In 1688, a teacher of arithmetic, W. Leybourn, doubtless thought he had made a hit by his title-page, which is thus fancifully arranged:—

A
Platform}for{Purchasers.
GuideBuilders.
MateMeasurers.

Another, of the same date, thought he had discovered an original method for obtaining the square and cube roots, and says—

'Now Logarithms lowre your sail,
And Algebra give place,
For here is found, that ne'er doth fail,
A nearer way to your disgrace.'

There was a struggle to live even a hundred years ago; we do not find that being a century nearer to the Golden Age than we are made much essential difference in men's characters:—The author of 'Arithmetick in Epitome,' published in 1740, entertains a professional jealousy of interlopers, for he observes, 'When a man has tried all Shifts, and still failed, if he can but scratch out anything like a fair Character, though never so stiff and unnatural, and has got but Arithmetick enough in his Head to compute the Minutes in a Year, or the Inches in a Mile, he makes his last Recourse to a Garret, and, with the Painter's Help, sets up for a Teacher of Writing and Arithmetick; where, by the Bait of low Prices, he perhaps gathers a Number of Scholars.'

Another, named Chappell, indulges in a little political illustration in his book, published in 1798—was he a disappointed place-hunter? He tells us in his versified tables—

'So 5 times 8 were 40 Scots,
Who came from Aberdeen,
And 5 times 9 were 45,
Which gave them all the spleen.'

The latter being an allusion to Wilkes' notorious No. 45 of the North Briton.

Some curious facts with respect to old systems of arithmetic were published at a meeting of the Schlesische Gesellschaft in Breslau in 1846. On that occasion Herr Löschke gave an account to the learned assembly of an old arithmetical work, 'Rechnen auf der Linie,' by the 'old Reckon-master,' Adam Rise. Adam was born about 1492; of his education nothing is known; he lived at Annaberg, and had three sons, Abraham, Isaac, and Jacob. His first 'Reckon-book,' in which he explained his peculiar method, appeared in 1518. It was somewhat on the principle of the calculating frame of the Chinese; a series of lines were drawn across a sheet of paper, on which, by the position of counters, numbers could be reckoned up to hundreds of thousands. The first line of the series was for units, the second for tens, the third for hundreds, the fourth for thousands, the fifth for ten thousands, and so on. It is remarkable that the highest counting-limit at that time was a thousand. The word 'million' was as yet unknown to the great body of calculators. Every number was counted, specified, and limited by thousands. The numeration of large numbers was thus expressed: the sum was divided into threes from right to left; a dot was placed over the first, and a second dot over the third of the following three, and so continued along the whole, until at last a dot stood over every fourth figure from the right. For example,

. . . . . . . .
6432798642102791527462,