query: What was Euclid's most important mathematical contribution?
passage: Euclid
Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης – Eukleídēs, pronounced[eu̯.klěː.dɛːs]; fl. 300 BC), sometimes given the name Euclid of Alexandria[1] to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry"[1] or the "father of geometry". He was active in Alexandria during the reign of PtolemyI (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.[2][3][4] In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor.
passage: History of science in early cultures
The level of achievement in Hellenistic astronomy and engineering is impressively shown by the Antikythera mechanism (150-100 BC). The astronomer Aristarchus of Samos was the first known person to propose a heliocentric model of the solar system, while the geographer Eratosthenes accurately calculated the circumference of the Earth. Hipparchus (c. 190 – c. 120 BC) produced the first systematic star catalog. In medicine, Herophilos (335 - 280 BC) was the first to base his conclusions on dissection of the human body and to describe the nervous system. Hippocrates (c. 460 BC – c. 370 BC) and his followers were first to describe many diseases and medical conditions. Galen (129 – c. 200 AD) performed many audacious operations—including brain and eye surgeries— that were not tried again for almost two millennia. The mathematician Euclid laid down the foundations of mathematical rigour and introduced the concepts of definition, axiom, theorem and proof still in use today in his "Elements", considered the most influential textbook ever written. Archimedes, considered one of the greatest mathematicians of all time, is credited with using the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of Pi. He is also known in physics for laying the foundations of hydrostatics and the explanation of the principle of the lever.