Xenocrates had succeeded Speusippus in 338 BCE as head of the Platonic Academy in Athens.

Feeling that the second generation of the Academy has overemphasized mathematics, he attempts to redirect the Academy’s primary focus to the Platonic forms, emphasizing their difference from mathematical and natural things.

He appears to have introduced a kind of formal atomism into geometry and physics.

Aristotle returns to Athens in 335 BCE to establish his own school, the Lyceum, or Peripatus.

In contrast to the Academy, which has become rather narrow in its interests since Plato's death, Aristotle intends the Peripatus to pursue a wider range of subjects than the Academy ever had, placing particular emphasis on the detailed study of nature.

Philo of Byzantium, who flourishes around 250 BCE, writes a textbook on mechanics (one of the earliest such known).

He is apparently supported by a wealthy patron, Ariston (to whom each extant section of his great book, three chapters of which survive in fragments, is dedicated).

Philo discusses in a probable nine chapters the lever, the construction of seaports and fortresses, catapults, pneumatics, automatic theaters, and military tactics. (Little else is known of Philo, although both Hero and Vitruvius mention him in their writings.)

Philo is supposedly the author of a work entitled Peri ton hepta theamaton (“Concerning the Seven Wonders of the World”).

In his listing of the monuments, the Pharos of Alexandria replaces the Walls of Babylon.

According to recent research, a section of Philo's Pneumatics which so far has been regarded as a later Arabic interpolation, includes the first description of a water mill in history, placing the invention of the water mill in the mid-third century BCE by the Greeks.

Philo's works also contain the oldest known application of a chain drive in a repeating crossbow.

Two flat-linked chains are connected to a windlass, which by winding back and forth will automatically fire the machine's arrows until its magazine is empty.

Philon also is the first to describe a gimbal: an eight-sided ink pot with an opening on each side could be turned so that any face is on top, dip in a pen and ink it-yet the ink never runs out through the holes of the side.

This is done by the suspension of the inkwell at the center, which is mounted on a series of concentric metal rings that remain stationary no matter which way the pot turns itself.

In his Pneumatics (chapter 31) Philon describes an escapement mechanism, the earliest known, as part of a washstand.

A counterweighted spoon, supplied by a water tank, tips over in a basin when full releasing a pumice in the process.

Once the spoon has emptied, it is pulled up again by the counterweight, closing the door on the pumice by the tightening string.

Philo’s comment that "its construction is similar to that of clocks" indicates that such escapements mechanism were already integrated in ancient water clocks.

In mathematics, Philo tackles the challenge of doubling the cube, necessitated by the following problem: given a catapult, construct a second catapult that is capable of firing a projectile twice as heavy as the projectile of the first catapult.

His solution is to find the point of intersection of a rectangular hyperbola and a circle, a solution that is similar to Heron's solution several centuries later.

Hero of Alexandria, a mathematician and engineer, probably Greek, who flourishes in Roman Egypt around 100 and is said to be the greatest experimenter of antiquity, devises a primitive steam engine.

It is almost certain that Hero taught at the Musaeum, which include, the famous Library of Alexandria, because most of his writings appear as lecture notes for courses in mathematics, mechanics, physics and pneumatics.

Ibn Yunis, writing around 1000, describes the properties of the pendulum: namely, that the pendulum executes simple harmonic motion, and that the period of each swing is constant, independent of the mass of the weight and the displacement, and dependent only on the pendulum's length.

Ibn al-Haytham (Alhazen) he had written his influential Book of Optics while being kept under house arrest from 1011 until al-Hakim's death in 1021.

His house arrest ended, he will write scores of other treatises on physics, astronomy and mathematics.

He will later travel to Islamic Spain.

During this period, he will have ample time for his scientific pursuits, which include optics, mathematics, physics, medicine, and practical experiments

Born around 965 in Basra, which was at that time part of the Buyid emirate, to an Arab family, Ibn al-Haytham had been educated there and in Baghdad, the capital of the Abbasid Caliphate.

During his time in Basra he had trained for government work and became Minister for the area.

One account of his career has him called to Egypt by Al-Hakim bi-Amr Allah, ruler of the Fatimid Caliphate, to regulate the flooding of the Nile, a task requiring an early attempt at building a dam at the present site of the Aswan Dam.

After deciding the scheme was impractical and fearing the caliph's anger, he had feigned madness, hence his decade-long confinement.

