### Rendering them useful to 100000.

A Number that consisteth of fife places being given, to find the Logarithm thereof.

I find the Logarithm of the first four Figures, rejecting the Charakteristick; then observe the difference between that and the next folloring, which multiply by the last Figure of the Number given, and cut off one Figure from the Product towards the right hand; the rest add to the Logarithm of the first four Figures. Lastly, if you prefix the proper Characteristick for the Number given, that Logarithm so ordered, is the number required.

Example. 19438 being propounded, I demand the Logarithm thereof: By the direction fore-going I find the Logarithm of the first four Figures, viz. 1943, to be (rejecting the Characteristick) 2884728, also I see the difference between that Number and the Number following to be 2235, which I multiply by the last figure of the Number propounded, being 8; and that sum is 17880. Wherefore I add 1788 to 2884728, and the prefix before it the proper Charcteristick for the Number given, which must be 4 - because that is the Charakteristick for all Numbers from 10000 to 100000, so is produced at last 4,2886516, which is the Logarithm for 19438, as was required.

Again,

Let it be required to find the Logarithm for 56724.

Having found the Logarithm of the first four figures to be 7537362, and the difference between that and the next 766, and multiplied the difference by 4, the last figure of the sum propounded, of which adding 306 to 7537362, they make 7537668, before which prefixing the Characteristick 4, the Logarithm for 56724 will be 4,7537668, the thing required.

And for 94395, it will be found 4,97449490, etc.

### FINIS © Rainer Stumpe URL: http://www.rainerstumpe.de