## 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 100

Page 5

...

...

**straight**lines , are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I.**Let**it be granted that a**straight**line**may**be drawn from any one point to any other point . II . That ... Page 7

...

...

**straight**line .**Let**AB be the given**straight**line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB , describe * the circle BCD , and from the centre B , at the distance BA , describe ... Page 8

...

...

**straight**line AB ; and upon it describe the equilateral triangle DAB , and produce the**straight**lines DA , DB , to E ...**Let**AB and C be the two given**straight**lines , whereof AB is the greater . It is required to cut off from AB , the ... Page 13

...

...

**straight**line BC upon EF ; the point C shall also coincide with the point F ...**Let**BAC be the given rectilineal angle , it is required to bisect it . Take ...**straight**line AF bisects the angle BAC . Because AD is equal to AE , and AF is ... Page 14

...

...

**straight**line AB is divided into two equal parts in the point D. Which was to be done . PROPOSITION XI . A D B PROB . - To draw a**straight**line at right angles to a given**straight**line , from a given point in the same .**Let**AB be a given ...### 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