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