Two discourses of the objects, pleasures and advantages, I. of science: II. of political science / By Henry Lord Brougham.

  • Henry Brougham, 1st Baron Brougham and Vaux
Date:
1846
Catalogue details

Licence: Public Domain Mark

Credit: Two discourses of the objects, pleasures and advantages, I. of science: II. of political science / By Henry Lord Brougham. Source: Wellcome Collection.

    35/206 page 29
    necessarily such,—they are truths of themselves, and wholly independent of facts and experiments,— they depend only upon reasoning ; and it is utterly impossible they should be otherwise than true. This is the case with all the properties which we find belong to numbers and to figures—2 and 2 must of necessity, and through all time, and in every place, be equal to 4: those numbers must necessarily be always divisible by 3, without leay- ing any remainder over, which have the sums of the figures they consist of divisible by 3; and circles must necessarily, and for ever and ever, be to one another in the exact proportion of the squares of their diameters. It cannot be otherwise ; we cannot conceive it in our minds to be otherwise. No man can in his own mind suppose to himself that 2 and 2 should ever be more or less than 4; it would be an utter impossibility—a contradiction in the very ideas; and if stated in words, those words would have no sense. The other properties of number, though not so plain at first sight as this, are proved to be true by reasoning, every one step of which follows from the step immediately before, asa matter of course, and so clearly and unavoid- ably, that it cannot be supposed, or even imagined, to be otherwise ; the mind has no means of fancying how it could be otherwise: the final conclusion, from all the steps of the reasoning or demonstration, as it is called, follows in the same way from the Cc
    No text description is available for this image
    No text description is available for this image
    No text description is available for this image