The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 35
... gnomon . Thus the parallelogram hg , together with the complements af , fc , is the gnomon , which is more briefly ex- pressed by the letters agk , or ehc , which h a e f are at the opposite angles of the parallelo- grams which make ...
... gnomon . Thus the parallelogram hg , together with the complements af , fc , is the gnomon , which is more briefly ex- pressed by the letters agk , or ehc , which h a e f are at the opposite angles of the parallelo- grams which make ...
Página 38
... gnomon cmg is equal to add1g , which is equal ( ii . 4. cor . ) to the square of cd ; therefore the gnomon cmg , together with 1g , is equal to the rectangle ad , db , together with the square of cd ; but the gnomon cmg and 1g make up ...
... gnomon cmg is equal to add1g , which is equal ( ii . 4. cor . ) to the square of cd ; therefore the gnomon cmg , together with 1g , is equal to the rectangle ad , db , together with the square of cd ; but the gnomon cmg and 1g make up ...
Página 39
... gnomon cmg and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db ... gnomon akf , together with the square ck ; therefore the gnomon akf , together with the square ck , is double of ak ...
... gnomon cmg and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db ... gnomon akf , together with the square ck ; therefore the gnomon akf , together with the square ck , is double of ak ...
Página 40
... gnomon aoh was demonstrated to be quadruple of ak ; therefore four times the rectangle ab , bc , is equal to the gnomon aoh . To each of these add xh , which is equal ( ii . 4. cor . ) to the square of ac : therefore four times the ...
... gnomon aoh was demonstrated to be quadruple of ak ; therefore four times the rectangle ab , bc , is equal to the gnomon aoh . To each of these add xh , which is equal ( ii . 4. cor . ) to the square of ac : therefore four times the ...
Página 138
... gnomon chl , there- fore ce , or the parallelogram ad , is greater than the parallelogram af . 1 d e akc b Next , let ak the base of af be less than ac , and the same construction being made , the parallelogram dh is equal to dig ( i ...
... gnomon chl , there- fore ce , or the parallelogram ad , is greater than the parallelogram af . 1 d e akc b Next , let ak the base of af be less than ac , and the same construction being made , the parallelogram dh is equal to dig ( i ...
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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