## 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 18

...

...

**Q. E. D. PROP**. VIII . THEOR . 1 If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal ... Page 19

...

...

**Q. E. D. PROP**. IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . it . Let BAC be the given rectilineal angle , it is required to bisect A Take any point D in AB , and from AC cut ( 3. 1 ... Page 22

...

...

**Q. E. D. PROP**. XIV . THEOR . IF , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the ... Page 23

...

...

**Q. E. D. PROP**. XV . THEOR . IF two straight lines cut one another , the vertical or opposite angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB ... Page 24

...

...

**Q. E. D. PROP**. XVII . THEOR . ANY two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is 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