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Pythagoras (c. 570 BC – c. 495 BC) – Euclidean geometry, Pythagorean theorem; Zeno of Elea (c. 490 BC – c. 430 BC) – Euclidean geometry; Hippocrates of Chios (born c. 470 – 410 BC) – first systematically organized Stoicheia – Elements (geometry textbook) Mozi (c. 468 BC – c. 391 BC) Plato (427–347 BC) Theaetetus (c. 417 BC ...
His great achievement in the field of cartography was the use of a new technique of charting with meridians, his imaginary north–south lines, and parallels, his imaginary west–east lines. [29] These axis lines were placed over the map of the Earth with their origin in the city of Rhodes and divided the world into sectors.
260 BC – Archimedes proved that the value of π lies between 3 + 1/7 (approx. 3.1429) and 3 + 10/71 (approx. 3.1408), that the area of a circle was equal to π multiplied by the square of the radius of the circle and that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height ...
More specifically, all north–south running lines (all range lines and half of all section lines), as with the prime meridian, are always established with reference to true, geodetic north. But it is a physical impossibility to meet this condition and still maintain a rectangular land grid, because such lines converge on the north pole.
A superpythagorean field F is a formally real field with the property that if S is a subgroup of index 2 in F ∗ and does not contain −1, then S defines an ordering on F. An equivalent definition is that F is a formally real field in which the set of squares forms a fan. A superpythagorean field is necessarily Pythagorean. [12]
This table lists two of the three numbers in what are now called Pythagorean triples, i.e., integers a, b, and c satisfying a 2 + b 2 = c 2. From a modern perspective, a method for constructing such triples is a significant early achievement, known long before the Greek and Indian mathematicians discovered solutions to this problem.
The ordinance directed the Geographer of the United States, Thomas Hutchins, to survey an initial east-west base line. Hutchins began in 1786, using as his starting point a stake on north bank of the Ohio River placed by a 1785 survey team from the states of Virginia and Pennsylvania to fix their common north-south boundary (now the boundary ...
The Tabula Peutingeriana (Peutinger table) is an itinerarium showing the cursus publicus, the road network in the Roman Empire. It is a 13th-century copy of an original map dating from the 4th century, covering Europe, parts of Asia (India) and North Africa.