Thus e1Xe1 = el, e 2 **Xe** 2 = - e l, e i X e 2 =e 2 X e 1 =e 2.

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.

Putting arrows on the frame diagram to indicate the direction of the forces, we see that the member EY must pull and therefore act as a tie, and that the member **XE** must push and act as a strut.

The weight load was pushing downwards, causing pressure on the strut.

In the beginning of the Lug .,(Ca Carlisle ".; **xe**/loduJr u m 'Aber/l ava Yinovro (8tne/uster)t 4th century the skilled artisans and builders, and the cloth and corn of Britain were equally famous on the continent.

The word was coined by Demiscianus, a Greek scholar, at the request of Federigo Cesi, founder of the Accademia dei Lincei, from the Greek ri **XE**, far, and ovoirEUU, to see.

If the origin of rectangular axes fixed in the lamina be shifted through a space whose projections on the original directions of the axes are X, u, and if the axes are simultaneously turned through an angle e, the coordinates of a point of the lamina, relative to the original axes, are changed from x, y to X+x cos ey sin e, u+x sin e+y cos e, or X + x ye, u + **Xe** + y, ultimately.

(8) If 0 be a point whose co-ordinates are (~, 1~), the moment of the couple when the forces are transferred to 0 as a new origin will be ~{(**xE**) Y(y~) X~.

Siace E2 + if + ~1, or ef, is necessarily an absolute invariant for all transformations of the (rectangular) co-ordinate axes, we infer that **XE** + un + v~ is also an absolute invariant.

Of knowledge they made use of " reason " (**Xe** yos), which was also one of their leading ethical conceptions.