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Calculated for the improvement of Youth at
School, and for the benefit of such as have
With an APPENDIX,
Eclipses, Plan of a perpetual Almanack, fome
for the AUTHOR.
P R E F A C E.
UMBER seems to have fome affinity to space and
duration. Space is indeterminate, duration eterAal and number indefinite. There are places in space, times in duration, and quantity is defined by numbers. Portions in Space respecting magnitude are expressible by numbers, periods of time, as portions in duration, are also explained by numbers. Hence it may be inferred, that every thing that is the object of fenfe or perception, whether extenfion, duration, magnitude, motion, weight or measure, borrows the affiftance of numbers to make our ideas thereof intelligible. Space indeterminate has neither bieginning or ending, but we can fuppofe a point any where to be a center in fpace, and there begin our reckoning, whence numbers becoine neceffary to define all extended diftances from that point; - But to speak of the limits of space is abfolately unintelligible. The prefent inftant in daration may be considered as a fixed ERA,to reckon from, forwards or backwards, and portions of time in years, months, &c. may be defined by numbers : but the largeft conceivable magnitude occupies no numerical part of space, neither does the longest stated period of time become any numerical part of eternity. One or unity, is the beginning of numbers and may be augmented, by addition of more units or parts of an unit;'or it may be diminished by a fubtraction of its parts ; but the ultimate sum or maximum in the first case falls not within our compre
nor in the latter case is the least part or minimum by us affignable, So that any proposed number