Fan Zhongyan, who had been prefect of Kaifeng, the imperial capital during the Northern Song era, in the 1030s, had been demoted to regional posts for criticizing the Chief Councilor.

In 1040, the Liao and Western Xia to the north were threatening Song security, and Fan had been brought back to organize a strong defense.

Ouyang Xiu, posted to Kaifeng four years after passing his jinshi examination in 1030, had begun his association with Fan from this time in Kaifeng.

Like Fan, he also had been demoted.

After Fan’s demotion, Ouyang had criticized Fan’s principle critic, resulting in his being sent to a minor post in Hubei.

Like Fan, he had been brought back to the capital in the 1040s where he was assigned to work on cataloguing the entire imperial library.

Fan Zhongyan had in 1041 submitted a ten-point memorial in which he outlined his reform objectives, divided into three categories: administrative efficiency; strengthening of local governments; and strengthening of defense.

The first set of proposals has met with deep resistance from groups of bureaucrats.

The second set, while farsighted, seems remote to the court.

The third seeks to correct Song over corrections for the Tang Dynasty’s mistakes of giving local military commanders too much independent authority.

Many of these reforms have been put into effect during 1043 and 1044.

However, without the full support of the emperor, there is never complete implementation of the reforms, and not long after they began, backlash from conservative elements at the court results in the reformers being brought down and sent out to remote postings in the provinces.

The Wujing Zongyao, a military treatise written and compiled by scholars Zeng Gongliang, Ding Du, and Yang Weide during the Song Dynasty, is the first book in history to include formulas for gunpowder and its use for various bombs (thrown by sling or trebuchet catapult).

Although the Wujing Zongyao emphasizes the importance of many weapons, it reserves high respect for the crossbow and the ability of crossbowmen to fell charging units of nomadic cavalrymen.

It also describes the double-piston pump flame thrower and a thermoremanence compass, a few decades before Shen Kuo wrote of the first known magnetic mariners compass.

The Chinese of the early eleventh century are thus aware that a piece of iron can be magnetized by heating until it is red hot and then quenched in water.

While quenching, it is oriented in the Earth's field to get the desired polarity.

The astronomical clock tower in Kaifeng features an escapement mechanism and the world's oldest known endless power-transmitting chain drive to operate the armillary sphere, opening doors, and mechanical-driven mannequins that rotate in shifts to announce the time on plaques.

Its construction in 1088 is based on a successful pilot model by polymath statesman and scientist Su Song.

The Dream Pool Essays represents the earliest known writing about the magnetic compass, movable type printing, experimentation with the camera obscura only decades after Ibn al-Haytham, and includes many different fields of study in essay and encyclopedic form, including geology, astronomy, botany, zoology, mineralogy, anatomy, pharmacology, geography, optics, economics, military strategy, philosophy, etc.

Published in this year by the polymath scientist and statesman Shen Kuo, the book features some of Shen's most advanced theories, including geomorphology and gradual climate change, while he improves Chinese astronomy by fixing the position of the pole star and correcting the lunar error by plotting its orbital course every night for a continuum of five years.

Shen's book is also the first to describe the drydock in China, and discusses the advantages of the relatively recent invention of the canal pound lock over the old flash lock.

Abu al-Salt has written an encyclopedic work of many treatises on the scientific disciplines known as quadrivium.

This work is probably known in Arabic as Kitāb al‐kāfī fī al‐ʿulūm.

His interests also include alchemy as well as the study of medicinal plants.

He is keen to discover an elixir able to transmute copper into gold and tin into silver.

His writings include Risāla fī al-amal bi‐l‐astrulab ("On the construction and use of the astrolabe"); a description of the three instruments known as the Andalusian equatoria; Ṣifat ʿamal ṣafīḥa jāmiʿa taqawwama bi‐hā jamīʿ al‐kawākib al‐sabʿa ("Description of the construction and Use of a Single Plate with which the totality of the motions of the seven planets"), where the seven planets refer to Mercury, Venus, earth, Moon, Mars, Jupiter, and Saturn; Kitāb al‐wajīz fī ʿilm al‐hayʾa ("Brief treatise on cosmology"); Ajwiba ʿan masāʾil suʾila ʿan‐ha fa‐ajāba or Ajwiba ʿan masāʾil fī al‐kawn wa‐ʾl‐ḥabīʿa wa‐ʾl‐ḥisāb ("Solution to questions on cosmology, physics, and arithmetic"); an introduction to astronomy; and A Summary of Ptolemy's Almagest.

