## 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

Results 1-5 of 100

Page 15

... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the

... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the

**triangle ABC**to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the R**angle ABC**to ... Page 16

...

...

**angle ABC**shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . Α Because AF is equal to AG , and AB to ... Page 18

...

...

**angle**which is contained by the two sides of the one shall be equal to the**angle**contained by the two sides equal to them , of the other . Let**ABC**, DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF ... Page 22

...

...

**angle**CBA be equal to ABD , each of them is a A D B C Ε D B A C right ( def . 10. )**angle**; but , if not , from the ...**ABC**; therefore the**angles**DBA ,**ABC**are equal to the three**angles**DBE , EBA ,**ABC**; but the**angles**CBE , EBD have ... Page 23

... ABC , ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common

... ABC , ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common

**angle ABC**, the remaining angle ABE is equal ( 3. Ax . ) to the re- maining angle ABD ...### 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