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Q.E.D. (manga)
Q.E.D. or QED is an initialism of the List of Latin phrases (full), Latin phrase , meaning "that which was to be demonstrated". Literally, it states "what was to be shown". Traditionally, the abbreviation is placed at the end of Mathematical proof#Ending a proof, mathematical proofs and Philosophy, philosophical Logical argument, arguments in print publications, to indicate that the proof or the argument is complete. Etymology and early use The phrase ''quod erat demonstrandum'' is a translation into List of Latin phrases, Latin from the Greek language, Greek (; abbreviated as ''ΟΕΔ''). The meaning of the Latin phrase is "that [thing] which was to be demonstrated" (with ''demonstrandum'' in the gerundive). The Greek phrase was used by many early Greek mathematicians, including Euclid and Archimedes. The Latin phrase is attested in a 1501 Euclid translation of Giorgio Valla. Its abbreviation ''q.e.d.'' is used once in 1598 by Johannes Praetorius, more in 1643 by Anton Deusi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Initialism
An acronym is a type of abbreviation consisting of a phrase whose only pronounced elements are the initial letters or initial sounds of words inside that phrase. Acronyms are often spelled with the initial letter of each word in all caps with no punctuation. For some, an initialism or alphabetism connotes this general meaning, and an ''acronym'' is a subset with a narrower definition; an acronym is pronounced as a word rather than as a sequence of letters. In this sense, ''NASA'' () is an acronym, but '' USA'' () is not. The broader sense of ''acronym'', ignoring pronunciation, is its original meaning and in common use. . Dictionary and style-guide editors dispute whether the term ''acronym'' can be legitimately applied to abbreviations which are not pronounced as words, and they do not agree on acronym spacing, casing, and punctuation. The phrase that the acronym stands for is called its . The of an acronym includes both its expansion and the meaning of its expans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ethics (Spinoza)
''Ethics, Demonstrated in Geometrical Order'' () is a philosophical treatise written in Latin by Baruch Spinoza (). It was written between 1661 and 1675 and was first published posthumously in 1677. The ''Ethics'' is perhaps the most ambitious attempt to apply Euclid's method in philosophy. Spinoza puts forward a small number of definitions and axioms from which he attempts to derive hundreds of propositions and corollaries, such as "when the Mind imagines its own lack of power, it is saddened by it", "a free man thinks of nothing less than of death", and "the human Mind cannot be absolutely destroyed with the Body, but something of it remains which is eternal." Summary Part I: Of God The first part of the book addresses the relationship between God and the universe. Spinoza was engaging with a tradition that held that God exists outside of the universe, that God created the universe for a reason, and that God could have created a different universe according to his will. Spi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Lemma (mathematics)
In mathematics and other fields, a lemma (: lemmas or lemmata) is a generally minor, proven Theorem#Terminology, proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to mathematical proof, prove; however, a lemma can also turn out to be more important than originally thought. Etymology From the Ancient Greek λῆμμα, (perfect passive εἴλημμαι) something received or taken. Thus something taken for granted in an argument. Comparison with theorem There is no formal distinction between a lemma and a theorem, only one of intention (see Theorem#Terminology, Theorem terminology). However, a lemma can be considered a minor result whose sole purpose is to help prove a more substantial theorem – a step in the direction of proof. Well-known lemmas Some powerful results in mathematics are known as lemmas, first named for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Theorem
In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formal system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Equilateral Triangle
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties. The equilateral triangle can be found in various tilings, and in polyhedrons such as the deltahedron and antiprism. It appears in real life in popular culture, architecture, and the study of stereochemistry resembling the molecular known as the trigonal planar molecular geometry. Properties An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition, stating that an isosceles triangle is defined at least as having two equal sides. Based on the modern definition, this leads to an equilateral triangle in which one of the three sides may be considered its base. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Diary
A diary is a written or audiovisual memorable record, with discrete entries arranged by date reporting on what has happened over the course of a day or other period. Diaries have traditionally been handwritten but are now also often digital. A personal diary may include a person's experiences, thoughts, and/or feelings, excluding comments on current events outside the writer's direct experience. Someone who keeps a diary is known as a diarist. Diaries undertaken for institutional purposes play a role in many aspects of human civilization, including government records (e.g. ''Hansard''), business ledgers, and military records. In British English, the word may also denote a preprinted journal format. Today the term is generally employed for personal diaries, normally intended to remain private or to have a limited circulation amongst friends or relatives. The word " journal" may be sometimes used for "diary," but generally a diary has (or intends to have) daily entries (f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Meditations On First Philosophy
''Meditations on First Philosophy, in which the existence of God and the immortality of the soul are demonstrated'' (), often called simply the ''Meditations'', is a philosophical treatise by René Descartes first published in Latin in 1641. The French translation (by the Duke of Luynes with Descartes' supervision) was published in 1647 as ''Méditations Métaphysiques''. The title may contain a misreading by the printer, mistaking ''animae immortalitas'' for ''animae immaterialitas'', as suspected by A. Baillet. The book is made up of six meditations, in which Descartes first discards all belief in things that are not absolutely certain, and then tries to establish what can be known for sure. He wrote the meditations as if he had meditated for six days: each meditation refers to the last one as "yesterday". (In fact, Descartes began work on the ''Meditations'' in 1639.) One of the most influential philosophical texts ever written, it is widely read to this day. The book cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
René Descartes
René Descartes ( , ; ; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and Modern science, science. Mathematics was paramount to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry. Descartes spent much of his working life in the Dutch Republic, initially serving the Dutch States Army, and later becoming a central intellectual of the Dutch Golden Age. Although he served a Dutch Reformed Church, Protestant state and was later counted as a Deism, deist by critics, Descartes was Roman Catholicism, Roman Catholic. Many elements of Descartes's philosophy have precedents in late Aristotelianism, the Neostoicism, revived Stoicism of the 16th century, or in earlier philosophers like Augustine of Hippo, Augustine. In his natural philosophy, he differed from the Scholasticism, schools on two major point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Proposition (mathematics)
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning. In mathematics, an ''axiom'' may be a " logical axiom" or a " non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example ''a'' + 0 = ''a'' in integer arithmetic. N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
