Discovery of Pythagorean Theorem

The Pythagorean theorem states that for a right triangle the square of the length of the hypotenuse equals the sum of the squares of the two remaining sides.

Among the many classical Greek schools of mathematics and philosophy the Pythagorean was the oldest and most venerable.

Pythagoras was born around 570 BC. Tradition has it that he came from the island of Samos and traveled widely before he established his school in Crotona in Southern Italy. He learned mathematics from Thales (624-547 BC), traditionally regarded as the founder of Greek mathematics.

In Egypt and Babylonia he absorbed the lore of mysticism and also learned the laws of numbers and geometry.

A legend says that Pythagoras discovered his theorem by observing a tiles floor in the place of Polycrates, the tyrant of Samos. However, many said that he did not discover the theorem.

The story of Pythagorean theorem begins long before that, at least as far as back 1800 BC in Babylonia. Pythagoras’s name became attached to the theorem because he was reputedly he first person to provide such a proof.
Discovery of Pythagorean Theorem

Averroes works on philosophy and science

Abu al-Walid Muhammad ibn Rushd (Latin: Averroes 1126-98) integrated Islamic traditions and Greek thought. Averroes is important figure in the history of Islamic intellectual and religious philosophy, who also influenced Western philosophy and Christian theology by inspiring the thirteenth-century movement called Averroism.

Aristotle who lived between 384–322 BC, states that a hidden force causes and determines the motions of matter. Then Averroes states that Aristotle’s force is composed of a primary and secondary force.

From Plato, Averroes adopted the analogy between a well-administered state and a healthy and sound soul.

Some of the most important philosophical works by Averroes or the Commentator, as he as called in the Middle Ages, were translated into Latin.

After Averroes’ death, his philosophy, or at least certain components in his variegated intellectual production, exercised a remarkable influence on the Latin West. Jewish philosopher began to translate Averroes’ work into early in the thirteen century.
Averroes works on philosophy and science

Philosophy of science by Anaximander of Miletus

Anaximander (611-547 BC) was the student of Thales, a leader in the early development of the Ionian school of thought.

He continued his teacher’s search to discover the one source of all things, whether material or spiritual. Anaximander followed Thales in believing that everything in nature was composed of a single fundamental substance which he called the apeiron, the ‘boundless’, which is sometimes translated as ‘the infinite,’ meaning that it not defined or limited by having specific properties.

He was the first to have developed anything like cosmological system; he was also the first among the Greeks who draft a map and to construct a globe.

He offered a much more detailed picture of the world. Anaximander maintained that the earth was in the center of all things, suspended freely and without support, whereas Thales regarded it as resting on water.

According to Anaximander, there is no reason for earth to move in one direction or another, a concept known as the ‘principle of the lack of a sufficient reason’. The use of this principle by Anaximander is said to mark the boundary between mythology and science, which always requires an explanation in terms of a sufficient cause.

Diogenes Laertius recorded that Anaximander was the first to introduce to the Greeks the sundial or gnomon, with which to gauge time by day and to approximate the summer and winter solstices and the fall and spring equinoxes.

He contended that thunder and lightning were cause by blasts of wind, not by Zeus’s thunderbolts. Anaximander appears to have stated that the world is governed by the opposites like hot and cold, wet and dry. It is by the working of the opposites that the world goes on.
Philosophy of science by Anaximander of Miletus

Heracleitus of Ephesus

Amongst the great Ionian who concerned themselves exclusively with philosophy was Heracleitus of Ephesus. He was the son of Blyson, or as some say, of Heraceon.

Almost nothing is known of Heracleitus’ life. He was aid lived during the period spanning the end of the sixth century and the beginning of the fifth century BC.

He grew up in one of the richest and most splendid cities in Asia Minor, Ephesus, at a time when it flourished under Persian rule. The city was founded about 1000 BC by colonists from Athens, it prospered by tapping the trade of both the Cayster and the Maeander.

He is specially remembered for his view that ‘everything is in a state of flux’. Fire, the most changeful of elements, is the origin and image of all things. Living creatures are formed of a mixture of the changeful essences of which fire and are types.

Heracleitus had definite ideas as to the question of diet, for he lived on herbs and abstained from meat. When he suffered from dropsy for instance, and held a consultation with most important physician in Ephesus, he suggested to them that his condition was like one after a heavy rain and a drought was needed to disperse the accumulation of water.
Heracleitus of Ephesus

Anaximander of Miletus

Anaximander (611-547 BC), Miletan pupils of Thales took much interest in geography. Anaximander is generally regarded as the second philosopher in the western philosophical tradition after Thales.

Anaximander also can be called the West’s first astronomer and geographer. He was the first among the Greeks to represent the details of the surface of the earth by maps. The idea of map-making was known in Egypt where plans of particular districts or objects as mines, houses and temples were being drawn up as early as 1400 BC. Anaximander, however, sought to convey a concrete picture of the surface of the earth as a whole.

From Babylon also he introduced the sun-dial. It consisted in essence of a gnomon, a fixed upright rod, the direction and length of the shadow of which can be measured hour by hour.

Anaximander was the first to speculate on the size and distance of the heavenly bodies. Departing from the Homeric view that the earth was a flat plate or disk, Anaximander characterized earth as a drum shaped cylinder suspended in midair. This idea looks remarkably like a guess at the celestial law of gravity.

This placement strongly suggested that the heavenly bodies passed through the sky and then under the Earth to reappear again the next day, thereby superseding earlier cosmological tendencies that limited the movement of heavenly bodies only to the sky above.

