The Encyclopaedia Britannica: a Dictionary of Arts, Sciences, And General ... 1

Cover The Encyclopaedia Britannica: a Dictionary of Arts, Sciences, And General ... 1
The Encyclopaedia Britannica: a Dictionary of Arts, Sciences, And General ... 1
T Spencer Thomas Spencer Baynes
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It affords strong confirmation of Uie safety of assuming the commutative law to exist in every branch of pure alcebra.
£x. The product of the cum of two squares by the sum of two squares can always be represented under the form of the sum of two squares.
For (c2 + 62)(c8 + (P)-(i + 5^'-l)j(a-6 7~l) ^{ae-hd)'* + (ad'^bcy.
Cor. (a«-»- 6*) (c« + ^-(vtt? + W)« + (ad-tc)*, or the pro- duct may be represented in two different ways, under the form of the sum of two squares.
Sect. V. — Peopobtion A2n>
...PEoaBEssiON.
46. In comparing together any two quantities of the some kind in rcapect of magnitude, we may consider how much the one is greater thfui the other, or else how many times the one contains either the whole or some part of the other; or^ which u the same thing, we may consider either [PBOPOBnoH ASt what i" the difference between the quantities, or will ii the quotient arisinir from the division of the one qnaotity by the other : the former of these is called their arithmdieal rUio, and the latter their geonutrical ratio, Tliese deno- minations, however, have been assumed arbitrarily, tod have little or no connection with the relations they in intended to ezpressi L ArUhiAetienl Proportion *tn4 Progretiitm, 47.


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