## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

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**given**in that book , as in this : but indeed there is scarce any need of it ...**species**of compound ratio . But Theon has made it the 5th def . of book 6 ...**given**, but they retain also Theon's , which they ought to have left out of the ... Page 365

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**given**in magnitude , when equals to them can be found . II . A ratio is said to be**given**, when a ratio of a**given**...**species**, which have each of their angles**given**, and the ratios of their sides**given**. IV . Points , lines , and ... Page 394

... given ( 1. dat . ) : but as LM to MN , so is GH to HK ; wherefore the ratio of GH to HK is given . 39 . PROP . XLII . Ir each of the sides of a triangle be given in magnitude , the triangle is

... given ( 1. dat . ) : but as LM to MN , so is GH to HK ; wherefore the ratio of GH to HK is given . 39 . PROP . XLII . Ir each of the sides of a triangle be given in magnitude , the triangle is

**given in species**. Let each of the sides of ... Page 395

... given and the points D , E are given ; therefore each of the straight lines DE , EF , FD is given ( 29. dat . ) in magnitude ; wherefore the triangle DEF is

... given and the points D , E are given ; therefore each of the straight lines DE , EF , FD is given ( 29. dat . ) in magnitude ; wherefore the triangle DEF is

**given in species**( 42. dat . ) ; and it is similar ( 4. 6. 1. def . 6. ) to the ... Page 396

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**given in species**. Let the sides of the triangle ABC have given ratios to one another , the triangle ABC is**given in species**. B A E F Take a straight line D given in magnitude ; and because the ratio of AB to BC is given , make the ...### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore