Euclid's Elements
Posted December 31st, 2010 at 09:31 AM by pixi666
Here's a short essay on The Elements that I wrote for my Latin class. Enjoy!
Euclid’s Elements
The Elements (Ancient Greek: Στοιχεῖα) was an ancient geometry textbook by Euclid (Ancient Greek: Εὐκλείδης), an ancient Greek mathematician who lived in Alexandria during the reign of Ptolemy I.
The Elements was really more of a compilation of previous works than an original book. Euclid took parts from Hippocrates of Chios (fl. 460 B.C.), Thaetetus (417-396 B.C.), and Theudius. The Elements does not only cover geometry (as it is widely believed), but also covers many other parts of mathematics. Books I-IV cover plane geometry. Book V covers ratios and proportions, and also looks at irrational numbers (i.e. numbers that cannot be expressed as a ratio between 2 numbers, such as √2 and π). Book VI uses the topics explored in Book V to investigate triangles and parallelograms. Books VII-IX look at what we now call ‘number theory’, the basic properties of positive integers (e.g. odd or even, prime or composite, etc.). The massive Book X (it takes up about ¼ of The Elements) concerns itself with ‘incommensurable magnitudes’, or as we call them today, irrational magnitudes. Books XI-XIII look at 3-dimensional geometry, including the famous Platonic Solids (the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron).
The Elements was widely known in the classical world. Geometry was considered a near-holy subject, partly due to the influence of the mystic Pythagoreans. The great philosopher Plato believed that all rulers should be rigorously trained in geometry. In fact, when the ruler of Egypt, Ptolemy I, wanted to learn geometry, he asked Euclid if there was a faster way to learn it than by reading The Elements, to which Euclid supposedly responded “There is no royal road to geometry”. Various mathematicians wrote commentaries on The Elements, and while no ancient Latin version of it has survived, it was definitely known to the Romans (it is mentioned by Cicero). Through the Byzantine Empire, it became known to Arab scholars who kept it alive through the Dark Ages. It was then translated into Latin by European monks in the Middle Ages. It exerted an enormous influence on such figures in the 17th century as Pierre de Fermat (founder of the modern theory of numbers), Johannes Kepler (one of the founders of modern astronomy), Rene Descartes (founder of modern philosophy and creator of coordinate geometry), and Isaac Newton (founder of modern physics, inventor of calculus). More recently, Albert Einstein said that The Elements was one of the two things in his childhood that inflamed his passion for science (the other being a compass), calling it a “holy little geometry book”.
But what makes The Elements particularly extraordinary is what it did for the scientific method. It showed that one could come to a conclusion using a framework of axioms, theorems, and proofs in a completely logical manner. These concepts are still the basis of all science and mathematics today.
Works Cited
Fardon, John. The great scientists / John Fardon and Alex Woolf, Anne Rooney, Liz Gogerly . Royston, Hertfordshire: Eagle Editions, 2006.
Gowers, Timothy. Mathematics: a very short introduction. Oxford : Oxford University Press, 2002.
Norman, Jeremy. "The Earliest Surviving Manuscript Closest to Euclid's Original Text (Circa 850) : From Cave Paintings to the Internet." Jeremy Norman’s HistoryofScience.com - Rare Books, Manuscripts & Autographs, Publications, Appraisals, Traditions & Culture of Collecting. N.p., n.d. 14 Nov. 2010. <http://www.historyofscience.com/G2I/timeline/index.php?id=2749>.
Taisbak, Christian Marinus, and Bartel Leendert van der Waerden. "Euclid (Greek mathematician) -- Britannica Online Encyclopedia." Encyclopedia - Britannica Online Encyclopedia. N.p., n.d. 14 Nov. 2010. <http://www.britannica.com/EBchecked/topic/194880/Euclid>.
Euclid’s Elements
The Elements (Ancient Greek: Στοιχεῖα) was an ancient geometry textbook by Euclid (Ancient Greek: Εὐκλείδης), an ancient Greek mathematician who lived in Alexandria during the reign of Ptolemy I.
The Elements was really more of a compilation of previous works than an original book. Euclid took parts from Hippocrates of Chios (fl. 460 B.C.), Thaetetus (417-396 B.C.), and Theudius. The Elements does not only cover geometry (as it is widely believed), but also covers many other parts of mathematics. Books I-IV cover plane geometry. Book V covers ratios and proportions, and also looks at irrational numbers (i.e. numbers that cannot be expressed as a ratio between 2 numbers, such as √2 and π). Book VI uses the topics explored in Book V to investigate triangles and parallelograms. Books VII-IX look at what we now call ‘number theory’, the basic properties of positive integers (e.g. odd or even, prime or composite, etc.). The massive Book X (it takes up about ¼ of The Elements) concerns itself with ‘incommensurable magnitudes’, or as we call them today, irrational magnitudes. Books XI-XIII look at 3-dimensional geometry, including the famous Platonic Solids (the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron).
The Elements was widely known in the classical world. Geometry was considered a near-holy subject, partly due to the influence of the mystic Pythagoreans. The great philosopher Plato believed that all rulers should be rigorously trained in geometry. In fact, when the ruler of Egypt, Ptolemy I, wanted to learn geometry, he asked Euclid if there was a faster way to learn it than by reading The Elements, to which Euclid supposedly responded “There is no royal road to geometry”. Various mathematicians wrote commentaries on The Elements, and while no ancient Latin version of it has survived, it was definitely known to the Romans (it is mentioned by Cicero). Through the Byzantine Empire, it became known to Arab scholars who kept it alive through the Dark Ages. It was then translated into Latin by European monks in the Middle Ages. It exerted an enormous influence on such figures in the 17th century as Pierre de Fermat (founder of the modern theory of numbers), Johannes Kepler (one of the founders of modern astronomy), Rene Descartes (founder of modern philosophy and creator of coordinate geometry), and Isaac Newton (founder of modern physics, inventor of calculus). More recently, Albert Einstein said that The Elements was one of the two things in his childhood that inflamed his passion for science (the other being a compass), calling it a “holy little geometry book”.
But what makes The Elements particularly extraordinary is what it did for the scientific method. It showed that one could come to a conclusion using a framework of axioms, theorems, and proofs in a completely logical manner. These concepts are still the basis of all science and mathematics today.
Works Cited
Fardon, John. The great scientists / John Fardon and Alex Woolf, Anne Rooney, Liz Gogerly . Royston, Hertfordshire: Eagle Editions, 2006.
Gowers, Timothy. Mathematics: a very short introduction. Oxford : Oxford University Press, 2002.
Norman, Jeremy. "The Earliest Surviving Manuscript Closest to Euclid's Original Text (Circa 850) : From Cave Paintings to the Internet." Jeremy Norman’s HistoryofScience.com - Rare Books, Manuscripts & Autographs, Publications, Appraisals, Traditions & Culture of Collecting. N.p., n.d. 14 Nov. 2010. <http://www.historyofscience.com/G2I/timeline/index.php?id=2749>.
Taisbak, Christian Marinus, and Bartel Leendert van der Waerden. "Euclid (Greek mathematician) -- Britannica Online Encyclopedia." Encyclopedia - Britannica Online Encyclopedia. N.p., n.d. 14 Nov. 2010. <http://www.britannica.com/EBchecked/topic/194880/Euclid>.
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