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− Flat
The plus and minus signs, and , are mathematical symbols used to represent the notions of positive and negative, respectively. In addition, represents the operation of addition, which results in a sum, while represents subtraction, resulting in a difference. Their use has been extended to many other meanings, more or less analogous. ''Plus'' and ''minus'' are Latin terms meaning "more" and "less", respectively. History Though the signs now seem as familiar as the alphabet or the Hindu-Arabic numerals, they are not of great antiquity. The Egyptian hieroglyphic sign for addition, for example, resembled a pair of legs walking in the direction in which the text was written (Egyptian could be written either from right to left or left to right), with the reverse sign indicating subtraction: Nicole Oresme's manuscripts from the 14th century show what may be one of the earliest uses of as a sign for plus. In early 15th century Europe, the letters "P" and "M" were generally us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dash
The dash is a punctuation mark consisting of a long horizontal line. It is similar in appearance to the hyphen but is longer and sometimes higher from the baseline. The most common versions are the endash , generally longer than the hyphen but shorter than the minus sign; the emdash , longer than either the en dash or the minus sign; and the horizontalbar , whose length varies across typefaces but tends to be between those of the en and em dashes. History In the early 1600s, in Okes-printed plays of William Shakespeare, dashes are attested that indicate a thinking pause, interruption, mid-speech realization, or change of subject. The dashes are variously longer (as in King Lear reprinted 1619) or composed of hyphens (as in Othello printed 1622); moreover, the dashes are often, but not always, prefixed by a comma, colon, or semicolon. In 1733, in Jonathan Swift's ''On Poetry'', the terms ''break'' and ''dash'' are attested for and marks: Blot out, correct, insert, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summa De Arithmetica
' (''Summary of arithmetic, geometry, proportions and proportionality'') is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a comprehensive summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting, written for use as a textbook and reference work. Written in vernacular Italian, the ''Summa'' is the first printed work on algebra, and it contains the first published description of the double-entry bookkeeping system. It set a new standard for writing and argumentation about algebra, and its impact upon the subsequent development and standardization of professional accounting methods was so great that Pacioli is sometimes referred to as the "father of accounting". Contents The ''Summa de arithmetica'' as originally printed consists of ten chapters on a series of mathematical topics, collectively covering essentially all of Renaissance mathematics. The first seven chapters form a summary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged. That is, when is the identity function, the equality is true for all values of to which can be applied. Definition Formally, if is a set, the identity function on is defined to be a function with as its domain and codomain, satisfying In other words, the function value in the codomain is always the same as the input element in the domain . The identity function on is clearly an injective function as well as a surjective function, so it is bijective. The identity function on is often denoted by . In set theory, where a function is defined as a particular kind of binary relation, the identity function is given by the identity relation, or ''diagonal'' of . Algebraic properties If is any function, then we have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operand
In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above example, '+' is the symbol for the operation called addition. The operand '3' is one of the inputs (quantities) followed by the addition operator, and the operand '6' is the other input necessary for the operation. The result of the operation is 9. (The number '9' is also called the sum of the augend 3 and the addend 6.) An operand, then, is also referred to as "one of the inputs (quantities) for an operation". Notation Expressions as operands Operands may be complex, and may consist of expressions also made up of operators with operands. :(3 + 5) \times 2 In the above expression '(3 + 5)' is the first operand for the multiplication operator and '2' the second. The operand '(3 + 5)' is an expression in itself, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary Operator
In mathematics, an unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function , where is a set. The function is a unary operation on . Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial ), functional notation (e.g. or ), and superscripts (e.g. transpose ). Other notations exist as well, for example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent of the argument. Examples Unary negative and positive As unary operations have only one operand they are evaluated before other operations containing them. Here is an example using negation: :3 − −2 Here, the first '−' represents the binary subtraction operation, while the second '−' represents the unary negation of the 2 (or '−2' could be taken to mean the integer −2). Therefore, the expression is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Operator
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation ''on a set'' is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. An operation of arity two that involves several sets is sometimes also called a ''binary operation''. For example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Such binary operations may be called simply binary functions. Binary operations are the keystone of most algebraic structures that are studied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Whetstone Of Witte
