48 H. §S. CARSLAW. 
it provide. If we have to deal with numbers between two 
consecutive black numbers, the ordinary rule of proportional 
parts would be used. 
We pass now to Napier’s work, and we are fortunate 
in being able to listen to his own words, as given in the 
preface to Wright’s translation of the Descriptio, published 
in London in 1616. Down to the reference to the change 
from the Latin into English, this is a literal translation of 
the preface to Napier’s original :— 
‘Seeing there is nothing (right well beloved students in the 
mathematics) that is so troublesome to mathematicall practise, nor 
that doth more molest and hinder calculators, than the multipli- 
cations, divisions, square and cubical extractions of great numbers, 
which, besides the tedious expence of time, are for the most part 
subject to many slippery errors; I began, therefore, to consider 
in my minde, by what certaine and ready art I might remove 
those hindrances. And having thought upon many things to this 
purpose, I found at length some excellent briefe rules to be treated 
of (perhaps) hereafter. But amongst all, none more profitable 
than this, which together with the hard and tedious multiplica? 
tions, divisions, and extractions of rootes, doth also cast away 
from the worke it selfe, even the very numbers themselves that 
are to be multiplied, divided, and resolved into rootes, and putteth 
other numbers in their place, which performe as much as they can 
do, onely by addition and subtraction, division by two, or division 
by three: which secret invention, being (as all other good things 
are) so much the better asit shall be the more common ; I thought 
good heretofore to set forth in Latine for the publique use of 
mathematicians. But now some of our Countrymen in this Island 
well affected to these studies, and the more publique good, procured 
a most learned mathematician to translate the same into our vulgar 
English tongue, who after he had finished it, sent the coppy of it 
to me, to bee seene and considered on by myself. I having most 
willingly and gladly done the same, finde it to bee most exact and 
precisely conformable to my minde and the originall. Therefore 
