## The first six books of the Elements of Euclid, with numerous exercises |

### From inside the book

Results 1-5 of 14

Page 13

... angles . COR . 2. And consequently that all the angles made by any number of lines meeting in one point , are together equal to four right angles . PROPOSITION XVI . - THEOREM . If one side of a triangle be produced , the

... angles . COR . 2. And consequently that all the angles made by any number of lines meeting in one point , are together equal to four right angles . PROPOSITION XVI . - THEOREM . If one side of a triangle be produced , the

**exterior angle**... Page 14

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**exterior angle**of the triangle bd c , it is greater ( i . 16 ) than the interior and opposite angle dcb ; but ad bis equal ( i . 5 ) to a bd , because the side a b is equal to the side ad ; therefore the angle abd is likewise greater ... Page 15

... angle bed of the triangle dcb is greater than its angle bdc , and that the greater ( i . 19 ) side is posite to the ...

... angle bed of the triangle dcb is greater than its angle bdc , and that the greater ( i . 19 ) side is posite to the ...

**exterior angle**of a triangle is greater than the interior and opposite angle , the**exterior angle**bdc of the ... Page 19

... angle gcb is equal to the angle dfe ; but dfe is , by the hypothesis , equal to the angle bca ; wherefore also the ...

... angle gcb is equal to the angle dfe ; but dfe is , by the hypothesis , equal to the angle bca ; wherefore also the ...

**exterior angle**bha of the triangle a hc is equal to its interior and opposite angle bca ; which is impossible ... Page 20

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**exterior angle**equal to the interior and opposite upon the same side of the line , or makes the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another . g h f LET ...### Other editions - View all

### Common terms and phrases

a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle