Page:The Construction of the Wonderful Canon of Logarithms.djvu/74

50 APPENDIX. For as in statics, from weights of 1, of 2, of 4, of 8, and of other like numbers of pounds in the same proportion, every number of pounds weight, which to us now are Logarithms, may be formed by addition; so, from the proportionals V, T, S, R, &c., which correspond to them, and from others also to be formed in duplicate ratio, the proportionals corresponding to every proposed Logarithm may be formed by corresponding multiplication of them among themselves, as experience will show.

The special difficulty of this method, however, is in finding the ten proportionals to twelve places by extraction of the fifth root from sixty places, but though this method is considerably more difficult, it is correspondingly more exact for finding both the Logarithms of proportionals and the proportionals of Logarithms.

F two numbers with known Logarithms be multiplied together, forming a third; the sum of their Logarithms will be the Logarithm of the third.

Also if one number be divided by another number, producing a third; the Logarithm of the second subtracted from the Logarithm of the first, leaves the Logarithm of the third,

If from a number raised to the second power, to the third power, to the fifth power, &c., certain other numbers be produced; from the Logarithm of the first multiplied by two, three, five, &c., the Logarithms of the others are produced.

Also