The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 59
... angle a straight line makes with the diameter at the point a , or however small an angle it makes with ae , the ... edf ; butedf gc e bf is a right angle , wherefore eba is a right angle ; and eb is drawn from the centre : but a ...
... angle a straight line makes with the diameter at the point a , or however small an angle it makes with ae , the ... edf ; butedf gc e bf is a right angle , wherefore eba is a right angle ; and eb is drawn from the centre : but a ...
Página 64
... angle bae equal to the angle abd , and produce bd , if necessary , to e ... edf at their circumferences . The circumference bkc is equal to the ... angle at g is equal to the angle at a g b k e C 1 d h f h ; therefore the base bc ...
... angle bae equal to the angle abd , and produce bd , if necessary , to e ... edf at their circumferences . The circumference bkc is equal to the ... angle at g is equal to the angle at a g b k e C 1 d h f h ; therefore the base bc ...
Página 65
... edf at the circum- ferences of the equal circles abc , def , stand upon the equal circum- ferences bc , ef . The angle bgc is equal to the angle ehf , and the angle bac to the angle edf . If the angle bgc be equal to the angle ehf , it ...
... edf at the circum- ferences of the equal circles abc , def , stand upon the equal circum- ferences bc , ef . The angle bgc is equal to the angle ehf , and the angle bac to the angle edf . If the angle bgc be equal to the angle ehf , it ...
Página 66
Euclides. the angle elf . But equal angles stand upon equal ( iii . 26 ) circumferences , when they are at the centres ; therefore the circumference bgc is equal to the circumference ehf . But the whole circle abc is equal to the whole edf ...
Euclides. the angle elf . But equal angles stand upon equal ( iii . 26 ) circumferences , when they are at the centres ; therefore the circumference bgc is equal to the circumference ehf . But the whole circle abc is equal to the whole edf ...
Página 77
... angle bac is equal ( i . 32 ) to the remaining angle edf : wherefore the triangle abc is equiangular to the triangle def , and it is inscribed in the circle abc . Which was to be done . PROPOSITION III . - PROBLEM . About a given circle ...
... angle bac is equal ( i . 32 ) to the remaining angle edf : wherefore the triangle abc is equiangular to the triangle def , and it is inscribed in the circle abc . Which was to be done . PROPOSITION III . - PROBLEM . About a given circle ...
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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