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

### From inside the book

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Page 39

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

are upon the same base BC , 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 * 34 . L DBC is the**half**of the parallelogram DBCF ... Page 40

is the

is the

**half**of the parallelogram DEFH , because the diameter DF bisects it : but the halves of * 7 Ax . equal things are * equal : therefore the triangle ABC is equal to the triangle DEF . Wherefore triangles , & c . Q. E. D. ' * 37 . Page 53

If a straight line be divided into two equal parts , and also into two unequal parts ; the rectangle 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 equal parts , and also into two unequal parts ; the rectangle 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 54

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 bi- . sected , is equal to the square of ... Page 58

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

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 section .### 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

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole