Archimedes Texts

SALV. I will express it better by drawing a Figure: therefore
I will suppose the line A B [in Fig. 3.] parallel to the Horizon,
and upon the point B, I will erect a perpendicular B C; and after
that I adde this slaunt line C A. Understanding now the line C
A to be an inclining plain exquisitely polished, and hard, upon
which descendeth a ball perfectly round and of very hard matter,
and such another I suppose freely to descend by the perpendicular
C B: will you now confess that the impetus of that which de
scends by the plain C A, being arrived to the point A, may be
equal to the impetus acquired by the other in the point B, after
the descent by the perpendicular C B?

SAGR. I resolutely believe so: for in effect they have both the
same proximity to the centre, and by that, which I have already
granted, their impetuosities would be equally sufficient to re-carry
them to the same height.

SALV. Tell me now what you believe the same ball would do
put upon the Horizontal plane A B?

SAGR. It would lie still, the said plane having no declination.

SALV. But on the inclining plane C A it would descend, but
with a gentler motion than by the perpendicular C B?

SAGR. I may confidently answer in the affirmative, it seem
ing to me necessary that the motion by the perpendicular C B
should be more swift, than by the inclining plane C A; yet ne
vertheless, is this be, how can the Cadent by the inclination ar
rived to the point A, have as much impetus, that is, the same de
gree of velocity, that the Cadent by the perpendicular shall have
in the point B? these two Propositions seem contradictory.

The veloeity by the
inclining plane e
qual to the veloci
ty by the perpendi
oular, and the mo
tion by the perpen
dicular swifter
than by the incli
nation.

SALV. Then you would think it much more false, should I
say, that the velocity of the Cadents by the perpendicular, and
inclination, are absolutely equal: and yet this is a Proposition
most true, as is also this that the Cadent moveth more swiftly by
the perpendicular, than by the inclination.

SAGR. These Propositions to my ears sound very harsh: and
I believe to yours Simplicius?

SIMPL. I have the same sense of them.

SALV. I conceit you jest with me, pretending not to compre
hend what you know better than my self: therefore tell me Sim
plicius, when you imagine a moveable more swift than ano
ther, what conceit do you fancy in your mind?

SIMPL. I fancie one to pass in the same time a greater space
than the other, or to move equal spaces, but in lesser time.