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◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-10-incommensurable-magnitudes / Subsection: Propositions from Book 10

Subsection: Propositions from Book 10

This subsection contains the propositions from Book 10 of Euclid's “Elements”.

Table of Contents

  1. Proposition: Prop. 10.001: Existence of Fraction of Number Smaller than Given Number
  2. Proposition: Prop. 10.002: Incommensurable Magnitudes do not Terminate in Euclidean Algorithm
  3. Proposition: Prop. 10.003: Greatest Common Measure of Commensurable Magnitudes
  4. Proposition: Prop. 10.004: Greatest Common Measure of Three Commensurable Magnitudes
  5. Proposition: Prop. 10.005: Ratio of Commensurable Magnitudes
  6. Proposition: Prop. 10.006: Magnitudes with Rational Ratio are Commensurable
  7. Proposition: Prop. 10.007: Incommensurable Magnitudes Have Irrational Ratio
  8. Proposition: Prop. 10.008: Magnitudes with Irrational Ratio are Incommensurable
  9. Proposition: Prop. 10.009: Commensurability of Squares
  10. Proposition: Prop. 10.010: Construction of Incommensurable Lines
  11. Proposition: Prop. 10.011: Commensurability of Elements of Proportional Magnitudes
  12. Proposition: Prop. 10.012: Commensurability is Transitive Relation
  13. Proposition: Prop. 10.013: Commensurable Magnitudes are Incommensurable with Same Magnitude
  14. Proposition: Prop. 10.014: Commensurability of Squares on Proportional Straight Lines
  15. Proposition: Prop. 10.015: Commensurability of Sum of Commensurable Magnitudes
  16. Proposition: Prop. 10.016: Incommensurability of Sum of Incommensurable Magnitudes
  17. Proposition: Prop. 10.017: Condition for Commensurability of Roots of Quadratic Equation
  18. Proposition: Prop. 10.018: Condition for Incommensurability of Roots of Quadratic Equation
  19. Proposition: Prop. 10.019: Product of Rational Numbers is Rational
  20. Proposition: Prop. 10.020: Quotient of Rational Numbers is Rational
  21. Proposition: Prop. 10.021: Medial is Irrational
  22. Proposition: Prop. 10.022: Square on Medial Straight Line
  23. Proposition: Prop. 10.023: Segment Commensurable with Medial Segment is Medial
  24. Proposition: Prop. 10.024: Rectangle Contained by Medial Straight Lines Commensurable in Length is Medial
  25. Proposition: Prop. 10.025: Rationality of Rectangle Contained by Medial Straight Lines Commensurable in Square
  26. Proposition: Prop. 10.026: Medial Area not greater than Medial Area by Rational Area
  27. Proposition: Prop. 10.027: Construction of Components of First Bimedial
  28. Proposition: Prop. 10.028: Construction of Components of Second Bimedial
  29. Proposition: Prop. 10.029: Construction of Rational Straight Lines Commensurable in Square When Square Differences Commensurable
  30. Proposition: Prop. 10.030: Construction of Rational Straight Lines Commensurable in Square Only When Square Differences Incommensurable
  31. Proposition: Prop. 10.031: Constructing Medial Commensurable in Square I
  32. Proposition: Prop. 10.032: Constructing Medial Commensurable in Square II
  33. Proposition: Prop. 10.033: Construction of Components of Major
  34. Proposition: Prop. 10.034: Construction of Components of Side of Rational plus Medial Area
  35. Proposition: Prop. 10.035: Construction of Components of Side of Sum of Medial Areas
  36. Proposition: Prop. 10.036: Binomial is Irrational
  37. Proposition: Prop. 10.037: First Bimedial is Irrational
  38. Proposition: Prop. 10.038: Second Bimedial is Irrational
  39. Proposition: Prop. 10.039: Major is Irrational
  40. Proposition: Prop. 10.040: Side of Rational plus Medial Area is Irrational
  41. Proposition: Prop. 10.041: Side of Sum of Medial Areas is Irrational
  42. Proposition: Prop. 10.042: Binomial Straight Line is Divisible into Terms Uniquely
  43. Proposition: Prop. 10.043: First Bimedial Straight Line is Divisible Uniquely
  44. Proposition: Prop. 10.044: Second Bimedial Straight Line is Divisible Uniquely
  45. Proposition: Prop. 10.045: Major Straight Line is Divisible Uniquely
  46. Proposition: Prop. 10.046: Side of Rational Plus Medial Area is Divisible Uniquely
  47. Proposition: Prop. 10.047: Side of Sum of Two Medial Areas is Divisible Uniquely
  48. Proposition: Prop. 10.048: Construction of First Binomial Straight Line
  49. Proposition: Prop. 10.049: Construction of Second Binomial Straight Line
  50. Proposition: Prop. 10.050: Construction of Third Binomial Straight Line
  51. Proposition: Prop. 10.051: Construction of Fourth Binomial Straight Line
  52. Proposition: Prop. 10.052: Construction of Fifth Binomial Straight Line
  53. Proposition: Prop. 10.053: Construction of Sixth Binomial Straight Line
  54. Proposition: Prop. 10.054: Root of Area contained by Rational Straight Line and First Binomial
  55. Proposition: Prop. 10.055: Root of Area contained by Rational Straight Line and Second Binomial
  56. Proposition: Prop. 10.056: Root of Area contained by Rational Straight Line and Third Binomial
  57. Proposition: Prop. 10.057: Root of Area contained by Rational Straight Line and Fourth Binomial
  58. Proposition: Prop. 10.058: Root of Area contained by Rational Straight Line and Fifth Binomial
  59. Proposition: Prop. 10.059: Root of Area contained by Rational Straight Line and Sixth Binomial
  60. Proposition: Prop. 10.060: Square on Binomial Straight Line applied to Rational Straight Line
