Near East (309–298 BCE): Euclid and the Foundations of Geometry

In the intellectual milieu of the Hellenistic Near East, the renowned mathematician Euclid, active in Alexandria around 300 BCE, fundamentally shapes the future of mathematics and science. He formulates a systematic set of axioms for geometry, laying the groundwork for a coherent, logical structure that will become known as Euclidean geometry. His influential text, the Elements, meticulously compiles these axioms and proofs, profoundly influencing the direction of mathematical thought.

Euclid’s scientific contributions extend beyond pure mathematics. In his works Optics and Catoptrics, he articulates the correct law of reflection, applying it rigorously to both plane and curved mirrors. He further references the phenomenon of refraction, demonstrating a sophisticated understanding of optical principles that will inform subsequent scientific inquiry in the Hellenistic world and beyond. Euclid’s work thus embodies the broader intellectual dynamism and methodological rigor characterizing the scholarly pursuits flourishing under the patronage of Hellenistic Alexandria.

Euclid, working in Hellenistic Alexandria in about 300 BCE, establishes a set of axioms for geometry.

Around the same time, he writes a treatise entitled Optics and Catoptrics, in which he sets forth the correct law of reflection and applies the law to the study of plane and curved mirrors.

He also mentions the phenomenon of refraction.

Ptolemy dies in about 170, leaving, in addition to his Geography and the earlier Almagest, three minor works: Apotelesmatika, in which he records astrological ideas from Enuma Anu Enlil; Tetrabiblos, in which he deals with astrology, and the Optics, in which he deals with reflection and refraction.

Alexander of Aphrodisias, the most distinguished of the later Greek commentators on Aristotle, composes several commentaries on the latter’s works, in which he seeks to escape a syncretistic tendency and to recover the pure doctrines of Aristotle.

His commentaries are still extant on Prior Analytics (Book 1), Topics, Meteorology, Sense and Sensibilia, and Metaphysics (Books 1-5).

The commentary on the Sophistical Refutations is deemed spurious, as is the commentary on the final nine books of the Metaphysics.

The lost commentaries include works on the De Interpretatione, Posterior Analytics, Physics, On the Heavens, On Generation and Corruption, On the Soul, and On Memory.

Simplicius of Cilicia mentions that Alexander provided commentary on the quadrature of the lunes, and the corresponding problem of squaring the circle.

It will be eported in April 2007, itthat imaging analysis had discovered an early commentary on Aristotle's Categories in the Archimedes Palimpsest, and Robert Sharples will suggest Alexander as the most likely author.

There are also several original writings by Alexander still extant.

These include: On the Soul, Problems and Solutions, Ethical Problems, On Fate, and On Mixture and Growth.

Three works attributed to him are considered spurious: Medical Questions, Physical Problems, and On Fevers.

Additional works by Alexander are preserved in Arabic translation, these include: On the Principles of the Universe, On Providence, and Against Galen on Motion.

Alexander's commentaries on Aristotle will by the sixth century be considered so useful that he will be referred to as "the commentator".

His commentaries will be greatly esteemed among the Arabs, who will translate many of them, and he will be heavily quoted by Maimonides.

The Church Council of Paris in 1210 will issue a condemnation, probably targeting the writings of Alexander among others.

Hs doctrine of the soul's mortality will be adopted in the early Renaissance by Pietro Pomponazzi (against the Thomists and the Averroists), and by his successor Cesare Cremonini.

This school will be known as Alexandrists.

Alexander's band is named after him: an optical phenomenon associated with rainbows, it occurs due to the deviation angles of the primary and secondary rainbows.

Both bows exist due to an optical effect called the angle of minimum deviation.

The refractive index of water prevents light from being deviated at smaller angles.

The term “glass” developed in the late Roman Empire.

It was in the Roman glassmaking center at Trier, now in modern Germany, that the late-Latin term glesum originated, probably from a Germanic word for a transparent, lustrous substance.

