The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 16
... BC , CD , each to each ; and the angle ACD is † Const . equal to the angle BCD ; there- fore the base AD is equal to the A * 4.1 . * 3.1 . * 1 . 1 . † Const . * D B base DB , and the straight line AB is divided into two equal parts in ...
... BC , CD , each to each ; and the angle ACD is † Const . equal to the angle BCD ; there- fore the base AD is equal to the A * 4.1 . * 3.1 . * 1 . 1 . † Const . * D B base DB , and the straight line AB is divided into two equal parts in ...
Page 17
... base DF is equal to the † Const . base EF ; therefore the angle DCF is equal to * 8 . 1 . the angle ECF : and they ... B C angle CBE , the less to the greater ; which is impossible : therefore two straight lines cannot have a common ...
... base DF is equal to the † Const . base EF ; therefore the angle DCF is equal to * 8 . 1 . the angle ECF : and they ... B C angle CBE , the less to the greater ; which is impossible : therefore two straight lines cannot have a common ...
Page 21
... base AB is equal to the base CF , * 4 . 1 . and the triangleAEB to the ... BC be bisected , and AC be produced to G , it may be demonstrated that the ... BC to D ; and be- cause ACD 294989.
... base AB is equal to the base CF , * 4 . 1 . and the triangleAEB to the ... BC be bisected , and AC be produced to G , it may be demonstrated that the ... BC to D ; and be- cause ACD 294989.
Page 26
... base DE to the base FG : the angle DCE is equal to the angle FAG . Therefore at the given point A in the given ... BC shall be greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other ...
... base DE to the base FG : the angle DCE is equal to the angle FAG . Therefore at the given point A in the given ... BC shall be greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other ...
Page 27
... base EG . And because DG is equal + Const . * 4.1 . G to DF , the angle DFG is equal to the angle DGF ; but the ... BC ; therefore BC is greater than EF . Therefore if two triangles , & c . Q. E. D. PROP . XXV . THEOR . If two triangles ...
... base EG . And because DG is equal + Const . * 4.1 . G to DF , the angle DFG is equal to the angle DGF ; but the ... BC ; therefore BC is greater than EF . Therefore if two triangles , & c . Q. E. D. PROP . XXV . THEOR . If two triangles ...
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