The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 89
A greater magnitude is said to be a multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a certain number of times exactly . III . Ratio is a mutual relation of two magnitudes of ...
A greater magnitude is said to be a multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a certain number of times exactly . III . Ratio is a mutual relation of two magnitudes of ...
Σελίδα 91
A multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude .
A multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude .
Σελίδα 92
If the first magnitude be the same multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same ...
If the first magnitude be the same multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same ...
Σελίδα 93
Because ef is the same multiple of an that gh is of c , there are as many magnitudes in ef equal to a , as are in gh equal to c . Let ef be di- fi vided into the magnitudes ek , kf , each equal to a , and gh into gl , lh , each equal to ...
Because ef is the same multiple of an that gh is of c , there are as many magnitudes in ef equal to a , as are in gh equal to c . Let ef be di- fi vided into the magnitudes ek , kf , each equal to a , and gh into gl , lh , each equal to ...
Σελίδα 94
For the same reason , mis the same multiple of b , that n is of d : and because , as a is to b , so is c to d ( hypoth . ) , and of a and c have been taken certain equimultiples k , 1 : с and of b and d have been taken certain ...
For the same reason , mis the same multiple of b , that n is of d : and because , as a is to b , so is c to d ( hypoth . ) , and of a and c have been taken certain equimultiples k , 1 : с and of b and d have been taken certain ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole