Chav. VIII.

GEOMETRY.

869

Fig. 1115.

Fig. 1114.

of the port-crayoif a flat piece of brass or wood is divided longitudinally into two columns,called BC and DE; the first is marked with the 180 degrees, as taken from the line ofchords on a sector; and on DE arc arranged the 60 equal parts; when these columns areplaced side by side it is more easy to read them off.

This instrument is now seldom made use of, but in France it was much employed,and considered sufficiently accurate for all ordinary surveys, or for setting out angles eithersalient or re-entering: spiral lines were frequently set out with it, and the gardener em-ployed under Le Nostre marked out the fanciful forms which were then in fashion withthis simple instrument.

To measure salient and re-entering Angles , as that of the angle LMN, drive a stumpat M, over which place thering G, straining FG and GIIagainst the sides of the angle,and drive a stump into each ofthe rings F and II.

Stretch the cord FI, whichmust be attached to the stumpF, until it touches the extre-mity II of the cord F GII, and qremark how many divisions ofthe cord FI there are from Fto II; then note on the line1) E of the port crayon whatdivision or degree of the linewhich answers to 50, as 112,which will be the requiredangle. To find the salientangle OPQ, either prolong OPto U, and QP to S, to formthe re-entering angle RPS, which may be measured by the preceding rule; or place thering G of the cord at the salient angle P, and stretch the side GF along QP, and G ITalong OP, of the salient angle OPQ; so that by measuring with the divided cord thedistance FII, number of divisions are obtained, which sought on the line of cords denotethe degrees of the angle II PS, as well as the salient angle OPQ, which is equal to it.

To reduce or etilarge a Plan on a given scale without using ascale or protractor: as, to reduce the plan A, which has for itsbase FE, to another plan having the base III. Draw a lineK L, and from the point K as a centre, with the base FE asa radius, describe an arc NM, on which set off the given baseIII from N to O, and draw a right line K P through O : takethe distance F G from the plan A, and describe from the pointK, an arc Q R, of which take the chord R Q, and from thepoint II of the given base, describe with this distance the arcS: from the plan A take the distance E G, and from thepoint K describe the arc TV, of which take the cord VT,and carry to the point I of the given base III ;«and from thispoint I describe the arc X, which will cut the arc S in V;from the point II, draw’ a right lineII ^ to the point Y, which will make Kthe side II ^ homologous or relativeto F G, on the plan A : to have theside relative to G13, it is only neces-sary to follow the same rule, that isto say, from the point K, with thedistance G 13, describe the arc a 5, andcarry its chord 5 a, to the other pointY, the extremity of the line H Y, andfrom the point Y describe the arc c;then take the distance E B, from theplan A, and with it describe an arciroin the point K; so that by takingits chord ed, from the point I of thegiven base an arc may be described, andobserving where the arc cuts c, as at g\then draw the line Y^, which will be homologous to G 13. All the other relative sides maybe found by the same rules, so as to reduce the plan A to another whose base is II I; bythis means, plans may be diminished or increased, provided the base is not double the other

3 k f

Fig. 1116.

Fig. 1117.