## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ... |

### From inside the book

Results 1-5 of 62

Page 7

...

...

**straight lines**† CA , CB , to the points D A B E A , B : ABC shall be an equilateral triangle . Because the point A is the centre of the circle BCD , * 3 Postu- late . + 1 Post .**AC**is equal to AB ; and because the point B is the centre ... Page 9

... A may be on D , and the

... A may be on D , and the

**straight line**AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE ,**AC**shall ⚫ Hyp . coincide with DF , because the angle BAC is equal to + Hyp . the ... Page 13

...

...

**straight line**BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF * . • Hyp . Therefore BC coinciding with EF ; BA and**AC**shall coincide with ED and DF ; for , if the base BC coincides with the base ... Page 14

...

...

**straight line**CD . cut into two equal parts in the point D. to AB is Because**AC**is equal to CB ‡ , and CD common to the two triangles ACD , BCD ; the two sides**AC**, CD are equal to BC , CD , each to each ; and the angle ACD is equal the ... Page 22

...

...

**straight line**AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done ...**AC**, equal to the two DE , DF , each to each , viz . AB equal to DE , and**AC**to DF ; but the angle BAC greater than the angle ...### Other editions - View all

### Common terms and phrases

ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angles equal base BC BC is equal bisected centre circle ABC circumference BC common section Constr describe diameter double draw equal angles equal to F equiangular equimultiples exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio join less Let ABC Let the straight likewise meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon PROB.-To proportionals Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle sides square of AC straight line AB straight line AC THEOR.-If three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore