The work of writers like Rouse Ball in England, and Cajori and D. E. Smith in America, in revealing the fascinating story of the history of- arithmetic, has shown the subject developing slowly but surely along the corridor of time. This development, which culminates in present-day arithmetic, proceeds not only by increase of subject-matter, but involves suppression and modification both of matter and methods. It is not the haphazard growth of the wild plant, but the steady and systematic development which results from the pruning and shaping of the skilled and sympathetic gardener.