Page:The Construction of the Wonderful Canon of Logarithms.djvu/64

40 CONSTRUCTION OF THE CANON. find the logarithm of this sine now contained in the table, and then add to it the logarithmic difference which the short table indicates as required by the preceding multiplication.

T is required to find the logarithm of the sine 378064. Since this sine is outside the limits of the Racial table, let it be multiplied by some proportional number in the foregoing short table, as by 20, when it will become 7561280. As this now falls within the Radical table, seek for its logarithm (by 50) and you will obtain 2795444.9, to which add 29957311.56, the difference in the short table corresponding to the proportion of twenty to one, and you have 32752756.4. Wherefore 32752756 is the required logarithm of the given sine 378064.

Let a b be radius, and a b c its double, on which as diameter is described a semicircle. On this lay off the given arc a e, bisect it in d, and from e in the direction of c lay off e h, the complement of d e, half the given arc. Then h c is necessarily equal to e h, since the quadrant d e h must equal the remaining quadrant made up of the arcs a d  and h e. Draw e i perpendicular to a ic, then e i is