The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 6
... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a b c to the angle def , and the angle a cb to dfe . Therefore , if two triangles have two sides of the one equal to two ...
... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a b c to the angle def , and the angle a cb to dfe . Therefore , if two triangles have two sides of the one equal to two ...
Σελίδα 7
... remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle acf to the angle abg , and the angle afc to the angle a gb : and because the ...
... remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle acf to the angle abg , and the angle afc to the angle a gb : and because the ...
Σελίδα 12
... angle dba is equal to the two angles dbe , eba , add to these equals the angle a bc , therefore the angles dba , abc ... remaining angle a be is equal ( 3 ax . ) to the remaining angle ab d , the less to the greater , which is im ...
... angle dba is equal to the two angles dbe , eba , add to these equals the angle a bc , therefore the angles dba , abc ... remaining angle a be is equal ( 3 ax . ) to the remaining angle ab d , the less to the greater , which is im ...
Σελίδα 13
Euclides. are equal to the angles aed , deb . Take away the common angle a ed , and the remaining angle cea is equal ( 3 ax . ) to the remaining angle de b . In the same manner it can be demonstrated , that the angles ceb , aed are equal ...
Euclides. are equal to the angles aed , deb . Take away the common angle a ed , and the remaining angle cea is equal ( 3 ax . ) to the remaining angle de b . In the same manner it can be demonstrated , that the angles ceb , aed are equal ...
Σελίδα 20
... angle bgh ; therefore the remaining angle agh is equal to the remaining angle ghd ; and they are alternate angles ; there- fore a b is parallel to cd . Wherefore , if a straight line , & c . Q. E. D. PROPOSITION XXIX . - THEOREM . If a ...
... angle bgh ; therefore the remaining angle agh is equal to the remaining angle ghd ; and they are alternate angles ; there- fore a b is parallel to cd . Wherefore , if a straight line , & c . Q. E. D. PROPOSITION XXIX . - THEOREM . If a ...
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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