Anaximander seems to have guessed at the biological process of evolution. He is recorded as having believed that humankind originally emerged from fishes to step forth onto land.
Anaximander of Miletus 

Thales of Miletus (c.624 – 565 BC)

It was in general, a time travel, a movement of the breakdown of old and of the rise of new civilizations.  Such was the stage such the atmosphere of change in which science became first clearly distinguished.

Science emerging can be seen into the light of historic day in the person of the Ionian Greek Thales.

Diogenes Laertius says that Ionian philosophy began with Anaximander but that Thales instructed Anaximander.  Aristotle considered Thales to be ‘the first founder of this kind of philosophy, for example, the thought of those subject who sought to find what he called the ‘material cause ‘ of things.

Though he was the son of a Phoenician mother, Thales of Miletus was a citizen of the Ionian city of Miletus.

He was a founder of the Ionian school and was numbered among the Seven Sages of Ancient Greece in the pre-Socratic Era. Thales was an astronomer, mathematician and philosopher.

Thales established a heritage of searching for knowledge for knowledge’s sake, development of the scientific method, establishment of practical methods and application of a conjectural approach to question of natural phenomena.

As a young man, he traveled to Egypt and the Near East to study geometry, a branch of mathematics concerned with points, lines and surfaces in two dimensions.

In Mesopotamian he learned of the ‘Saronic cycle’ that is to say the interval of eighteen years and eleven days, a multiple of which the observation of ages by temple star-gazers had shown to be usual between eclipses of the sun. Knowledge of this enabled the shrewd travel to make a lucky forecast of the eclipse visible at Miletus in 585 BC.

It was Thales of Miletus, who was credited with the discovery of the electrostatic attraction. Thales noted that after amber was rubbed, straw was attracted to the piece of amber.

The Neo-Platonist philosopher Proclus, writing in the fifth century AD, says that Thales learned geometry from the Egyptian and brought the knowledge back to Greece. Thales was also supposed to be the first to prove various geometrical theorems and it was said that he used geometry to measure the heights of the pyramids in Egypt and the distance of ships at sea.
Thales of Miletus

Al-Kindi (801–873 CE)

Al-Kindi or Abu Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī was a Muslim Arab philosopher, polymath, mathematician, physician and musician. He was known as Al-Kindus by Western world.

Al-Kindi began his education at either Kufah or Basra, and completed it at Baghdad the centers of culture of his day.

Both Kufah and Basra were places of intense and original intellectual activity by the tome of Al-Kindi’s birth; this activity centered on a number of disciplines indigenous to Islamic culture such as Arabic grammar, the explication of the Qur'an and the principles of law, all of which would have important consequences for philosophy.

He studied Fiqh and the new born discipline called, kalam, but it seems that he was more interested in science and philosophy, to which he unsecrated the rest of his life, especially after he went to Baghdad.

Al-Kindi learnt Greek, but certainly he mastered the syriac language from which he translated several works.

He became well known in the Abbasid capital as a scholar and physician, enjoyed the patronage of the caliphs al Ma’mun and al-Mu’tasim and was appointed tutor of the latter’s son Ahmad.

Al-Kindi wrote hundred of papers on Greek philosophy, science, ethics, cosmology, metaphysics and what is known today as psychology, from an Islamic perspective.

He is a major contributor to the introduction of Greek philosophy to the Muslim World, although he was not afraid to contradict the Greek thinkers if he believed it conflicted with Islamic teachings.

Al-Kindi died on 873 in Baghdad, Iraq.
Al-Kindi (801–873 CE)

Isaac Newton and Philosophiae Naturalis Principia Mathematica

Isaac Newton and Philosophiae Naturalis Principia Mathematica
Sir Isaac Newton, President of the Royal Society was an English mathematician, physicist, astronomer, alchemist, and natural philosopher who is generally regarded as one of the greatest scientists and mathematicians in history.

 Newton wrote the Philosophiae Naturalis Principia Mathematica, in which he described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics. By deriving Kepler's laws of planetary motion from this system, he was the first to show that the motion of objects on Earth and of celestial bodies are governed by the same set of natural laws. The unifying and deterministic power of his laws was integral to the scientific revolution and the advancement of heliocentrism.

The Philosophiæ Naturalis Principia Mathematica (Latin: "mathematical principles of natural philosophy", often Principia or Principia Mathematica for short) is a three-volume work by Isaac Newton published on July 5, 1687. It contains the statement of Newton's laws of motion forming the foundation of classical mechanics, as well as his law of universal gravitation and a derivation of Kepler's laws for the motion of the planets (which were first obtained empirically).

The Principia is widely regarded as one of the most important scientific works ever written. It has been claimed that the Principia is the greatest work in the history of the physical sciences. By demonstrating that the motion of all bodies was controlled by the same universal laws, Isaac Newton brought to the scientific community a vision of an orderly, harmonious universe which could be understood independent of any supreme being. Divided into three books,

Book I develops general dynamics from a mathematical standpoint for the entire work and begins with the motion of mass particles.

Book II is a treatise on fluid mechanics.

Book III is devoted to astronomical and physical problems. Newton addressed and resolved a number of issues including the motions of comets and the influence of gravitation. For the first time, he demonstrated that the same laws of motion and gravitation ruled everywhere under a single mathematical law.

Newton's scientific accomplishments were vast. He was the co-discoverer with Leibniz of differential calculus and the founder of mathematical physics. He made important studies in optics and yet had time to devote to theology, alchemy and chemistry.
Isaac Newton and Philosophiae Naturalis Principia Mathematica