While naturally occurring glass, especially the volcanic glass obsidian, had been used by many Stone Age societies across the globe for the production of sharp cutting tools and, due to its limited source areas, was extensively traded, archaeological evidence suggests that the first true glass was made in coastal north Syria, Mesopotamia or Ancient Egypt.

The earliest known glass objects, of the mid-third millennium BCE, were beads, perhaps initially created as accidental byproducts of metalworking (slags) or during the production of faience, a pre-glass vitreous material made by a process similar to glazing.

Glass remained a luxury material, and the disasters that overtook Late Bronze Age civilizations seem to have brought glassmaking to a halt.

Indigenous development of glass technology in South Asia may have begun in 1730 BCE, whereas in ancient China, glassmaking seems to have a late start, compared to ceramics and metal work.

In the Roman Empire, glass objects have been recovered across the Roman Empire in domestic, industrial and funerary contexts.

Glass begins to be used extensively during the Middle Ages.

Anglo-Saxon glass has been found across England during archaeological excavations of both settlement and cemetery sites.

Glass in the Anglo-Saxon period is used in the manufacture of a range of objects including vessels, beads, windows and was also used in jewelry.

Optical glass for spectacles has been in use since the late Middle Ages.

The production of lenses has become increasingly proficient, aiding astronomers as well as having other application in medicine and science.

Glass is employed from the tenth century onward in stained glass windows of churches and cathedrals, with famous examples at Chartres Cathedral and the Basilica of Saint Denis.

Architects by the fourteenth century are designing buildings with walls of stained glass such as Sainte-Chapelle, Paris, (1203-1248) and the East end of Gloucester Cathedral.

Stained glass has a major revival with Gothic Revival architecture in the nineteenth century.

The use of large stained glass windows becomes less prevalent with the Renaissance and a change in architectural style.

The use of domestic stained glass increases until it is general for every substantial house to have glass windows.

These are initially of small panes leaded together, but with the changes in technology, glass can be manufactured relatively cheaply in increasingly larger sheets, leading to larger window panes, and, in the twentieth century, to much larger windows in ordinary domestic and commercial premises.

Such new types of glass as laminated glass, reinforced glass and glass bricks in the twentieth century increase the use of glass as a building material and result in new applications of glass.

Multistory buildings are frequently constructed with curtain walls made almost entirely of glass.

Similarly, laminated glass is widely applied to vehicles for windscreens.

While glass containers have always been used for storage and are valued for their hygienic properties, glass has been utilized increasingly in industry.

Glass is also employed as the aperture cover in many solar energy systems.

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.

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.

Medieval Economic Growth and Technological Innovations

The High and Late Middle Ages witnessed a surge in economic expansion, driven by technological advancements that transformed agriculture, trade, and knowledge dissemination. These innovations not only increased productivity but also facilitated the rise of urban centers, merchant classes, and long-distance trade networks, reshaping the medieval economy.

Key Technological Innovations and Their Impact

• The Windmill – First appearing in Europe by the late 12th century, windmills provided an efficient means of mechanized milling for grain and other agricultural products, reducing reliance on manual labor and allowing for greater food production in wind-rich regions such as northern France, the Low Countries, and England.

• Paper Manufacturing – Introduced from China via the Islamic world, paper production expanded in Atlantic West Europe during the 12th and 13th centuries. It gradually replaced expensive parchment, making writing materials more accessible and supporting record-keeping, education, and the expansion of literacy, particularly in the growing urban centers.

• The Spinning Wheel – Revolutionizing textile production, the spinning wheel significantly increased efficiency in turning raw fibers into yarn. This advancement fueled the growth of cloth industries, particularly in Flanders and northern France, where high-quality wool production became a cornerstone of the medieval economy.

• The Magnetic Compass – First used in Europe by the late 12th century, the magnetic compass transformed navigation, allowing for longer and safer sea voyages. This advancement greatly benefited maritime trade networks, particularly along the Atlantic coast, strengthening connections between ports in England, France, the Low Countries, and the Iberian Peninsula.

