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Revision as of 18:14, 1 October 2022


Contents

 [hide

Decimal Dystem

[Expand]rank


Numeration

[Expand]units


[Expand]decade


[Expand]tens


[Expand]hundreds


[Expand]thousands


[Expand]tens of thousands


[Expand]hundreds of thousands


[Expand]millions


Positional System

[Expand]decimal place


[Expand]dust letters


[Expand]empty rank


[Expand]Indo-Arabic numerals


[Expand]numeral


[Expand]numerical value


[Expand]
numerical value - definition


[Expand]place holder


[Expand]place-holding


[Expand]positional value


[Expand]
positional value - definition


[Expand]zero


Arithmetic Operations

Addition

[Expand]addition


[Expand]
addition - definition


[Expand]to add, to sum


[Expand]sum


[Expand]addend


[Expand]additive


[Expand]plus



Change of Denominator

[Expand]change of denominator


[Expand]to change denominator


Composing

[Expand]composing denominators


[Expand]composed


Conversion

[Expand]conversion


[Expand]to convert


Decomposing to a Fraction

[Expand]decomposing to a fraction


[Expand]to decompose to a fraction


Denomination

[Expand]denomination


[Expand]to denominate


Determining the Common Denominator

[Expand]determining the common denominator


Division

[Expand]division


[Expand]
division - definition


[Expand]dividing


[Expand]to divide


[Expand]divisor


[Expand]greatest common divisor


[Expand]true divisor


[Expand]dividend


[Expand]divisible


[Expand]result of division, quotient


[Expand]part


[Expand]result of division


[Expand]share


Doubling

[Expand]doubling


[Expand]
doubling - definition


[Expand]to double


[Expand]double, twice


Expansion to a Common Denominator

[Expand]expansion to a common denominator


[Expand]
expansion to a common denominator - definition


Exponentiation

[Expand]cubing


[Expand]to cube


[Expand]cubed number


[Expand]to square


[Expand]squared number


[Expand]higher power


Extraction of Roots

[Expand]extraction of roots


[Expand]to extract a root


[Expand]to extract a square root


[Expand]to extract a cube root


[Expand]to have a root


[Expand]root


[Expand]square root


[Expand]cube root


[Expand]higher root


[Expand]approximate root


[Expand]expressible


[Expand]inexpressible


[Expand]radicand


[Expand]binomial


Factorization

[Expand]factorization


[Expand]to factorize


Forming a Fracion

[Expand]forming a fracion


[Expand]to form a fracion


Halving

[Expand]halving


[Expand]
halving - definition


[Expand]to halve


[Expand]half of


Lowering the rank

[Expand]lowering the rank


[Expand]to lower the rank


Multiplication

[Expand]multiplication


[Expand]
multiplication - definition


[Expand]multiplication table


[Expand]to multiply


[Expand]to triple


[Expand]multiplied


[Expand]multiplicand


[Expand]multiplier


[Expand]result of multiplication, product


[Expand]factor


[Expand]common factor


[Expand]to find a common factor


[Expand]to share a common factor


[Expand]multiple


[Expand]common multiple


[Expand]least common multiple


[Expand]to share a common multiple


[Expand]times



Methods of Multiplication

[Expand]multiplication by partial shifting


[Expand]multiplication by shifting


[Expand]multiplication without shifting


[Expand]gelosia


[Expand]horizontal multiplication


[Expand]vertical multiplication


[Expand]multiplication tower


[Expand]multiplication wings


[Expand]cross-multiplication


[Expand]triplets method


Raising the rank

[Expand]raising the rank


[Expand]to raise the rank


[Expand]raised to a higher rank


Reduction

[Expand]reduction


[Expand]
reduction- definition


[Expand]reduced


[Expand]to reduce


Rounding

[Expand]rounding


[Expand]rounded number


[Expand]to round


Subtraction

[Expand]subtraction


[Expand]
subtraction - definition


[Expand]to subtract


[Expand]minuend


[Expand]subtrahend


[Expand]subtractive


