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A logic translation is a translation of a text into a logical system. For example, translating the sentence "all skyscrapers are tall" as ∀ x ( S ( x ) → T ( x ) ) {\displaystyle \forall x(S(x)\to T(x))} is a logic translation that expresses an English language sentence in the logical system known as first-order logic .
Machine translation, like DeepL or Google Translate, is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Wikipedia. Do not translate text that appears unreliable or low-quality.
Broadcast translator, rebroadcasting a radio signal at a different frequency; Translation (physics), movement that changes the position of an object, moving every point the same distance in the same direction, without rotation, reflection or change in size; Translation operator, an alternative name for the displacement operator in quantum optics
Machine translation, like DeepL or Google Translate, is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Wikipedia. Do not translate text that appears unreliable or low-quality.
The above discussion uses modern mathematical notation for the types of problems that the book discusses. However, in al-Khwārizmī's day, most of this notation had not yet been invented, so he had to use ordinary text to present problems and their solutions. For example, for one problem he writes, (from an 1831 translation)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is ...
Click [show] for important translation instructions. Machine translation, like DeepL or Google Translate , is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Wikipedia.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.