## The Contents of the Fifth and Sixth Books of Euclid (with a Note on Irrational Numbers) Arranged and Explained |

### Contents

SECTION II | 12 |

To divide a finite segment of a straight line into any number of equal parts | 19 |

If all values of r s which make rAsB also make rCsD and if all values | 32 |

If from any vertex of a triangle a perpendicular be drawn to the opposite side | 103 |

SECTION X | 110 |

BX | 117 |

If three magnitudes be in proportion the first has to the third the duplicate ratio | 141 |

### Common terms and phrases

ABCD angles assumed base called centre circle commensurable common measure compounded Consequently consider construction corresponding corresponding sides defined definition described difficulty divided draw drawn ENUNCIATION equal equal angles Euclid's EXAMPLE exists Fifth Book figure follows four given greater Hence integer irrational number Join kind length less lower class magnitudes mean proportional meet multiple necessary NOTE opposite parallel parallelogram perpendicular positive possible produced proof Prop proportional PROPOSITION prove ratio rational fraction rational numbers rect rectangle contained rectilineal figure regard respectively result right angle satisfied segments separation shown sides similar similarly square straight line Suppose Take taken term third triangle triangle ABC triangles are similar