Page:The Construction of the Wonderful Canon of Logarithms.djvu/113

Notes. 89

From RABDOLOGIÆ:, Book I, Chapter IV.
Note on Decimal Arithmetic.

The preceeding
example:—divi-
sion by 861094 by
432.

861‍118

86‍141

8‍402

429

861094(1993¹¹⁸⁄₄₃₂

432

3888

8‍3888

86‍1296

861094‍64

86109‍136

8610‍316

861‍118,000

86‍141

8‍402

429

861094,000(1993,273

432

3888

8‍3888

86‍1296000‍

8610‍864

8610‍3024

86109‍1296

But if these fractions be unsatisfactory which have different denominators, owing to the difficulty of working with them, and those give more satisfaction whose denominators are always tenths, hundredths, thousandths, &c., which fractions that learned mathematician, Simon Stevin, in his Decimal Arithmetic denotes thus—①, ②, ③ naming them firsts, seconds, thirds: since there is the same facility in working with these fractions as with whole numbers, you will be able after com- pleting the ordinary division, and adding a period or comma, as in the margin, to add to the dividend or to the remainder one cypher to obtain tenths, two for hundredths, three for thousandths, or more afterwards as required ; and with these you will be able to proceed with the working as above. For instance, in the preceding example, here repeated, to which we have added three cyphers, the quotient will become 1993,273, which signifies 1993 units and 273 thousandth parts or $\scriptstyle {\frac {273}{1000}}$ or, according to Stevin, 1993,2^′7^″3^‴ further the last remainder, 64, is neglected in this decimal arithmetic because 30 ae it is of small value, and similarly in like examples.

Simon Stevin, to whom Napier here refers, was born at Bruges in 1548, and died at The Hague in 1620, He published various mathematical works in Dutch. The Tract on Decimal Arithmetic, which introduced the idea of decimal fractions and a notation for them, was published in 1585 in Dutch, under the title of ‘De Thiende,’ and in the same year in French, under the title of ‘La Disme.’

We find Briggs, in his ‘Remarks on the Appendix,’ while sometimes employing the point, also using the notation 25118865 for $\scriptstyle 2{\frac {5118865}{10000000}}$, distinguishing the fractional part by retaining the line separating the numerator and denominator, but omitting the latter. The form 2|5118865 has also been used. If we take any number such as $\scriptstyle 94{\frac {1305}{10000}}$, the following will give an idea of some of the different notations employed at various times :—

	⓪①②③④
94⓪1①3②0③5④;	941605;

941^′3^″0^‴5^⁗; 941305; 94|1305; 94.1305.