[Expand]result of subtraction


[Expand]minus


[Expand]carrying over from a higher rank


[Expand]to remain


[Expand]to leave a remainder


Supplementing

[Expand]additive supplementation


[Expand]to supplement additively


[Expand]additive supplement


[Expand]multiplicative supplementation


[Expand]to supplement multiplicatively


[Expand]multiplicatively supplemented


Check

[Expand]check


[Expand]to check


[Expand]scales


Casting Out

[Expand]casting out


[Expand]cast out nines


[Expand]result of casting out


[Expand]to cast out


False Position

[Expand]double false position


[Expand]single false position


[Expand]guess in a false position


[Expand]error of a false position


Arithmetic Terms

[Expand]arithmetic


[Expand]
arithmetic - definition


[Expand]arithmetician


[Expand]integer


[Expand]to be an integer


[Expand]number


[Expand]
number - definition


[Expand]unit


[Expand]
unit - definition


[Expand]unity


[Expand]small


[Expand]large


[Expand]to estimate


[Expand]to extract


[Expand]to suffice


[Expand]given number


[Expand]required


[Expand]unknown


[Expand]difference


[Expand]deficit


[Expand]to be worth


[Expand]procedure


[Expand]calculation diagram


[Expand]accurately


[Expand]exact


[Expand]analogous


[Expand]corresponding


[Expand]endlessly


[Expand]order


[Expand]total


[Expand]extreme


[Expand]mean


[Expand]term


[Expand]sameness


[Expand]otherness


Alternation

[Expand]alternation


[Expand]to alternate


Approximating

[Expand]approximate


[Expand]to approximate


[Expand]approximately


Calculation

[Expand]calculation


[Expand]to calculate


[Expand]one who calculates


Counting

[Expand]counting


[Expand]counted


[Expand]to count


Decreasing

[Expand]decreasing


[Expand]to decrease


Increasing

[Expand]increasing


[Expand]to increase


Measuring

[Expand]measure


[Expand]
measure - definition


[Expand]to measure


[Expand]measured


Result

[Expand]result


[Expand]to result


Set Aside

[Expand]set aside


[Expand]to set aside



Correct

[Expand]correct


[Expand]to correct



Excess

[Expand]excess


[Expand]exceeding


[Expand]to exceed


Error

[Expand]error


[Expand]erroneous, incorrect


[Expand]to err


Equal

[Expand]equal


[Expand]unequal


[Expand]to be equal to


Quantity

[Expand]quantity


[Expand]continuous quantity


[Expand]discrete quantity, discontinuous quantity


[Expand]numerical quantity


[Expand]relative quantity


Fractions

[Expand]fraction


[Expand]part = fraction


[Expand]fraction of fraction


[Expand]denominator


[Expand]common denominator


[Expand]numerator


[Expand]sexagesimal fraction


[Expand]degree


[Expand]minute


[Expand]second


[Expand]zodiac sign


Progression

[Expand]progression


[Expand]natural succession


[Expand]successive


[Expand]
successive - definition


[Expand]sequential number


[Expand]successively


[Expand]increment


[Expand]number of terms


[Expand]aₙ₋₁


[Expand]aₙ₊₁


[Expand]chess


[Expand]chessboard square


Proportion

[Expand]proportion


[Expand]arithmetic proportion


[Expand]
arithmetic proportion - definition


[Expand]geometric proportion


[Expand]
geometric proportion - definition


[Expand]harmonic proportion


[Expand]
harmonic proportion - definition


[Expand]subcontrary proportion


[Expand]proportional


[Expand]
proportional numbers- definition


[Expand]proportional triad


[Expand]proportional hexad - proportion of six numbers


[Expand]rule of three


[Expand]
rule of three - definition


[Expand]arithmetic mean


[Expand]
arithmetic mean - definition


[Expand]geometric mean


[Expand]
geometric mean - definition


[Expand]harmonic mean


[Expand]
harmonic mean - definition


Ratio

[Expand]ratio


[Expand]to relate


[Expand]equality ratio


[Expand]inequality


multiple ratio

[Expand]multiple ratio = ratio in which the greater term is a product of the less by an integer (m·n):m


