The calculation of the expressions in brackets may be simplified by taking the pairs in terms from the outside; by finding the successive differences of uo + um, ill + um_l, ..., or of uI u i +umi, ..
Thus the figure represents a section the (ideally simplified) uni verse cut perpendicular to C P' D the planes AB and CD between which the stars are contained, 1 This number is the 3/2th power of the ratio of the brightness of stars differing by a unit magnitude.
He sometimes altered and contorted the facts; he very often unduly simplified his problems; he was very apt when he had proved a favourite opinion true to infer it to be the whole truth.
Analysis showed that all the required sounds could be conveyed with 47 syllables, and having selected the ideographs that corresponded .to those sounds, they reduced them, first, to forms called hiragana, and, secondly, to still more simplified forms called katakana.
The question is greatly simplified when two of the principal moments are equal, say A=B.