12 CONSTRUCTION OF THE CANON.
easily which arise by subtraction of an easy part of the number from the whole number.
14.We call easy parts of a number, any parts the denominators of which ave made up of unity and a number of cyphers such parts being obtained by rejecting as many of the figures at the end of the principal number as there are cyphers in the denominator.
Thus the tenth, hundredth, thousandth, 10000th, 100000th 1000000th, 10000000th parts are easily obtained, because the tenth part of any number is got by deleting its last figure, the hundredth its last two, the thousandth its last three figures, and so with the others, by always deleting as many of the figures at the end as there are cyphers in the denominator of the part. Thus the tenth part of 99321 is 9932, its hundredth part is 993, its thousandth 99, &c.
15.The half, twentieth, two hundredth, and other parts denoted by the number two and cyphers, are also tolerably easily obtained; by rejecting as many of the figures at the end of the principal number as there are cyphers in the denominator, and dividing the remainder by two.
Thus the 2000th part of the number 9973218045 is 4986609, the 20000th part is 498660.
16.Hence it follows that if from radius with seven cyphers added you subtract its 100000000th part, and from the number thence arising tts 10000000th part, and so on, a hundred numbers may very easily be continued geometrically in the proportion subsisting between radius and the sine less than it by unity, namely between 10000000 and 9999999; and this series of proportionals we name the First table.
Thus
