## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

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**parallelograms**are equal to one another , and the diameter bisects them , that is , divides them into two equal ...**parallelogram**, of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another and ... Page 38

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**parallelogram**ACDB into two equal parts . Q. E. D. PROP . XXXV . THEOR .**PARALLELOGRAMS**upon the same base , and between the same parallels , are equal to one another . * Let the**parallelograms**ABCD , EBCF be upon the same base BC , and ... Page 39

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**parallelogram**; and it is equal ( 35. 1. ) to ABCD , because it is upon the same base BC , and between the same parallels BC , AD : for the like reason , the**parallelogram**EFGH is equal to the same EBCH ; therefore also the**parallelogram**... Page 40

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**parallelogram**EBCA , because the diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the pa ...**parallelogram**; and they are equal ( 36. 1. ) to one another , because they are upon equal bases BC , EF , and between ... Page 41

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**parallelogram**and triangle be upon the same base , and between the same parallels ; the**parallelogram**shall be double of the triangle . Let the**parallelogram**ABCD and the triangle EBC be upon F A DE the same base BC , and between the ...### Other editions - View all

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

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore