The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 7
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to a af , the less , and join ... than the other : let ab be the greater ; and from it cut ( i . 3 ) off db equal to ac , the less , and join dc ...
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to a af , the less , and join ... than the other : let ab be the greater ; and from it cut ( i . 3 ) off db equal to ac , the less , and join dc ...
Página 8
... greater than it ; which is impossible . e f C d But if one of the vertices , as d , be within the other triangle acb ; produce ac , ad to e , f ; therefore , because ac is equal to ad in the triangle acd , the angles ecd , fdc upon the ...
... greater than it ; which is impossible . e f C d But if one of the vertices , as d , be within the other triangle acb ; produce ac , ad to e , f ; therefore , because ac is equal to ad in the triangle acd , the angles ecd , fdc upon the ...
Página 13
... greater than either of the interior opposite angles . LET abc be a triangle ... f , and make ef equal to be ; join also fc , and produce acto g . a e f ... greater than the angle ecf ; therefore the angle acd is greater than bae ...
... greater than either of the interior opposite angles . LET abc be a triangle ... f , and make ef equal to be ; join also fc , and produce acto g . a e f ... greater than the angle ecf ; therefore the angle acd is greater than bae ...
Página 18
... greater than the base ef ; the angle bac is likewise greater than the angle edf . For , if it be not greater , it ... f and it was shewn that it is not equal to it ; therefore the angle bac is greater than the angle edf . Wherefore ...
... greater than the base ef ; the angle bac is likewise greater than the angle edf . For , if it be not greater , it ... f and it was shewn that it is not equal to it ; therefore the angle bac is greater than the angle edf . Wherefore ...
Página 43
... f the squares of ba , ae : take away the square of ae , which is common to ... greater than the squares of the sides contain- ing the obtuse angle , by ... greater than the squares of ac , cb , by twice the rectangle bc , cd ...
... f the squares of ba , ae : take away the square of ae , which is common to ... greater than the squares of the sides contain- ing the obtuse angle , by ... greater than the squares of ac , cb , by twice the rectangle bc , cd ...
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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