• Eyeglasses – Invented in Italy around the late 13th century, eyeglasses improved vision for scholars, scribes, and craftsmen, enabling them to extend their productivity and enhance intellectual and artistic output. This innovation played a key role in the expansion of medieval learning and craftsmanship.

• The Astrolabe – A sophisticated instrument inherited from Islamic and Greek traditions, the astrolabe allowed for astronomical measurements and navigation, assisting in maritime exploration and furthering scientific advancements in Europe’s growing centers of learning.

• Hindu-Arabic Numerals – Introduced through Islamic scholars in Spain and southern France, this numerical system gradually replaced Roman numerals, revolutionizing mathematics, accounting, and commerce. The new system allowed for more efficient calculations in trade, banking, and taxation, further accelerating economic complexity.

Economic and Social Transformations

These technological advances fueled economic expansion, leading to:

• The revival of urban centers, with trade hubs such as Bruges, Ghent, and Bordeaux emerging as key commercial strongholds.
• The rise of a merchant class, who increasingly influenced local governance and economic policies.
• Long-distance trade networks, strengthened by improved navigation and financial record-keeping, which facilitated exchanges between Atlantic West Europe, the Mediterranean, and beyond.

Together, these innovations set the stage for the broader economic and intellectual transformations of the Late Middle Ages, paving the way for the Commercial Revolution and, ultimately, the transition toward the Renaissance.

Scientific and Technological Contributions of the Islamic World to Europe

During the medieval period, the Islamic world makes significant advancements in science and technology, many of which are later transmitted to Europe, influencing the Renaissance and the Scientific Revolution.

Major Scientific Contributions

• Algebra – Developed by Al-Khwarizmi, whose works introduce systematic methods for solving equations.
• Chemistry (Alchemy) – Islamic scholars refine distillation, crystallization, and experimental methods, laying the groundwork for modern chemistry.
• Geology – The concept of uniformitarianism is introduced by Al-Biruni, influencing later European geological thought.
• Spherical Trigonometry – Used in astronomy and navigation, further developed by Al-Tusi and Al-Battani, paving the way for advancements in European cartography.
• Medicine – Figures such as Avicenna (Ibn Sina) and Al-Razi compile comprehensive medical treatises, which are later used in European universities.

Technological and Agricultural Transfers to Europe

• Astronomical Instruments – The astrolabe, perfected by Islamic astronomers, enables more accurate navigation and timekeeping, later adopted by European explorers.
• Irrigation Techniques – Advanced water management systems, such as qanats and norias, improve European agriculture.
• New Crops – Various plants, including sugarcane, rice, citrus fruits, cotton, and coffee, are introduced to Europe via Al-Andalus and the Crusades.

These Islamic contributions play a crucial role in the transmission of knowledge to medieval Europe, particularly through centers of learning in Al-Andalus, Sicily, and the Crusader States, helping to bridge the classical world with the emerging European scientific tradition.

The Evolution of Optical Lenses and the Birth of the Spectacle Industry (13th Century–1303)

By the late 13th century, optical lenses began evolving from crude magnifying devices into more refined spectacles, marking the dawn of the optical industry in Europe. The widespread use of spectacles for reading likely began in Italy during the 1280s, though the first recorded mention of spectacles appears in 1303.

The Rise of Spectacle-Making in Italy and Northern Europe

With the growing demand for vision correction, Italian craftsmen in Venice and Florence pioneered the grinding and polishing of lenses, establishing Europe’s first centers of spectacle production. Over time, spectacle-making spread to the Netherlands and Germany, where artisans further refined lens-making techniques.

Empirical Advancements in Vision Correction

Early spectacle makers relied on empirical observation rather than formal optical theory to improve lens types. Through trial and error, they created lenses that gradually enhanced the correction of farsightedness and presbyopia, laying the foundation for more scientific advancements in optics in the centuries to come.