THE YOUNG STUDENT's POCKET COMPANION, OR ARITHMETIC, GEOMETRY, TRIGONOMETRY, and MENSURATION, Calculated for the improvement of Youth at With an APPENDIX, Of the Gregorian Kalendar, Determination of By JOHN DRAPER. Learning is unto á wife man as mament WHITEHAVEN THE PREFA C E. N UMBER feems to have fome affinity to space and duration. Space is indeterminate, duration eternal and number indefinite. There are places in space, times in duration, and quantity is defined by numbers. Portions in Space refpecting magnitude are expreffible by numbers, periods of time, as portions in duration, are affo 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 meafure,borrows the affiftance of numbers to make our ideas there of intelligible. Space indeterminate has neither beginning 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 fpace is abfolutely unintelligible. The prefent inftant in duration may be confidered 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 largest conceivable magnitude occupies no numerical part of fpace, neither does the longeft ftated 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 fum or maximum in the firft cafe falls not within our compre henfion, nor in the latter cafe is the least part or minimum by us affignable, So that any propofed number |