## The Elements of Euclid |

### From inside the book

Page 41

1 . they are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the

1 . they are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the

**half**of the paralleloF Book I. gram EBCA , because the diameter AB bisects OF EUCLID . 41. Page 42

Book I. gram EBCA , because the diameter AB bisects e it ; and the triangle DBC is the

Book I. gram EBCA , because the diameter AB bisects e it ; and the triangle DBC is the

**half**of the parallelogram DBCF , because C 34. 1 . the diameter DC bisects it : but the halves of equal things are 07. Ax . equal d ; therefore the ... Page 55

If a straight line be divided into two cqual parts , and also into two unequal parts ; the rectangl . contained by the unequal parts , together with the square of the line between the points of section , is equal to the square of

If a straight line be divided into two cqual parts , and also into two unequal parts ; the rectangl . contained by the unequal parts , together with the square of the line between the points of section , is equal to the square of

**half**... Page 56

2 If a straight line be bisected , and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of

2 If a straight line be bisected , and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of

**half**the line bisected , is equal to the square of the ... Page 59

THEOR , IF a straight line be divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double of the square of

THEOR , IF a straight line be divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double of the square of

**half**the line , and of the square of the line between the points of ...### 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