The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 35
... contained by any two of the straight lines which contain one of the right angles . d II . In every parallelogram ... rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the ...
... contained by any two of the straight lines which contain one of the right angles . d II . In every parallelogram ... rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the ...
Página 36
... rectangles contained by the whole and each of the parts are together equal to the square of the whole line . LET the straight line ab be divided into any two parts in the point c ; the rectangle contained by ab , bc , together with the ...
... rectangles contained by the whole and each of the parts are together equal to the square of the whole line . LET the straight line ab be divided into any two parts in the point c ; the rectangle contained by ab , bc , together with the ...
Página 37
... rectangle contained by ac , cb , for gc is equal to cb ; therefore ge is also equal to the rectangle ac , cb ; wherefore ag , ge are equal to twice the rectangle ac , cb . And hf , ck are the squares of ac , cb ; wherefore the four ...
... rectangle contained by ac , cb , for gc is equal to cb ; therefore ge is also equal to the rectangle ac , cb ; wherefore ag , ge are equal to twice the rectangle ac , cb . And hf , ck are the squares of ac , cb ; wherefore the four ...
Página 38
... contained by ad , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomoncmg ; there- the rectangle ad , db : to each of these fore the gnomon cmg is equal to add1g , which is equal ( ii . 4. cor . ) to the ...
... contained by ad , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomoncmg ; there- the rectangle ad , db : to each of these fore the gnomon cmg is equal to add1g , which is equal ( ii . 4. cor . ) to the ...
Página 39
... rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle ab , bc ...
... rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle ab , bc ...
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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