  61. Proposition: Prop. 10.061: Square on First Bimedial Straight Line applied to Rational Straight Line
  62. Proposition: Prop. 10.062: Square on Second Bimedial Straight Line applied to Rational Straight Line
  63. Proposition: Prop. 10.063: Square on Major Straight Line applied to Rational Straight Line
  64. Proposition: Prop. 10.064: Square on Side of Rational plus Medial Area applied to Rational Straight Line
  65. Proposition: Prop. 10.065: Square on Side of Sum of two Medial Area applied to Rational Straight Line
  66. Proposition: Prop. 10.066: Straight Line Commensurable with Binomial Straight Line is Binomial and of Same Order
  67. Proposition: Prop. 10.067: Straight Line Commensurable with Bimedial Straight Line is Bimedial and of Same Order
  68. Proposition: Prop. 10.068: Straight Line Commensurable with Major Straight Line is Major
  69. Proposition: Prop. 10.069: Straight Line Commensurable with Side of Rational plus Medial Area
  70. Proposition: Prop. 10.070: Straight Line Commensurable with Side of Sum of two Medial Areas
  71. Proposition: Prop. 10.071: Sum of Rational Area and Medial Area gives rise to four Irrational Straight Lines
  72. Proposition: Prop. 10.072: Sum of two Incommensurable Medial Areas give rise to two Irrational Straight Lines
  73. Proposition: Prop. 10.073: Apotome is Irrational
  74. Proposition: Prop. 10.074: First Apotome of Medial is Irrational
  75. Proposition: Prop. 10.075: Second Apotome of Medial is Irrational
  76. Proposition: Prop. 10.076: Minor is Irrational
  77. Proposition: Prop. 10.077: That which produces Medial Whole with Rational Area is Irrational
  78. Proposition: Prop. 10.078: That which produces Medial Whole with Medial Area is Irrational
  79. Proposition: Prop. 10.079: Construction of Apotome is Unique
  80. Proposition: Prop. 10.080: Construction of First Apotome of Medial is Unique
  81. Proposition: Prop. 10.081: Construction of Second Apotome of Medial is Unique
  82. Proposition: Prop. 10.082: Construction of Minor is Unique
  83. Proposition: Prop. 10.083: Construction of that which produces Medial Whole with Rational Area is Unique
  84. Proposition: Prop. 10.084: Construction of that which produces Medial Whole with Medial Area is Unique
  85. Proposition: Prop. 10.085: Construction of First Apotome
  86. Proposition: Prop. 10.086: Construction of Second Apotome
  87. Proposition: Prop. 10.087: Construction of Third Apotome
  88. Proposition: Prop. 10.088: Construction of Fourth Apotome
  89. Proposition: Prop. 10.089: Construction of Fifth Apotome
  90. Proposition: Prop. 10.090: Construction of Sixth Apotome
  91. Proposition: Prop. 10.091: Side of Area Contained by Rational Straight Line and First Apotome
  92. Proposition: Prop. 10.092: Side of Area Contained by Rational Straight Line and Second Apotome
  93. Proposition: Prop. 10.093: Side of Area Contained by Rational Straight Line and Third Apotome
  94. Proposition: Prop. 10.094: Side of Area Contained by Rational Straight Line and Fourth Apotome
  95. Proposition: Prop. 10.095: Side of Area Contained by Rational Straight Line and Fifth Apotome
  96. Proposition: Prop. 10.096: Side of Area Contained by Rational Straight Line and Sixth Apotome
  97. Proposition: Prop. 10.097: Square on Apotome applied to Rational Straight Line
  98. Proposition: Prop. 10.098: Square on First Apotome of Medial Straight Line applied to Rational Straight Line
  99. Proposition: Prop. 10.099: Square on Second Apotome of Medial Straight Line applied to Rational Straight Line
  100. Proposition: Prop. 10.100: Square on Minor Straight Line applied to Rational Straight Line
  101. Proposition: Prop. 10.101: Square on Straight Line which produces Medial Whole with Rational Area applied to Rational Straight Line
  102. Proposition: Prop. 10.102: Square on Straight Line which produces Medial Whole with Medial Area applied to Rational Straight Line
  103. Proposition: Prop. 10.103: Straight Line Commensurable with Apotome
  104. Proposition: Prop. 10.104: Straight Line Commensurable with Apotome of Medial Straight Line
  105. Proposition: Prop. 10.105: Straight Line Commensurable with Minor Straight Line
  106. Proposition: Prop. 10.106: Straight Line Commensurable with that which produces Medial Whole with Rational Area
  107. Proposition: Prop. 10.107: Straight Line Commensurable With That Which Produces Medial Whole With Medial Area
  108. Proposition: Prop. 10.108: Side of Remaining Area from Rational Area from which Medial Area Subtracted
  109. Proposition: Prop. 10.109: Two Irrational Straight Lines arising from Medial Area from which Rational Area Subtracted
  110. Proposition: Prop. 10.110: Two Irrational Straight Lines arising from Medial Area from which Medial Area Subtracted
  111. Proposition: Prop. 10.111: Apotome not same with Binomial Straight Line
  112. Proposition: Prop. 10.112: Square on Rational Straight Line applied to Binomial Straight Line
  113. Proposition: Prop. 10.113: Square on Rational Straight Line applied to Apotome
  114. Proposition: Prop. 10.114: Area contained by Apotome and Binomial Straight Line Commensurable with Terms of Apotome and in same Ratio
  115. Proposition: Prop. 10.115: From Medial Straight Line arises Infinite Number of Irrational Straight Lines

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