[Expand]double ratio = ratio of two to one, 2n:n


[Expand]
double ratio - definition


[Expand]duplicate


[Expand]triple ratio = ratio of three to one, 3n:n


[Expand]
triple ratio - definition


[Expand]triplicate


[Expand]quadruple = ratio of four to one, 4n:n


[Expand]
quadruple - definition


[Expand]quintuple = ratio of five to one, 5n:n


[Expand]sextuple = ratio of six to one, 6n:n


[Expand]septuple = ratio of seven to one, 7n:n


[Expand]octuple = ratio of eight to one, 8n:n


[Expand]nonuple = ratio of nine to one, 9n:n


[Expand]decuple = ratio of ten to one, 10n:n


superparticular ratio

[Expand]superparticular = the ratio of two consecutive integer numbers (n+1):n


[Expand]sesquialter = ratio of one and a half to one, (1+½):1 or 3:2


[Expand]
sesquialter ratio - definition


[Expand]sesquitertian = ratio of one and a third to one, (1+⅓):1 or 4:3


[Expand]
sesquitertian ratio - definition


[Expand]sesquiquartan = ratio of one and a quarter to one, (1+¼):1 or 5:4


[Expand]
sesquiquartan ratio - definition


[Expand]sesquiquintan = ratio of one and a fifth to one, (1+⅕):1 or 6:5


[Expand]
sesquiquintan ratio - definition


[Expand]sesquisextan = ratio of one and a sixth to one, (1+⅙):1 or 7:6


[Expand]sesquiseptan = ratio of one and a seventh to one, (1+⅐):1 or 8:7


[Expand]sesquioctavian = ratio of one and an eighth to one, (1+⅛):1 or 9:8


[Expand]sesquinona = ratio of one and a ninth to one, (1+⅑):1 or 10:9


[Expand]sesquidecima = ratio of one and a tenth to one, (1+⅒):1 or 11:10


superpartient ratio

[Expand]superpartient = ratio in which the greater term exceeds the less by more than a unit (n+m):n


superbipartient ratio
[Expand]superbipartient = ratio of one and two parts to one, (1+²/ₙ):1


[Expand]
superbipartient ratio - definition


[Expand]superbitertian = ratio of one and two thirds to one, (1+⅔):1 or 5:3


[Expand]superbiquartan = ratio of one and two quarters to one, (1+²/₄):1 or 6:4


[Expand]superbiquintan = ratio of one and two fifths to one, (1+⅖):1 or 7:5


[Expand]superbisextan = ratio of one and two sixths to one, (1+²/₆):1 or 8:6


[Expand]superbiseptan = ratio of one and two sevenths to one, (1+²/₇):1 or 9:7


[Expand]superbinona = ratio of one and two ninths to one, (1+²/₉):1 or 11:9


supertripartient ratio
[Expand]supertripartient = ratio of one and three parts to one, (1+³/ₙ):1


[Expand]
supertripartient ratio - definition


[Expand]supertriquartan = ratio of one and three quarters to one, (1+¾):1 or 7:4


[Expand]supertriquintan = ratio of one and three fifths to one, (1+⅗):1 or 8:5


[Expand]supertrisextan = ratio of one and three sixths to one, (1+³/₆):1 or 9:6


superquadripartient ratio
[Expand]superquadripartient = ratio of one and four parts to one, (1+⁴/ₙ):1


[Expand]
superquadripartient ratio - definition


[Expand]superquadriquintan = ratio of one and four fifths to one, (1+⅘):1 or 9:5


[Expand]superquadrisextan = ratio of one and four sixths to one, (1+⁴/₆):1 or 10:6


multiple superparticular ratio

[Expand]multiple superparticular


double superparticular
[Expand]double superparticular


[Expand]double sesquialter ratio = ratio of two and a half to one, (2+½):1 or 5:2


[Expand]double sesquitertian ratio = ratio of two and a third to one, (2+⅓):1 or 7:3


[Expand]double sesquiquartan ratio = ratio of two and a quarter to one, (2+¼):1 or 9:4


[Expand]double sesquiquintan ratio = ratio of two and a fifth to one, (2+⅕):1 or 11:5


triple superparticular
[Expand]triple superparticular


[Expand]triple sesquialter ratio = ratio of three and a half to one, (3+½):1 or 7:2


