7 Aug. 1814

Logic

2

Ch. │ │ Methodization

'. │ │ Subjects of Denominant

7

Quantitia continua et discreta: discreta the sole measure of continua

Where quantity is considered, it may be considered either with or without regard to the relation between part and whole: and if considered in one or other of these ways it can not but be considered: the division is therefore an exhaustive one.

Where quantity is considered, or at least attempted to be considered without regard to the relation between part and whole, it is considered with reference to figure. But if without regard to the relation between part and whole the idea of figure if indeed it be capable of being entertained, is indeterminate and confused.

Quantity according to the Logicians of old is either continuous or discrete. By continuous quantity they mean quantity considered with regard to figure, and without regard to the relation between part and whole. By discrete quantity they mean quantity considered with regard to the relation between part and whole and without regard to figure.

If the three branches of mathematical discipline be separately considered, continuous quantity is the subject of geometry, discrete quantity the subject of arithmetic and algebra.

But it is only by arithmetic, that either in relation to any proposition appertaining to geometry, or /any more than/ in relation to any proposition in algebra can be obtained. Divide a circle into a number of parts, for instance those called degrees, clear and distinct ideas are obtainable respecting the whole, and those or any other parts into which it is capable of being divided or conceived to be divided. Refuse all such division the best idea you can obtain of a circle will have neither determinate form nor use.

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