AN
APPENDIX,
In which is contained certain
THE OREMS and their DEMONSTRATIONS:
Formerly written by the ſame Author, touching the
CENTER of GRAVITY, of
SOLIDS.
APPENDIX,
In which is contained certain
THE OREMS and their DEMONSTRATIONS:
Formerly written by the ſame Author, touching the
CENTER of GRAVITY, of
SOLIDS.
POSTVLATVM.
We preſuppoſe equall Weights to be alike diſpo
ſed in ſever all Ballances, if the Center of Gra
vity of ſome of thoſe Compounds ſhall divide the Ballance
according to ſome proportion, and the Ballance ſhall
alſo divide their Center of Gravity according to the
ſame proportion.
ſed in ſever all Ballances, if the Center of Gra
vity of ſome of thoſe Compounds ſhall divide the Ballance
according to ſome proportion, and the Ballance ſhall
alſo divide their Center of Gravity according to the
ſame proportion.
LEMMA.
Let the line A B be cut in two equall parts in C,
whoſe half A C let be divided in E, ſo that as B E is to
E A, ſo may A E be to E C. I ſay that B E is double
165[Figure 165]
to E A. For as B E is to E
A, ſo is E A to E C: there
fore by Compoſition and by Permutation of Proportion, as
B A is to A C, ſo is A E to E C: But as A E is to E C,
that is, B A to A C, ſo is B E to E A: Wherefore B
E is double to E A.
whoſe half A C let be divided in E, ſo that as B E is to
E A, ſo may A E be to E C. I ſay that B E is double
165[Figure 165]to E A. For as B E is to E
A, ſo is E A to E C: there
fore by Compoſition and by Permutation of Proportion, as
B A is to A C, ſo is A E to E C: But as A E is to E C,
that is, B A to A C, ſo is B E to E A: Wherefore B
E is double to E A.
This ſuppoſed, we will Demonſtrate, That,