## 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 52

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**Constr**. + 3 Ax . 1 Ax . * 2. 1 . + 3 Post . † 15 Def .**Constr**. § 1 Ax . From the point A to B draw * the straight line AB ; and upon it describe the equilateral triangle DAB , and produce the straight lines DA , DB , to E and F ; from ... Page 9

... . Therefore , if two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise the angles contained by those sides equal to one another , * 3. 1 . +

... . Therefore , if two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise the angles contained by those sides equal to one another , * 3. 1 . +

**Constr**. + Hyp , BOOK I. PROP . V. 9. Page 10

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**Constr**. + Hyp , 14. 1 . §**Constr**. ¶ Hyp . * 3 Ax . + 4. 1 . + 3 Ax . their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each . Which ... Page 11

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**Constr**. For , if AB be not equal to AC , one of them is greater than the other . Let AB be the greater ; and from it cut * off DB equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC ... Page 14

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**Constr**. § 4. 1 . * 3. 1 . † 1. 1 . +**Constr**. || 24 Def . § 8. 1 . ¶ 10 Def . * 10 Def . Describe * upon it an equilateral triangle ABC , and bisect the angle ACB by the straight line CD . cut into two equal parts in the point D. to AB ...### 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