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The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.
It builds upon the propositions of the previous books and applies them with further specificity than in Book 1 to the motions observed in the Solar System. Here (introduced by Proposition 22, [ 34 ] and continuing in Propositions 25–35 [ 35 ] ) are developed several of the features and irregularities of the orbital motion of the Moon ...
The Condemnation of 1210 was issued by the provincial synod of Sens, which included the Bishop of Paris as a member (at the time Pierre II de la Chapelle []). [3] The writings of a number of medieval scholars were condemned, apparently for pantheism, and it was further stated that: "Neither the books of Aristotle on natural philosophy or their commentaries are to be read at Paris in public or ...
On 1 June 1642 [1] the English Lords and Commons approved a list of proposals known as the Nineteen Propositions, sent to King Charles I of England, who was in York at the time. [2] In these demands, the Long Parliament sought a larger share of power in the governance of the kingdom.
Sections 10, 11, 12: Properties of a variable extended to all individuals: section 10 introduces the notion of "a property" of a "variable". PM gives the example: φ is a function that indicates "is a Greek", and ψ indicates "is a man", and χ indicates "is a mortal" these functions then apply to a variable x.
The first book contains a proof of the law of the lever and culminates with propositions on the centre of gravity of the triangle and the trapezium. [1] [2] The second book, which contains ten propositions, examines the centres of gravity of parabolic segments. [1]
There are two books to On the Equilibrium of Planes: the first contains seven postulates and fifteen propositions, while the second book contains ten propositions. In the first book, Archimedes proves the law of the lever, which states that: Magnitudes are in equilibrium at distances reciprocally proportional to their weights.
The book presents a loosely Cartesian doctrine (that the proposition is a combining of ideas rather than terms, for example) within a framework that is broadly derived from Aristotelian and medieval term logic. Between 1664 and 1700, there were eight editions, and the book had considerable influence after that. [90]