1ter, as the double of the greater Baſe together with the Leſſer is to the
double of the leſſer together with the greater. Which is the Propoſition
more elegantly expreſſed.
double of the leſſer together with the greater. Which is the Propoſition
more elegantly expreſſed.
PROPOSITION.
If any number of Magnitudes ſo diſpoſed to one
another, as that the ſecond addeth unto the firſt
the double of the firſt, the third addeth unto
the ſecond the triple of the firſt, the fourth
addeth unto the third the quadruple of the
firſt, and ſo every one of the following ones
addeth unto the next unto it the magnitude of
the firſt multiplyed according to the number
which it ſhall hold in order; if, I ſay, theſe
Magnitudes be ſuſpended ordinarily on the
Ballance at equal diſtances; the Center of the
Equilibrium of all the compounding Magni
tudes ſhall ſo divide the Beam, as that the part
towards the leſſer Magnitudes is triple to the
remainder.
another, as that the ſecond addeth unto the firſt
the double of the firſt, the third addeth unto
the ſecond the triple of the firſt, the fourth
addeth unto the third the quadruple of the
firſt, and ſo every one of the following ones
addeth unto the next unto it the magnitude of
the firſt multiplyed according to the number
which it ſhall hold in order; if, I ſay, theſe
Magnitudes be ſuſpended ordinarily on the
Ballance at equal diſtances; the Center of the
Equilibrium of all the compounding Magni
tudes ſhall ſo divide the Beam, as that the part
towards the leſſer Magnitudes is triple to the
remainder.
Let the Beam be L T, and let ſuch Magnitudes as were ſpoken of
hang upon it; and let them be A, F, G, H, K; of which A is in
the firſt place ſuſpended at T. I ſay, that the Center of the Equi
librium ſo cuts the Beam T L as that the part towards T is triple to the
reſt. Let T L be triple to L I; and S L triple to L P: and Q L to L N,
173[Figure 173]
and L P to L O: I P,
P N, N O, and O L
ſhall be equal. And
in F let a Magnitude
be placed double to A;
in G another trebble to
the ſame; in H ano
ther Quadruple; and
ſo of the reſt: and let
thoſe Magnitudes be
taken in which there
is A; and let the ſame
be done in the Magni
tudes F, G, H, K. And
becauſe in F the remaining Magnitude, to wit B, is equal to A; take it
hang upon it; and let them be A, F, G, H, K; of which A is in
the firſt place ſuſpended at T. I ſay, that the Center of the Equi
librium ſo cuts the Beam T L as that the part towards T is triple to the
reſt. Let T L be triple to L I; and S L triple to L P: and Q L to L N,
173[Figure 173]and L P to L O: I P,
P N, N O, and O L
ſhall be equal. And
in F let a Magnitude
be placed double to A;
in G another trebble to
the ſame; in H ano
ther Quadruple; and
ſo of the reſt: and let
thoſe Magnitudes be
taken in which there
is A; and let the ſame
be done in the Magni
tudes F, G, H, K. And
becauſe in F the remaining Magnitude, to wit B, is equal to A; take it