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

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Page 36

The opposite sides and angles of

The opposite sides and angles of

**parallelograms**are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . N.B. – A**parallelogram**is a four - sided figure , of which the opposite sides are ... Page 37

BC divides the

BC divides the

**parallelogram**ACDB into two equal parts . Q. E. D. 2d and 3d ין * 34. 1 . PROP . XXXV . THEOR .**Parallelograms**upon the same base , and between the same parallels , are equal to one another . Let the**parallelograms**ABCD ... Page 38

FDC from the trapezium ABCF , and from the same trapezium take the triangle EAB , and the * 3 Ax . remainders * are equal ; that is , the

FDC from the trapezium ABCF , and from the same trapezium take the triangle EAB , and the * 3 Ax . remainders * are equal ; that is , the

**parallelogram**ABCD is equal to the**parallelogram**EBCF . Therefore**parallelograms**upon the same ... Page 39

C draw CF parallel to BD : therefore each of the figures EBCA , DBCF is at

C draw CF parallel to BD : therefore each of the figures EBCA , DBCF is at

**parallelogram**: Def . and EBCA is equal * to DBCF , because they 35.2 . - are upon the same base BC , and between the same parallels BC , EF ; and the triangle ... Page 40

is the half of 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 .### 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