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compasses from G to 8, and this extent laid from 9 the same%vay will reach to 12, the fourth proportion required.
4th. “ To find a mean proportional between any two givennumbers.” Suppose 8 and 32; extend the compasses from8 on the left-hand part of line to 32 on the right, thenbisecting this distance, its half will reach from 8 forward,or from 32 backward to 16; the mean proportional sought.
5lh. “ To extract the square root of any number.” Sup-pose 25; bisect the distance between 1 on the scale, andthe point representing 25, then the half of this distance setoff from 1, will give the point representing the root 5. Inthe same manner, the cube root, or that of any other higherpower may be found by dividing the distance, on the linebetween 1 and the given number, into as many equal partsas the index of the power expresses ; then one of theseparts set from 1, will find the point representing the rootrequired.
Gunter s Quadrant. — One made of wood, brass, &c.containing a kind of stereographic projection of the sphere,on the plane of the equinoctial, the eye being supposed tobe placed in one of the poles. Besides the use of thisquadrant in finding heights and distances, it serves also tofind the hour of the day, the sun’s azimuth, &c. and otherproblems of the globe.
Gunters Scale, —Usually called by seamen the Gunter, isa large plane scale, having various lines upon it, of greatuse in working the cases or questions in navigation. Thisscale is nearly two feet long, and about an inch and a halfbroad, with various lines upon it, both natural and loga-rithmic, relating to trigonometry, navigation, &c. On theone side are the natural lines, and on the other the artificialor logarithmic ones; the former side is first divided intoinches and tenths, and numbered from 1 to 24 inches, run-ning the whole length near one edge. One half the lengthof this side, consists of two plain diagonal scales for takingoff dimensions to three places of figures. On the otherhalf or foot of this side, are contained various lines relatingto trigonometry, in the natural manner, and marked thus,viz.
Rumb, the rumb or points of the compass ;
Sine, the line of sines ;
Tang, the line of tangents;
S.T. the sine tangents; and all the other end of thishalf are,
Leag. leagues or equal parts;