## The Elements of Euclid |

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Page 341

... except in the case when the figures are triangles : the ' símilar

... except in the case when the figures are triangles : the ' símilar

**position**of the sides which contain the figures ... In the preceding books , Euclid has**given**no definition of equal figures , and it is certain he did not give this ... Page 367

Points , lines , and spaces are said to be

Points , lines , and spaces are said to be

**given in position**, which have always the same situation , and which are either actuale ly exhibited , or can be found . A. An angle is said to be**given in position**which is contained by ... Page 387

are given : therefore FB the excess of AB above a given magnitude AF has a given ratio to D. ” 25 . PROP . XXVIII . PROP . IF two lines

are given : therefore FB the excess of AB above a given magnitude AF has a given ratio to D. ” 25 . PROP . XXVIII . PROP . IF two lines

**given in position**cut one another , See N. the point or points in which they cut one another are ... Page 388

IF one of the extremities of a straight line

IF one of the extremities of a straight line

**given in position**and magnitude be given ; the other extremity shall also be given . Let the point A be given , to wit , one of the extremities of a straight line given in magnitude ... Page 389

IF a straight line be drawn to a given point in a straight line

IF a straight line be drawn to a given point in a straight line

**given in position**, and makes a given angle with it ... Because the angle is given , one equal to it can be found e ; let this a 1. def . be the angle at D : at the given A ...### 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