717359
a)
Sit , Achilles.
,
[Translation: Let be Achilles, the tortoise.
,
[Translation: Let be Achilles, the tortoise.
Sit ratio motus , ad motus ,
ut: , ad .
nempe: 10 ad
[Translation: Let the ratio of the motion of to the motion of be as to , namely, 1 to 10.
ut: , ad .
nempe: 10 ad
[Translation: Let the ratio of the motion of to the motion of be as to , namely, 1 to 10.
Et sit distantia , et . . nempe 1 mille
[Translation: And let the distance between and be , namely, one thousand pases.
[Translation: And let the distance between and be , namely, one thousand pases.
Et sit motus utriusque in eadem linea et ad easdem partes, nempe
ab , et versus
[Translation: And suppose the motion of both is in the same line and in the same direction, namely, from and towards .
ab , et versus
[Translation: And suppose the motion of both is in the same line and in the same direction, namely, from and towards .
Quæritur ex datis punctum ubi Achilles comprehendet
[Translation: From what is given there is sought the point where Achilles catches up with the ]
[Translation: From what is given there is sought the point where Achilles catches up with the ]
Quæestio solvitur exhibendo summam infinitæ progressionis decrescentis
ut sequitur: (species summa infinitæ progressionis decrescentis
ut in doctrinam de progressionisgeometricæ:
[Translation: The problem is solved by producing the sum of an infinite decreasing progression as follows: (the case of the sum of an infinite decreasing progression as in the teaching of geometric porgressions is:)
ut sequitur: (species summa infinitæ progressionis decrescentis
ut in doctrinam de progressionisgeometricæ:
[Translation: The problem is solved by producing the sum of an infinite decreasing progression as follows: (the case of the sum of an infinite decreasing progression as in the teaching of geometric porgressions is:)
Alia
[Translation: Other ]
[Translation: Other ]
(ut Archimedes de
quad: parab: pr:
[Translation: (as Archimedes in the quadrature of the parabola, proposition ]
quad: parab: pr:
[Translation: (as Archimedes in the quadrature of the parabola, proposition ]