Abu al-Salt was born in Denia, al-Andalus.

After the death of his father while he was a child, he had become a student of al‐Waqqashi (1017–1095) of Toledo (a colleague of Al-Zarqali).

Upon completing his mathematical education in Seville, and because of the continuing conflicts during the reconquista, he had set out with his family to Alexandria and then Cairo in 1096.

In Cairo, he had entered the service of the Fatimid ruler Abū Tamīm Ma'add al-Mustanṣir bi-llāh and the Vizier Al-Afdal Shahanshah.

His service had continued until 1108, when, according to Ibn Abī Uṣaybiʿa, his attempt to retrieve a very large Felucca laden with copper, that had capsized in the Nile River, ended in failure.

Abu al-Salt had built a mechanical tool to retrieve the Felucca, and was close to success when the machine's silk ropes fractured.

The Vizier Al-Afdal had ordered Abu al-Salt's arrest, and he was imprisoned for more than three years, only to be released in 1112.

Abu al-Salthad then left Egypt for Kairouan in Tunisia, where he had entered the service of the Zirids in Ifriqiya.

He also occasionally travels to Palermo and works in the court of Roger I of Sicily as a visiting physician.

He dies in 1134 in Bejaia, in present Algeria.

Abu'l-Barakāt al-Baghdaadi, famed as Awhad al-Zamān (Unique One of his Time), was born in Balad, a town on the Tigris above Mosul in modern-day Iraq.

As a renowned physician, he has served at the courts of the caliphs of Baghdad and the Seljuq sultans.

He has converted to Islam in old age.

Abu'l Barakat does not refer to his conversion in his writings, and the historical sources give contradictory episodes of his conversion.

According to the various reports, he had converted either out of "wounded pride", fear of the personal consequences of the death of Sultan Mahmud's wife while under his care as a physician or fear of execution when he was taken prisoner in a battle between the armies of the caliph and that of the sultan.

Isaac, the son of the Abraham Ibn Ezra and the son-in-law of Judah Halevi, was one of his pupils, to whom Abu'l-Barakāt, Jewish at the time, dictated a long philosophical commentary on Ecclesiastes, written in Arabic using Hebrew aleph bet.

Isaac wrote a poem in his honor as introduction to this work Al-Baghdaadi described an early scientific method emphasizing repeated experimentation, influenced by Ibn Sina.

Al-Baghdaadi's theory of motion distinguished between velocity and acceleration and showed that force is proportional to acceleration rather than velocity.

The 1fourteenth-century philosophers Jean Buridan and Albert of Saxony will later refer to Abu'l-Barakat in explaining that the acceleration of a falling body is a result of its increasing impetus.

Abu'l-Barakat also modified Ibn Sina's theory of projectile motion, and stated that the mover imparts a violent inclination (mayl qasri) on the moved and that this diminishes as the moving object distances itself from the mover.

Al-Baghdaadi also suggested that motion is relative, writing that "there is motion only if the relative positions of the bodies in question change."

He also stated that "each type of body has a characteristic velocity that reaches its maximum when its motion encounters no resistance."

Al-Baghdaadi criticized Aristotle's concept of time as "the measure of motion" and instead redefines the concept with his own definition of time as "the measure of being", thus distinguishing between space and time, and reclassifying time as a metaphysical concept rather than a physical one.

He upheld the unity of the soul, denying that there is a distinction between it and the intellect.

For him, the soul's awareness of itself is the definitive proof that the soul is independent of the body and will not perish with it.

He wrote a critique of Aristotelian philosophy and Aristotelian physics entitled Kitab al-Mu'tabar (the title may be translated as "The Book of What Has Been Established by Personal Reflection").

According to Abu'l-Barakāt, Kitāb al-Muʿtabar consists in the main of critical remarks jotted down by him over the years while reading philosophical text, and published at the insistence of his friends, in the form of a philosophical work.

The work "presented a serious philosophical alternative to, and criticism of, Ibn Sina".

He also developed concepts which resemble several modern theories in physics.

He dies in 1165 in Baghdad.

Abu'l-Barakāt's thought had a deep influence on Islamic philosophy but none on Jewish thought.

His works are not translated into Hebrew, and he is seldom cited in Jewish philosophy, probably because of his conversion to Islam.