## The Thirteen Books of Euclid's Elements, Volume 3Volume 3 of three-volume set containing complete English text of all 13 books of the Elements plus critical apparatus analyzing each definition, postulate, and proposition in great detail. Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; classical, medieval, Renaissance and modern commentators; refutations, supports, extrapolations, reinterpretations and historical notes. Vol. 3 includes Books 10-13: Commensurable magnitudes, solids, cones, cylinders. |

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The very personal computer

### Contents

I | 1 |

II | 10 |

III | 14 |

IV | 17 |

V | 20 |

VI | 22 |

VII | 24 |

VIII | 26 |

LXVI | 142 |

LXVII | 143 |

LXVIII | 145 |

LXIX | 147 |

LXX | 149 |

LXXI | 150 |

LXXII | 151 |

LXXIII | 155 |

IX | 28 |

XII | 31 |

XIII | 33 |

XIV | 34 |

XV | 36 |

XVI | 37 |

XVII | 39 |

XVIII | 40 |

XIX | 41 |

XX | 45 |

XXI | 47 |

XXII | 49 |

XXIII | 51 |

XXIV | 53 |

XXV | 55 |

XXVI | 56 |

XXVII | 58 |

XXVIII | 60 |

XXIX | 61 |

XXX | 66 |

XXXI | 68 |

XXXII | 69 |

XXXIII | 71 |

XXXIV | 75 |

XXXV | 78 |

XXXVI | 80 |

XXXVII | 83 |

XXXVIII | 84 |

XXXIX | 85 |

XL | 87 |

XLI | 88 |

XLII | 89 |

XLIII | 92 |

XLIV | 94 |

XLV | 95 |

XLVI | 98 |

XLVII | 99 |

XLIX | 101 |

L | 102 |

LI | 104 |

LII | 106 |

LIII | 109 |

LIV | 110 |

LV | 112 |

LVI | 116 |

LVII | 120 |

LVIII | 124 |

LIX | 125 |

LX | 128 |

LXI | 130 |

LXII | 132 |

LXIII | 135 |

LXIV | 137 |

LXV | 139 |

LXXIV | 158 |

LXXV | 159 |

LXXVI | 161 |

LXXVII | 163 |

LXXVIII | 164 |

LXXIX | 165 |

LXXX | 167 |

LXXXI | 168 |

LXXXII | 170 |

LXXXIII | 172 |

LXXXIV | 173 |

LXXXV | 174 |

LXXXVI | 177 |

LXXXVII | 178 |

LXXXVIII | 180 |

LXXXIX | 181 |

XC | 184 |

XCI | 186 |

XCII | 188 |

XCIII | 190 |

XCIV | 194 |

XCV | 199 |

XCVI | 203 |

XCVII | 206 |

XCVIII | 209 |

XCIX | 212 |

C | 215 |

CI | 218 |

CII | 221 |

CIII | 224 |

CIV | 227 |

CV | 229 |

CVI | 231 |

CVII | 232 |

CVIII | 233 |

CIX | 234 |

CX | 235 |

CXI | 236 |

CXII | 238 |

CXIII | 240 |

CXIV | 243 |

CXV | 248 |

CXVI | 252 |

CXVII | 254 |

CXVIII | 255 |

CXIX | 260 |

CXX | 272 |

CXXI | 365 |

CXXII | 436 |

CXXIII | 438 |

CXXIV | 508 |

CXXVI | 515 |

523 | |

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### Common terms and phrases

applied area a medial binomial straight line bisected circle ABCD circle EFGH commensurable in length commensurable in square cone cube cut in extreme cylinder decagon Deff diameter dodecahedron equiangular equilateral Euclid extreme and mean greater segment Hence icosahedron inscribed irrational straight line joined Lemma let the square magnitudes mean ratio medial area medial straight line medial whole parallelepipedal solids parallelogram pentagon perpendicular plane angles plane of reference polygon prism proposition proved pyramid ABCG ratio triplicate rational and incommensurable rational area rational straight line rectangle AC rectangle contained remainder right angles second apotome side Similarly solid angle solid CD square number square on AB squares on AC straight lines commensurable surable triangle twice the rectangle vertex whence