1ball got to the ground, when the little one is ſtill within leſs than
a yard of the top of the Tower.
a yard of the top of the Tower.
SAGR. That this propoſition is moſt falſe, I make no doubt in
the world; but yet that yours is abſolutely true, I cannot well
aſſure my ſelf: nevertheleſs, I believe it, ſeeing that you ſo
ſolutely affirm it; which I am ſure you would not do, if you had
not certain experience, or ſome clear demonſtration thereof.
the world; but yet that yours is abſolutely true, I cannot well
aſſure my ſelf: nevertheleſs, I believe it, ſeeing that you ſo
ſolutely affirm it; which I am ſure you would not do, if you had
not certain experience, or ſome clear demonſtration thereof.
SALV. I have both: and when we ſhall handle the buſineſs
of motions apart, I will communicate them: in the interim, that
we may have no more occaſions of interrupting our diſcourſe, we
will ſuppoſe, that we are to make our computation upon a ball of
Iron of an hundred (a) pounds, the which by reiterated
ments deſcendeth from the altitude of an hundred (b) yards, in
five ſecond-minutes of an hour. And becauſe, as we have ſaid,
the ſpaces that are meaſured by the cadent moveable, increaſe in
double proportion; that is, according to the ſquares of the times,
being that the time of one firſt-minute is duodecuple to the time
of five ſeconds, if we multiply the hundred yards by the ſquare of
12, that is by 144, we ſhall have 14400, which ſhall be the
ber of yards that the ſame moveable ſhall paſs in one firſt-minute
of an hour: and following the ſame rule becauſe one hour is 60
minutes, multiplying 14400, the number of yards paſt in one
nute, by the ſquare of 60, that is, by 3600, there ſhall come forth
51840000, the number of yards to be paſſed in an hour, which
make 17280 miles. And deſiring to know the ſpace that the ſaid
ball would paſs in 4 hours, let us multiply 17280 by 16, (which
is the ſquare of 4) and the product will be 276480 miles: which
number is much greater than the diſtance from the Lunar concave
to the centre of the Earth, which is but 196000 miles, making the
diſtance of the concave 56 ſemidiameters of the Earth, as that
dern Author doth; and the ſemidiameter of the Earth 3500 miles,
of 3000 ^{*}Braces to a †mile, which are our Italian miles.
of motions apart, I will communicate them: in the interim, that
we may have no more occaſions of interrupting our diſcourſe, we
will ſuppoſe, that we are to make our computation upon a ball of
Iron of an hundred (a) pounds, the which by reiterated
ments deſcendeth from the altitude of an hundred (b) yards, in
five ſecond-minutes of an hour. And becauſe, as we have ſaid,
the ſpaces that are meaſured by the cadent moveable, increaſe in
double proportion; that is, according to the ſquares of the times,
being that the time of one firſt-minute is duodecuple to the time
of five ſeconds, if we multiply the hundred yards by the ſquare of
12, that is by 144, we ſhall have 14400, which ſhall be the
ber of yards that the ſame moveable ſhall paſs in one firſt-minute
of an hour: and following the ſame rule becauſe one hour is 60
minutes, multiplying 14400, the number of yards paſt in one
nute, by the ſquare of 60, that is, by 3600, there ſhall come forth
51840000, the number of yards to be paſſed in an hour, which
make 17280 miles. And deſiring to know the ſpace that the ſaid
ball would paſs in 4 hours, let us multiply 17280 by 16, (which
is the ſquare of 4) and the product will be 276480 miles: which
number is much greater than the diſtance from the Lunar concave
to the centre of the Earth, which is but 196000 miles, making the
diſtance of the concave 56 ſemidiameters of the Earth, as that
dern Author doth; and the ſemidiameter of the Earth 3500 miles,
of 3000 ^{*}Braces to a †mile, which are our Italian miles.
(a) (b) Note that
theſe Calculations
are made in
an weights and
meaſures. And 100
pounds
poiſe make 131 l.
Florentine. And
100 Engliſh yards
makes 150 2/5 Braces
Florent. ſo that the
brace or yard of
our Author is 3/4
of cur yard.
theſe Calculations
are made in
an weights and
meaſures. And 100
pounds
poiſe make 131 l.
Florentine. And
100 Engliſh yards
makes 150 2/5 Braces
Florent. ſo that the
brace or yard of
our Author is 3/4
of cur yard.
Therefore, Simplicius, that ſpace from the concave of the Moon
to the centre of the Earth, which your Accomptant ſaid could
not be paſſed under more than ſix days, you ſee that (computing
by experience, and not upon the fingers ends) that it ſhall be
ſed in much leſs than four hours; and making the computation
exact, it ſhall be paſſed by the moveable in 3 hours, 22 min. prim.
and 4 ſeconds.
to the centre of the Earth, which your Accomptant ſaid could
not be paſſed under more than ſix days, you ſee that (computing
by experience, and not upon the fingers ends) that it ſhall be
ſed in much leſs than four hours; and making the computation
exact, it ſhall be paſſed by the moveable in 3 hours, 22 min. prim.
and 4 ſeconds.