The rectangle contained by rational straight lines (which are) commensurable in square only is irrational, and its square root is irrational - let it be called medial. * For let the rectangle $AC$ be contained by the rational straight lines $AB$ and $BC$ (which are) commensurable in square only. * I say that $AC$ is irrational, and its square root is irrational - let it be called medial.
Thus, a medial straight line has a length expressible as \(\delta^{1/4},\) for some positive rational number $\delta$.
Proofs: 1
Corollaries: 1 2
Proofs: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73
Propositions: 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125