Transcriber's notes: (1) Numbers following letters (without space) like C2 were originally printed in subscript. Letter subscripts are preceded by an underscore, like C_n. (2) Characters following a carat (^) were printed in superscript. (3) Side-notes were relocated to function as titles of their respective paragraphs. (4) Macrons and breves above letters and dots below letters were not inserted. (5) [root] stands for the root symbol; [alpha], [beta], etc. for greek letters. (6) The following typographical errors have been corrected: ARTICLE LOGARITHM: "... tangents and secants for every minute of the quadrant to 10 places; these were obtained by calculating the logarithms of the natural sines, &c. given in the Thesaurus mathematicus of Pitiscus (1613)." 'these' amended from 'there'. ARTICLE LOGARITHM: "The final step was made by John Newton in his Trigonometria Britannica (1658) ..." 'Trigonometria' amended from 'Trigononometria'. ARTICLE LOGIC: "S is not P." 'P' amended from 'M'. ARTICLE LOGIC: "... Jevons proceeded to confuse analytic deduction from consequence to ground with hypothetical deduction from ground to consequence under the common term 'inverse deduction.'" 'consequence' amended from 'conseguence'. ARTICLE LOGIC: "But in induction the given particulars are the evidence by which we discover the universal, e.g. particular magnets attracting iron are the origin of an inference that all do ..." 'attracting' amended from 'attracing'. ARTICLE LOGIC: "... but which is to other regards deductive as syllogism, is set up in contrast to syllogism 906 and enumeration alike." 'contrast' amended from 'constrast' ARTICLE LOGIC: "67a 39-63." '-63'-63' amended from '-b 3'. ARTICLE LOIRE: "Owing to the extreme irregularity of the river in different seasons these canals form the only certain navigable way." 'extreme' amended from 'exteme'. ARTICLE LOLLARDS: "He summed up their doctrines under eleven heads: they condemn the having and using of images in the churches ..." added 'of'. ARTICLE LOMBARDY: "G. T. Rivoira in Origini dell' Architettura Lombarda (2 vols. Rome, 1901-1907) ..." 'Architettura' amended from 'Architetturo'. ARTICLE LONDONDERRY: "The scenery of the Roe valley, with the picturesque towns of Limavady and Dungiven, is also attractive, and the roads from the latter place to Draperstown and to Maghera ..." 'attractive' amended from 'atrractive'. ARTICLE LONGOMONTANUS: "... Problemata duo Geometrica (1638) ..." 'Geometrica' amended from 'Goemetrica'. ARTICLE LOOM: "... and, as appears from Grew (Mus. Reg. Soc. p. 69), it was formerly given to the little grebe or dabchick (P. fluviatilis or minor)." 'as' amended from 'ns'. ENCYCLOPAEDIA BRITANNICA