## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 32

... and between the same parallels BC , EF ; and the triangle ABC is the

... and between the same parallels BC , EF ; and the triangle ABC is the

**half**of the parallelogram EBCA , because the diameter AB bisects * it ; and the triangle DBC is the**half**of the parallelogram DBCF , because the diameter DC * Ax ... Page 43

... of

... of

**half**the line . Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D : the rectangle AD , DB , together with the square of CD , shall be equal to the square of CB . Page 44

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

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 47

anIf 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

anIf 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 section . Page 48

If a straight line be bisected , and produced to any point , the square of the whole line thus produced , and the square of the part of it produced , are together double of the square of

If a straight line be bisected , and produced to any point , the square of the whole line thus produced , and the square of the part of it produced , are together double of the square of

**half**the line bisected , and of the square of the ...### What people are saying - Write a review

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

### Common terms and phrases

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