Pseudo Euclid de ponderoso et levi 2002 MPIWG PMcL en eucli_ponde_01_en_2002 060.xml

A Fragment of Euclid on the Light and the Heavy

Definitions.

1 Bodies are equal in size that fill equal places. 2 Bodies are different in size that fill places that are not equal. 3 Bodies are said to be greater in size that are more ample in place. 4 Bodies are equal in power whose motions through equal intervals and with respect to the same time, air and water are equal . 5 Bodies are different in power whose motions in different times are equal. 6 Of bodies different in power, that is said to be greater in power which takes less time to move; but that [is said to be] lesser in power whose time is more ample. 7 Bodies are of the same kind which, if they are equal in size, are also equal in power. 8 Bodies are different in kind which, if they are equal in size, are not equal in power, assuming they are moved through the same medium. 9 Of bodies different in kind, that is said to be more powerful which is more solid [dense].

Theorems

First Theorem

Of bodies different in power that which moves that through more ample space has more ample power.

Second Theorem

Of bodies the same in kind, if these are among themselves multiples, their powers will be likewise be multiples.

Third Theorem

Of bodies the same in kind the proportion in both size and power is the same.

Fourth Theorem

Those bodies equal in power to a body of the same kind, are of the same kind among themselves, namely equals having been removed from that third, the forces of these will be equal, since the powers [were] equals of the third.