[Expand]triple sesquitertian ratio = ratio of three and a third to one, (3+⅓):1 or 10:3


[Expand]triple sesquiquartan ratio = ratio of three and a quarter to one, (3+¼):1 or 13:4


quadruple superparticular
[Expand]quadruple superparticular ratio


[Expand]quadruple sesquialter ratio: ratio of four and a half to one, (4+½):1 or 9:2


[Expand]quadruple sesquiquartan ratio: ratio of four and a quarter to one, (4+¼):1 or 17:4


multiple superpartient ratio

[Expand]multiple superpartient = ratio in which the greater term exceeds the multiple of the less by more than a unit ((n·m)+a):n


Types of Numbers

[Expand]composite number


[Expand]
composite - definition


[Expand]relatively composite


[Expand]
relatively composite - definition


[Expand]relatively prime


[Expand]
relatively prime - definition


[Expand]prime incomposite number


[Expand]
prime incomposite number - definition


[Expand]even number


[Expand]
even number - definition


[Expand]even-times-even number


[Expand]
even-times-even number - definition


[Expand]even-times-odd number


[Expand]
even-times-odd number - definition


[Expand]even-times-even-times-odd number


[Expand]
even-times-even-times-odd number - definition


[Expand]odd number


[Expand]
odd number - definition


[Expand]odd-times-odd number


[Expand]composite odd number


[Expand]
composite odd number - definition


[Expand]perfect number


[Expand]
perfect number - definition


[Expand]superabundant number


[Expand]
superabundant number - definition


[Expand]deficient number


[Expand]
deficient number - definition


[Expand]amicable numbers


[Expand]
amicable numbers - definition


[Expand]plane number


[Expand]
plane number - definition


[Expand]linear number


[Expand]
linear number - definition


[Expand]circular number


[Expand]polygonal number


[Expand]triangular number


[Expand]square number


[Expand]
square number - definition


[Expand]pentagonal number


[Expand]hexagonal number


[Expand]heptagonal number


[Expand]octagonal number


[Expand]nonagonal number


[Expand]decagonal number


[Expand]cyclic number


[Expand]solid number


[Expand]
solid number - definition


[Expand]cubic number


[Expand]
cubic number - definition


[Expand]beam number


[Expand]oblong number


[Expand]heteromecic number


[Expand]
heteromecic number - definition


[Expand]spherical number


[Expand]scalene number


[Expand]parallelepipedon number


[Expand]brick number


[Expand]pyramidal number


[Expand]triangular pyramidal number: pyramidal number that represents a triangular pyramid, ⅙∙(n³+3n²+2n)


[Expand]square pyramidal number: pyramidal number that represents a square pyramid, ⅙∙(2n³+3n²+n)


[Expand]pentagonal pyramidal number: pyramidal number that represents a pentagonal pyramid, ⅙∙(3n³+3n²)


  1. natural number
[Expand]sieve


[Expand]
sieve - definition


Combinatorics

[Expand]collection


[Expand]n!


[Expand]combination


[Expand]permutation


[Expand]variation


Algebraic Terms

[Expand]algebra


[Expand]algebraist


[Expand]algebraic species


[Expand]algebraic expression


[Expand]fixed number


[Expand]
number (algebraic context)- definition


[Expand]root


[Expand]
root- definition


[Expand]square


[Expand]
square- definition


[Expand]cube


[Expand]higher power of x


[Expand]additional unknown


[Expand]equation


[Expand]side of an equation


[Expand]six canonical equations


[Expand]compound canonical equation


[Expand]simple canonical equation


[Expand]indeterminate equation


Definitions

[Expand]simple canonical equation


[Expand]compound canonical equation


[Expand]Muḥammad al-Khwārizmī

Algebraic Operations

[Expand]balancing an equation


[Expand]confrontation


[Expand]
confrontation- definition


[Expand]to confront/ to be confronted


[Expand]to equate/to be equated


[Expand]normalization


[Expand]to normalize/to be normalized


[Expand]restoration


[Expand]
restoration- definition


[Expand]to restore/to be restored


[Expand]transformation between kinds


[Expand]to transform between kinds/to be transformed between kinds


Geometric Terms

[Expand]geometry


[Expand]
geometry - definition


[Expand]geometrician


[Expand]geometrical shape


[Expand]magnitude


[Expand]area


[Expand]distance


[Expand]dimension


[Expand]
dimension - definition


[Expand]length


[Expand]width


[Expand]depth


[Expand]end


Point

[Expand]point


[Expand]apex


[Expand]center


[Expand]center of a sphere


[Expand]center of a circle


Line

[Expand]line


[Expand]
line - definition


[Expand]straight line


[Expand]circular line


[Expand]parallel lines


[Expand]intersecting lines


[Expand]tangent lines


[Expand]apotome


[Expand]
apotome- definition


[Expand]diagonal


[Expand]diameter


[Expand]
diameter - definition


[Expand]
diameter of a sphere: a line that passes through the center of the sphere and reaches the surface of the sphere at its both sides


[Expand]
diameter of a circle: a line that passes through the center of the circle and reaches the circumference of the circle at its both sides


[Expand]height


[Expand]perimeter


[Expand]side


[Expand]segment


[Expand]parallel


[Expand]straight


[Expand]to draw a line


[Expand]to extend a line


[Expand]to meet a line


to cut a line

[Expand]to cut a line


[Expand]to be cut into two segments


[Expand]to cut into two unequal segments


[Expand]to be cut into two unequal segments


[Expand]to cut randomly at point


[Expand]to be cut randomly at point


[Expand]to halve a line at point


[Expand]to be halved at point


Angle

[Expand]right angle


[Expand]
right angle - definition


[Expand]acute angle


[Expand]
acute angle - definition


[Expand]obtuse angle


[Expand]
obtuse angle - definition



plane

[Expand]plane


[Expand]surface


[Expand]
surface - definition


[Expand]triangle


[Expand]
triangle - definition


[Expand]equilateral triangle


[Expand]quadrilateral


[Expand]
quadrilateral - definition


[Expand]square


[Expand]
square - definition


[Expand]rectangle


[Expand]
rectangle - definition


[Expand]rhombus


[Expand]
rhombus - definition


[Expand]parallelogram


[Expand]
parallelogram - definition


[Expand]polygon


[Expand]
polygon- definition


[Expand]trapezoid


[Expand]
trapezoid- definition


[Expand]circle


[Expand]
circle - definition


[Expand]gnomon


isosceles

[Expand]isosceles triangle


[Expand]isosceles trapezoid: trapezoid whose two nonparallel sides are equal


acute-angled

[Expand]acute-angled triangle: triangle in which all the three internal angles are acute


[Expand]
acute-angled triangle - definition


obtuse-angled

[Expand]obtuse-angled triangle: triangle in which one angle is greater than a right angle


[Expand]
obtuse-angled triangle - definition


[Expand]obtuse trapezoid: trapezoid that has one interior angle greater than 90°


right-angled

[Expand]right-angled triangle: triangle in which one angle is a right angle


[Expand]
right-angled triangle - definition


scalene

[Expand]scalene triangle: triangle in which all three sides are unequal in length


[Expand]irregular quadrilateral: quadrilateral that have two or more unequal sides and two or more unequal angles


[Expand]scalene trapezoid: trapezoid whose four sides are unequal in length



solid

[Expand]solid


[Expand]
solid - definition


[Expand]cube


[Expand]parallelepiped


[Expand]prism


[Expand]square prism: prism that has two identical parallel square faces and the four other faces are rectangular


[Expand]hexagonal prism


[Expand]triangular prism: prism that has two identical parallel triangular faces and the three other faces are rectangular


[Expand]
triangular prism - definition


[Expand]pentagonal prism: prism that has two identical parallel pentagonal faces and the five other faces are rectangular


