PRINCIPLE OF CARPENTERS’ SQUARES. ] 1
line performing the half of a semi-revolution, or it is thequarter of a complete revolution.
Right angles, such as RAC or DAC, fig. 8, pi. 1, orangles formed by a quarter of a revolution, are requiredto be made, or measured, almost every moment, in orderto carry into effect a great number of practical opera-tions.
When a body of troops, drawn up in line, in the di-rection AB, fig. 8, are required to face in a direction per-pendicular, or at right angles to it, they turn round thepoint A. If they were to revolve completely round inthe same direction, they would face as at first; bymaking only a quarter of a revolution, they face perpen-dicularly to their former position. Of course they can becommanded to face either to the right or the left.
Now let us suppose two other right lines, MON andOL, figs. 9 and 10, pi. 1, the position of OL being suchthat the two angles NOL and MOL are equal; thesetwo angles are equal to the two former angles, BAGand CAD of fig. 8, which are right angles.
To demonstrate this, place the right line, DAB, fig. 8, on MON,fig. 9, in such a manner that they coincide exactly at every point,as must be the case with two right lines, and that the pointA falls on the point O, the side AC will then coincide exactlywith the side OL. Let us suppose it possible that AC , fig. 9 ,has some other position, and falls to the left of OL. It isevident, as the angles CAB, CAD, are equal to each other,that MOL, which is greater by COL than the first angle, andNOL, which is less by COL than the second angle, cannot be equalto each other. On the contrary, if AC , fig. 10, fall to the right ofOL, the angles BAC, DAC , being equal to each other, and MOLbeing smaller than DAC , and NOL larger than BAC, cannot be equalto each other. Consequently AC cannot fall either to the right orthe left of OL, and must fall directly on it. The right angles, formedin the one case by the right lines, AC , BD, and on the other, by thetwo different right lines, OL, MN, are always equal to each other.
This is the first principle on which the use of the squareis founded. A square may be formed of two parts ofthe right line AB, AC , fig. 11, pi. 1, fixed firmly to-gether at A, so as to form a right angle - When it is de-