''The Whetstone of Witte'' is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being ''The whetstone of , is the : The ''Coßike'' practise, with the rule of ''Equation'': and the of ''Surde Nombers. The book covers topics including whole numbers, the extraction of roots and irrational numbers. The work is notable for containing the first recorded use of the equals sign and also for being the first book in English to use the plus and minus signs. Recordian notation for exponentiation, however, differed from the later Cartesian notation p^q = p \times p \times p \cdots \times p. Recorde expressed indices and surds larger than 3 in a systematic form based on the prime factorization of the exponent: a factor of two he termed a ''zenzic'', and a factor of three, a ''cubic''. Recorde termed the larger prime numbers appearing in this factorization ''sursolids'', distinguishing between them by use of ordinal numbers: that is, he defined 5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equals Sign
The equals sign (British English, Unicode) or equal sign (American English), also known as the equality sign, is the mathematical symbol , which is used to indicate equality in some well-defined sense. In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value. In Unicode and ASCII, it has the code point U+003D. It was invented in 1557 by Robert Recorde. History The etymology of the word "equal" is from the Latin word "''æqualis",'' as meaning "uniform", "identical", or "equal", from ''aequus'' ("level", "even", or "just"). The symbol, now universally accepted in mathematics for equality, was first recorded by Welsh mathematician Robert Recorde in ''The Whetstone of Witte'' (1557). The original form of the symbol was much wider than the present form. In his book Recorde explains his design of the "Gemowe lines" (meaning ''twin'' lines, from the Latin '' gemellus'')See also g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Recorde
Robert Recorde () was an Anglo-Welsh physician and mathematician. He invented the equals sign (=) and also introduced the pre-existing plus and minus signs, plus sign (+) to English speakers in 1557. Biography Born around 1512, Robert Recorde was the second and last son of Thomas and Rose Recorde of Tenby, Pembrokeshire, in Wales. Recorde entered the University of Oxford about 1525, and was elected a Fellow of All Souls College, Oxford, All Souls College there in 1531. Having adopted medicine as a profession, he went to the University of Cambridge to take the degree of M.D. in 1545. He afterwards returned to Oxford, where he publicly taught mathematics, as he had done prior to going to Cambridge. He invented the "equals" sign. It appears that he afterwards went to London, and acted as physician to King Edward VI of England, Edward VI and to Mary I of England, Queen Mary, to whom some of his books are dedicated. He was also controller of the Royal Mint and served as Comptroll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henricus Grammateus
Henricus Grammateus (also known as Henricus Scriptor, Heinrich Schreyber or Heinrich Schreiber; 1495 – 1525 or 1526) was a German mathematician. He was born in Erfurt. In 1507 he started to study at the University of Vienna, where he subsequently taught. Christoph Rudolff was one of his students. From 1514 to 1517 he studied in Cracow and then returned to Vienna. But when the plague affected Vienna Schreiber left the city and went to Nuremberg. In 1518 he published details of a new musical temperament, which is now named after him, for the harpsichord. It was a precursor of the equal temperament. In 1525 Schreiber was back in Vienna, where he is listed as "Examinator", i.e. eligible to work holding exams. Works * ''Algorithmus proportionum una cum monochordi generalis dyatonici compositione'', pub. Volfgangvm De Argentina, Cracow, 1514 * ''Libellus de compositione regularum pro vasorum mensuratione. Deque arte ista tota theoreticae et practicae'', Vienna, 1518 * ''Ayn ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Widmann
Johannes Widmann (c. 1460 – after 1498) was a German mathematician. The + and - symbols first appeared in print in his book ''Mercantile Arithmetic'' or ''Behende und hüpsche Rechenung auff allen Kauffmanschafft'' published in Leipzig in 1489 in reference to surpluses and deficits in business problems. Born in Eger, Bohemia, Widmann attended the University of Leipzig in the 1480s. In 1482 he earned his "Baccalaureus" (Bachelor of Art degree) and in 1485 his " Magister" (doctorate). Widman published ''Behende und hübsche Rechenung auff allen Kauffmanschafft'' (German; i.e. Nimble and neat calculation in all trades), his work making use of the signs, in Leipzig in 1489. Further editions were published in Pforzheim, Hagenau, and Augsburg. Handwritten entries in a surviving collection show that after earning his "Magister" Widman announced holding lectures on e.g. calculating on the lines of a calculating board and on algebra. There is evidence that the lecture on algebra actuall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Widmann-Mercantile Arithmetic 1489
Johannes is a Medieval Latin form of the personal name that usually appears as "John" in English language contexts. It is a variant of the Greek and Classical Latin variants (Ιωάννης, ''Ioannes''), itself derived from the Hebrew name '' Yehochanan'', meaning "Yahweh is gracious". The name became popular in Northern Europe, especially in Germany because of Christianity. Common German variants for Johannes are ''Johann'', ''Hannes'', '' Hans'' (diminutized to ''Hänschen'' or ''Hänsel'', as known from "''Hansel and Gretel''", a fairy tale by the Grimm brothers), '' Jens'' (from Danish) and ''Jan'' (from Dutch, and found in many countries). In the Netherlands, Johannes was without interruption the most common masculine birth name until 1989. The English equivalent for Johannes is John. In other languages *Joan, Jan, Gjon, Gjin and Gjovalin in Albanian *'' Yoe'' or '' Yohe'', uncommon American form''Dictionary of American Family Names'', Oxford University Press, 2013. *Yaḥy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
