Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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>AN
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APPENDIX,
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In which is contained certain
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THE OREMS and their DEMONSTRATIONS:
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Formerly written by the ſame Author, touching the
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CENTER
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of
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GRAVITY,
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of
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SOLIDS.</
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We preſuppoſe equall Weights to be alike diſpo
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ſed in ſever all Ballances, if the Center of Gra
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vity of ſome of thoſe Compounds ſhall divide the Ballance
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according to ſome proportion, and the Ballance ſhall
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alſo divide their Center of Gravity according to the
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ſame proportion.
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>LEMMA.</
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Let the line A B be cut in two equall parts in C,
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whoſe half A C let be divided in E, ſo that as B E is to
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E A, ſo may A E be to E C. </
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>I ſay that B E is double
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to E A. </
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>For as B E is to E
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A, ſo is E A to E C: there
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fore by Compoſition and by Permutation of Proportion, as
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B A is to A C, ſo is A E to E C: But as A E is to E C,
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that is, B A to A C, ſo is B E to E A: Wherefore B
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E is double to E A.
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This ſuppoſed, we will Demonſtrate, That,
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