[Expand]pyramid


[Expand]triangular pyramid: pyramid with a triangular base


[Expand]square pyramid: pyramid with a square base


[Expand]truncated pyramid


[Expand]sphere


[Expand]
sphere - definition


[Expand]hemisphere


[Expand]cone


[Expand]
cone - definition


[Expand]cylinder


[Expand]ellipsoid


[Expand]
ellipsoid - definition


[Expand]beam


[Expand]solid angle


[Expand]sharp solid


[Expand]volume


[Expand]face



[Expand]to complete a surface


[Expand]to cut off


[Expand]to construct


[Expand]to contain


[Expand]to draw


[Expand]to hold


[Expand]to intersect


[Expand]to join


[Expand]to be situated




[Expand]to revolve around


[Expand]truncated


[Expand]section


geometric relations

[Expand]to encompass


[Expand]encompassed


[Expand]
encompassed - definition


[Expand]inscribed


[Expand]
inscribed - definition


[Expand]congruent surfaces


[Expand]
congruent surfaces - definition


[Expand]congruent solids: solids that are completely identical in size and shape


[Expand]
congruent solids - definition


[Expand]similar solids: solids of the same shape, whose corresponding faces are similar surfaces


[Expand]
similar solids - definition


[Expand]similar surfaces


[Expand]
similar surfaces - definition


[Expand]
commensurable - definition


[Expand]
incommensurable: magnitudes that cannot be measured by the same measure


[Expand]
commensurable in square- definition


[Expand]
incommensurable in square: straight lines such that the squares on them cannot be measured by the same area


[Expand]to cut off


[Expand]to join



  1. perpendicular
  2. curve
  3. uniform line
  4. extension
  5. to complete a surface
  6. plane surface
  7. convex surface
  8. concave surface
  9. angle
  10. plane angle
  11. midpoint
  12. pentagon
  13. hexagon
  14. to circle
  15. sector
  16. versine
  17. chord
  18. arc
  19. circular segment
  20. semicircle
  21. less than a semicircle
  22. greater than a semicircle
  23. hypotenuse
  24. to be situated
  25. to cut
  26. to be drawn
  27. upper base
  28. standing
  29. to contain
  30. to attach
  31. attached
  32. axis
  33. pole
  34. to construct
  35. to draw a circle
  36. to touch
  37. base

Economic Terms

[Expand]coinage


Coins

[Expand]dinar

[Expand]dirham

[Expand]fals


[Expand]florin


[Expand]carlino


[Expand]grosso


[Expand]ducat


[Expand]tari


[Expand]grano


Weights and Measures

[Expand]barley: sixtieth of a cubit



Euclid's Elements

[Expand]Elements II-4


[Expand]Elements II-4: definition


[Expand]Elements II-5


[Expand]Elements II-6


[Expand]Elements II-7: definition


[Expand]Elements VI-17


[Expand]Elements VI-17: definition


[Expand]Elements VIII-11


[Expand]Elements VIII-11: definition


[Expand]Elements VIII-12


[Expand]Elements VIII-12: definition



General Terminology

[Expand]authors


  1. mathematics


[Expand]Indian scholars


[Expand]Arab scholars



Science

[Expand]science


[Expand]external science


[Expand]practical science


[Expand]ethics


[Expand]metaphysics


[Expand]optics


[Expand]physics


[Expand]politics


Astrology

عِلْم النُجوم

[Expand]astrology


[Expand]astrologer


[Expand]upper world


[Expand]sublunar world


[Expand]heavenly sphere


[Expand]earth


[Expand]conjunction of planets


Linguistics

[Expand]grammarian


[Expand]linguistics


[Expand]grammarian


Logic

[Expand]logic


[Expand]analogy


[Expand]to assume


[Expand]to deduce


[Expand]proof


[Expand]to prove


[Expand]demonstrative


[Expand]Q.E.D


[Expand]essence


[Expand]example


[Expand]to give an example


[Expand]proposition


[Expand]reason


[Expand]rule


Philosophy

[Expand]philosophy


[Expand]philosopher


[Expand]wisdom


[Expand]wise



Music

[Expand]music


[Expand]harmony


[Expand]diatessaron


[Expand]diapente


[Expand]diapason


Geographical locations

Spain

[Expand]Aragon


[Expand]Barcelona


[Expand]Castile


[Expand]Oriola


[Expand]Valencia


[Expand]Zaragoza


Turky

[Expand]Bursa


[Expand]Constantinople


[Expand]İskenderun - Alexandria