The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 10
... third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles , which have the two sides AB , AC ...
... third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles , which have the two sides AB , AC ...
Page 23
... third side . Let ABC be a triangle : any two sides of it together shall be greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the ...
... third side . Let ABC be a triangle : any two sides of it together shall be greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the ...
Page 24
... third side , the two sides BA , AE , of the triangle ABE are greater than BE . To each of these add EC ; therefore +4 . Ax . the sides BA , AC are greater + than BE , EC . Again , because the two sides CE , ED of the † 20. 1. triangle ...
... third side , the two sides BA , AE , of the triangle ABE are greater than BE . To each of these add EC ; therefore +4 . Ax . the sides BA , AC are greater + than BE , EC . Again , because the two sides CE , ED of the † 20. 1. triangle ...
Page 25
... third . * Let A , B , C , be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B ; and B and C greater than A. It is required to make a triangle ...
... third . * Let A , B , C , be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B ; and B and C greater than A. It is required to make a triangle ...
Page 28
... third angle BAC to the third angle EDF B CE For , if AB be not equal to DE , one of them must be greater than the other . Let AB be the greater of the two , and make BG equal † to DE , and join GC : therefore , because BG is equal to DE ...
... third angle BAC to the third angle EDF B CE For , if AB be not equal to DE , one of them must be greater than the other . Let AB be the greater of the two , and make BG equal † to DE , and join GC : therefore , because BG is equal to DE ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole