## The Elements of Euclid |

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Page 313

... as this was the proper place for it ; duplicate and triplicate ratio being

... as this was the proper place for it ; duplicate and triplicate ratio being

**species**of compound ratio . ... 23 , book 6 , and which Clavius , Herigon , and Barrow have likewise**given**, but they retain also Theon's , which they ought ... Page 367

Rectilineal figures are said to be

Rectilineal figures are said to be

**given in species**, which have each of their angles given , and the ratios of their sides given . IV . Points , lines , and spaces are said to be given in position , which have always the same situation ... Page 396

c 1. data . tude ; and the ratio of LM to MN is therefore given ; but as LM to MN , so is GH to HK ; wherefore the ratio of GH to ... See N. IF each of the sides of a triangle be given in magnitude , the triangle is

c 1. data . tude ; and the ratio of LM to MN is therefore given ; but as LM to MN , so is GH to HK ; wherefore the ratio of GH to ... See N. IF each of the sides of a triangle be given in magnitude , the triangle is

**given in species**. Page 397

DEF is

DEF is

**given in species**d ; and it is similar e to the triangle d 42 dat . ABC : which is therefore**given in species**. ( 4.6 . 1. def . ( 6 . e PROP . XLIV . 41 , IF one of the angles of a triangle be given , and if the sides about it ... Page 398

Scé N. IF the sides of a triangle have to one another given ratios , the triangle is

Scé N. IF the sides of a triangle have to one another given ratios , the triangle is

**given in species**. ... Take a straight line D given in magnitude ; and because the ratio of AB to BC is given , make the ratio of D to E the same 2 2.### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole