The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 1 - 5 από τα 23.
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 98
... ratio to equal magnitudes . d a e b f C LET a and b be equal magnitudes , and c any other . a and b have each of ... greater than fg , and k the multiple of d which is next less than 1 . Then , because 1 is the multiple of d which is ...
... ratio to equal magnitudes . d a e b f C LET a and b be equal magnitudes , and c any other . a and b have each of ... greater than fg , and k the multiple of d which is next less than 1 . Then , because 1 is the multiple of d which is ...
Σελίδα 99
... greater than fg ; that is , fg is not less than k . And since ef is the same multiple of ac that fg is of cb ; fg is ... ratio than bc has to d . Also d has to bc a greater ratio than it has to ab . For , having made the same ...
... greater than fg ; that is , fg is not less than k . And since ef is the same multiple of ac that fg is of cb ; fg is ... ratio than bc has to d . Also d has to bc a greater ratio than it has to ab . For , having made the same ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle