Galilei, Galileo - The systems of the world

Galilei, Galileo, The systems of the world, 1661

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SAGR. I do not very well underſtand the queſtion.

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?

The impetuoſity of
moveables equally
approaching to the
centre, are equal.

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?

Vpon an horizon
tall plane the move
able lieth ſtill.

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.

SALV. Very well: and for moveables equally ſwift, what's
your conceit of them?

SIMPL. I fancie that they paſs equal ſpaces in equal times.

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