GNOMONICS

, the same as Dialling; or the art of drawing sun and moon dials, on any given plane; being so called, because it shews how to find the hour of the day or night by the shadow of a Gnomon or style.

GOLDEN Number, is the particular year of the Metonic or Lunar Cycle. See Lunar Cycle.

To find the Golden Number: Add 1 to the given year, and divide the sum by 19, and what remains will be the Golden Number; unless 0 remain, for then 19 is the Golden Number.

Thus, the Golden Number for the year 1791, is 6; as by the operation in the margin.

Golden Rule, a rule so called on account of its excellent use, in arithmetic, and especially in ordinary calculations, by which numbers are found in certain proportions, viz, having three numbers given, to find a 4th number, that shall have the same proportion to the 3d as the 2d hath to the 1st. On this account, it is otherwise called The Rule of Three, and The Rule of Proportion. See Rule of Three.

Having stated, or set down in a line, the three terms, in the order in which they are proportional, multiply the 2d and 3d together, and divide the product by the 1st, so shall the quotient be the answer, or the 4th term sought.

Thus, if 3 yards of cloth cost a guinea or 21 shillings, what will 20 yards cost. Here the two prices or values must bear the same proportion to each other as the two quantities, or number of yards of cloth, i. e. 3 must bear the same proportion to 20, as 21s, the value of the former, must bear to the value of the latter: and therefore the stating and operation of the numbers will be thus,

Then multiplying the 2d and 3d together, and dividing the product by the 1st, it gives 140s. or 7l. for the answer, being the cost of 20 yards.

GONIOMETRICAL Lines, are lines used for measuring or determining the quantity of angles: such as sines, tangents, secants, versed sines, &c.

Mr. Jones, in the Philos. Trans. number 483, sect. 26, gave a paper, containing a commodious disposition of equations for exhibiting the relations of Goniometrical Lines; from which a multitude of curious theo-| rems may be derived. See also Robertson's Elem. of Navigation, vol. 1, p. 181, Edit. 4.