The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 89
... greater contains the less a certain number of times exactly . III . Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when ...
... greater contains the less a certain number of times exactly . III . Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when ...
Página 94
... greater than m , 1 is greater than n : and if equal , equal ; if less , less ( v . def . 5 ) . And k , 1 are any ... ratio to the second , which the third has to the fourth , then also any equimultiples whatever of the first and third have ...
... greater than m , 1 is greater than n : and if equal , equal ; if less , less ( v . def . 5 ) . And k , 1 are any ... ratio to the second , which the third has to the fourth , then also any equimultiples whatever of the first and third have ...
Página 95
... ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also greater than the fourth ; and if equal , equal ; if less , less . TAKE any equimultiples of each of them , as the doubles of ...
... ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also greater than the fourth ; and if equal , equal ; if less , less . TAKE any equimultiples of each of them , as the doubles of ...
Página 98
... greater than f , e is greater than f ; and if equal , equal ; if less , less . And d , e are any equimultiples of a , b , and f is any multiple of c . Therefore ( v . def . 5 ) , as a is to c , so is b to c . Likewise c has the same ratio ...
... greater than f , e is greater than f ; and if equal , equal ; if less , less . And d , e are any equimultiples of a , b , and f is any multiple of c . Therefore ( v . def . 5 ) , as a is to c , so is b to c . Likewise c has the same ratio ...
Página 99
... greater than fg ; that is , fg is not less than k . And since ef is the of cb same multiple of ac that fg is of cb ... ratio than be has to d . e T e a c f a gb 1 khd gb 1 kd Also d has to be a greater ratio than it has to ab . For ...
... greater than fg ; that is , fg is not less than k . And since ef is the of cb same multiple of ac that fg is of cb ... ratio than be has to d . e T e a c f a gb 1 khd gb 1 kd Also d has to be a greater ratio than it has to ab . For ...
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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