# Yx sentence example

yx

- 13 C figure of the three lines YX, XE, EY in the frame, and represents the three forces in equilibrium at the point YXE of the frame.
- The direction of YX, being a thrust upwards, shows the direction in which we must go round the triangle YXE to find the direction of the two other forces; doing this we find that the force XE must act down towards the point YXE, and the force EY away from the same point.
- But, assuming the distributive principle, the product of two lines appeared to give the expression xx' - yy' - zz' +i(yx' +xy')+j(xz' i j (yz' +zy').
- For it is easy to establish] the formula (yx) 2 0 4 = 2f.4-2(f y 1) 2 connecting the Hessian with the quartic and its first and second polars; now a, a root of f, is also a root of Ox, and con se uentl the first polar 1 of of q y p f?
- 67 b, superimposed and divided so that the length AX represents the load AX, the length AB the load AB, the length YX the reaction YX, and so forth.Advertisement
- If there are no redundant members in the frame there will be only two members abutting at the point of support, for these two members will be sufficient to balance the reaction, whatever its direction may be; we can therefore draw two triangles, each having as one side the reaction YX, and having the two other sides parallel to these two members; each of these triangles will represent a polygon of forces in equilibrium at the point of support.
- And now a directed line in space came to be represented as ix+jy+kz, while the product of two lines is the quaternion - + yy ' +2z') +i (yz ' - zy') +j (zx' - xz') +k (x y ' - yx').
- The three conditions of equilibrium arc therefore ~(X) = o, ~(Y) = o, ~(xY yX) = o.