not really free.

Levi ben Gershon, better known by his Latinised name as Gersonides or the abbreviation of first letters as RaLBaG ( 1288 – 1344 ), philosopher, Talmudist, mathematician, astronomer / astrologer.

: 6. creation and miracles, in respect to which Gersonides deviates widely from the position of Maimonides.

In contrast to the theology held by other Jewish thinkers, Jewish theologian Louis Jacobs argues, Gersonides held that God does not have complete foreknowledge of human acts.

" Gersonides, bothered by the old question of how God's foreknowledge is compatible with human freedom, holds that what God knows beforehand is all the choices open to each individual.

Gersonides posits that people's souls are composed of two parts: a material, or human, intellect ; and an acquired, or agent, intellect.

For Gersonides, Seymour Feldman points out, " Man is immortal insofar as he attains the intellectual perfection that is open to him.

Gersonides wrote Maaseh Hoshev in 1321 dealing with arithmetical operations including extraction of square and cube roots, various algebraic identities, certain sums including sums of consecutive integers, squares, and cubes, binomial coefficients, and simple combinatorial identities.

Gersonides is the only astronomer before modern times to have estimated correctly stellar distances.

Ne ' eman argued that after Gersonides reviewed Ptolemy's model with its epicycles he realized that it could be checked, by measuring the changes in the apparent brightnesses of Mars and looking for cyclical changes along the conjectured epicycles.

This desire, I went on, growing voluble as my conviction was aroused, had mounted at such a rate recently that I now found its realization necessary not only to my physical but also to my spiritual wellbeing.

It was certain now that Jess was in the house, but also, presumably, was Stacey Black.

But it also made him conspicuous to the enemy, if it was the enemy, and he hadn't been spotted already.

He was asking had it been she who left the love note in his sheets ( she also served as maid ) when he saw the Grafin followed by a stately blond girl approaching his table.

This was also a corpse -- a male, judging from the coral arm bands, the tribal scars still discernible on the maggoty face, the painted bone of the warrior caste which still pierced the septum of the rotting nose.

His superiors had also preached this, saying it was the way for eternal honor.

Charles, also fifteen, was tall and skinny, scraggly, with straight black hair like an Indian's and sharp brown eyes.

Although New Orleans was not to learn of it for a spell, she also was a sadist, a nymphomaniac and unobtrusively mad -- the perpetrator of some of the worst crimes against humanity ever committed on American soil.

There was also a dog, a dingo dog.

There was also a long wooden spear and a woomera, a spear-throwing device which gives the spear an enormous velocity and high accuracy.

There was also a boomerang, elaborately carved.

It was also subtly familiar, for it was the odor of the human body, but multiplied innumerable times because of the fact that the aborigines never bathed.

It was to provide a safe and spacious crossing for these caravans, and also to make a pleasance for the city, that Shah Abbas 2, in about 1657 built, of sun-baked brick, tile, and stone, the present bridge.

There was also a lesson, one that has served ever since to keep Americans, in their conflicts with one another, from turning from the ballot to the bullet.

Joseph Jastrow, the younger son of the distinguished rabbi, Marcus Jastrow, was a friendly, round-faced fellow with a little mustache, whose field was psychology, and who was also a punster and a jolly tease.

And just as `` Laurie '' Lawrence was first attracted to bright Jo March, who found him immature by her high standards, and then had to content himself with her younger sister Amy, so Joe Jastrow, who had also been writing Henrietta before he came to Johns Hopkins, had to content himself with her younger sister, pretty Rachel.

she also went to Washington and appealed to Senator George William Norris of Nebraska, the Fighting Liberal, from whose office a sympathetic but cautious harrumphing was heard.

The Indians who came aboard ship to collect the mail also interested her greatly, even if she was suitably shocked, according to the customs of the society in which she had been reared, to find them `` naked, except a piece of cotton cloth wrapped around their middle ''.

He also disliked Runyon, for no good reason other than the fact that the Demon's talent was so marked as to put him well beyond the Hetman's say-so or his supervision.