2ZO

Mechanics.

pi.xiii.

Fig. 9.

the whole Doctrine whereof (as it standson a Mathematical Theory J may be re-duced

zz a a x — x’, whose Fluxion a a x — 3 x x x — 0,

gives x — which shews the Angle BAE=:

3

35 0 , 16'', as in the Examples above.

7. Since we are upon the Subject of Maximum !, Ishall here add Examples of two or three other Cafes ofthe fame Kind, which it is hoped will be acceptable tothe Curious, and yet not besides the Purpose of Mecha-nical Gentlemen. Let B B be a Piece of Wood placedhorizontally, and supported by the Pieces AB, AB,which make a given Angle ABC with the former ; itis required to find the Positions of two other PiecesAC, AC, given in Length, such that they shall sup-port the Piece B B with the greatest Force possible.

8. The Pieces AC, are fixed in A and C so as not toslip, they are supposed to have no considerable Weight.Then make BH ~\ AC, and from the Points A andH draw the Lines A G, H K, at right Angles to BR.If A C exp esses the absolute Strength of the Piece A C,then A G will express the Strength with which it sup-ports the Piece B B, as being perpendicular thereto.Now A G multiplied by the Lever (or Distance) B Cfrom the Centre of Motion B, (which expresses theMomentum or Force of the Piece AC) ought to be aMaximum.

9. To this End, put AC — a, GA =: x ; also HK=»,and KB—m ; then CC — ^/aa — xx, and because of thesimilar Triangles HKB, AGB, we have HK : KB : :

A G : G B — - and so BC — a a — xx — — x, andn n

AGXBC —x'Jaa — xx —— xx, whose Fluxion maden

/ X X X 9 jj j

equal to nothing is x V aa —xx — — - — _ x x

V aa—-,xx n

~ 0.