The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 9
... bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal ... bisected b by the straight line af . Which was to be done . d e f C PROPOSITION X. - PROBLEM . To bisect a given ...
... bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal ... bisected b by the straight line af . Which was to be done . d e f C PROPOSITION X. - PROBLEM . To bisect a given ...
Página 10
... bisect ( i . 9 ) the angle ac b by the straight linecd . abis cut into two equal parts in the point d . Because ac is equal to cb , and cd common to the two triangles acd , bcd ; the two sides a c , cd are equal to bc , cd , each to ...
... bisect ( i . 9 ) the angle ac b by the straight linecd . abis cut into two equal parts in the point d . Because ac is equal to cb , and cd common to the two triangles acd , bcd ; the two sides a c , cd are equal to bc , cd , each to ...
Página 11
... bisect ( i . 10 ) fg in h , and join h cf , ch , cg ; the straight a f g b line ch , drawn from the d given point c , is perpendicular to the given straight line a b . Because fh is equal to hg , and he common to the two triangles fhc ...
... bisect ( i . 10 ) fg in h , and join h cf , ch , cg ; the straight a f g b line ch , drawn from the d given point c , is perpendicular to the given straight line a b . Because fh is equal to hg , and he common to the two triangles fhc ...
Página 13
... Bisect ( i . 10 ) ac in e , join be and produce it to f , and make ef equal to be ; join also fc , and produce ... bisected , it may be demon- strated that the angle bcg , that is , ( i . 15 ) the angle acd , is greater than the ...
... Bisect ( i . 10 ) ac in e , join be and produce it to f , and make ef equal to be ; join also fc , and produce ... bisected , it may be demon- strated that the angle bcg , that is , ( i . 15 ) the angle acd , is greater than the ...
Página 28
... Bisect ( i . 10 ) bc in e , join ae , and at the point e in the straight line ec make ( i . 23 ) the angle cef equal to d ; and through a draw ( i . 31 ) b a f e c 8 d ag parallel to ec , and through c draw cg pa- rallel to ef ...
... Bisect ( i . 10 ) bc in e , join ae , and at the point e in the straight line ec make ( i . 23 ) the angle cef equal to d ; and through a draw ( i . 31 ) b a f e c 8 d ag parallel to ec , and through c draw cg pa- rallel to ef ...
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Términos y frases comunes
ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle