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4.34 Emerson’* Arithmetic of Infinites, bU»ncr, that this ufeful branch of fcience may be obtained with very little ftudy.In the fcholium to prop. vi. the author very juftly obferves, that in the arithmetic of infinites applied to praice, * lines are fuppoied to be made up of an infinite number of equidiftant points; plain figures of an infinite number of parallel lines, like the threads in apiece of cloth ; and folids of an infinite number of planes, like the leaves of a book. Yet thefe points, lines and furfaces, are not really fuch, but are called lb by reafon of the fimiiitude. For thefe points are in ftrinefs, infinitely fiiort lines j the lines infinitely narrow parallelograms ; and the planet that compofe the folids, infinitely thin folids j fo that whenever we fpeak of points, lines, or planes, compofing any geometrical magnitude, it muft always be underftood in the fenfe here mentioned.’For want of attending to this particular fenfe of the words pointy line-y and furface ^ very falfe ideas of the arithmetic of infinites have been formed ; and even the wholedorine fuppofed to have been built on a fandy foundation. It has been faid, that a point, which in the language of geometricians, has no parts, can, confequently, form no part of a line.; that a line, which in the common definition, is faid to have no breadth, can form no part of afurface j and a furface without thicknefs, can form no part of a folid. This is undoubtedly true, when the terms are taken in their common acceptation, but far otherwife, when in the fenfe mentioned by our author; and which is their true import whenever they occur in the arithmetic of infinites. We will go a little further, and obferva, that their dimenfions in the praical part of this dofitrine, will be greater or fmaller in proportion to the accuracy required in the foiution. Thus, for inftance, if the area of a parallelogram were required, when nothing lefs than a fuperficial inch is to be regarded, it will be fufficient to take the dimenfions true to the tenth part of an inch; and confequently the lines in this parallelogram, will be one tenth of an inch broad. If a greater degree of accuracy be required, their dimenfions will be lefs in proportion : the fame may be obferved of points and furfaces.
Newspaper Details
Monthly Review
London, Middlesex, GB
Tue, Dec 01, 1767
Page 17
Full Page
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USA 30 Jun 2024
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