RATIFICATION

(Lat. ratum, determined, facio, / make. ) Th e solemn act by which a competent authority gives validity to an instrument, agreement, . The term is ordinarily used in international law for the sanction given by governments to treaties contracted by their representatives. In French law, ratification is defined the approbation or confirmation of what has been done or promised. Thus, in many instances, a person, on attaining his majority, ratifies acts done by himself or his guardian in his minority. And ratification is either expre or tacit; the latter resulting, by implication, from his silence for ten years after arttaining his majority. RATIO (Lat.), in Geometry, is defined by Euclid {Elements, book v. def. 3.) to be " a mutual relation of two magnitudes of the same kind to one another in respect of qiiantity." This definition has been much criticised. Dr. Barrow (l.cctioncs Math.) calls it a metaphysical definition, inasmuch as it is not properly a mathematical definition, since nothing in mathematics depends on it, or can be deduced from it; and supposes that Euclid had probably no other design in making it than to give a general summary idea of ratio to beginners. It has been remarked, that as the word quantity in our language, if not quite synonymous with magnitude, has a signification only a little more general, the definition as above rendered is either tautological or unmeaning. Dr. Simson supposes it to be the interpolation of some unskilful editor. Leslie {Eleinents of Geometry) ingeniously supposes that the Greek word ^viXtxiTn;, which is usually translated quantity, may have reference to vnvltitude or number, as well as to magnitude, and that Euclid's definition may be rendered as follows: — " Ratio is a certain mutual habitude of two homogeneous magnitudes with respect to qxwtity, or numerical composition." Dr. Wallis {Opera Mathematic a, torn. il. p. 665.) translates the same word by the Latin quantiiplicitas, which relers to the number of times the one magnitude is contained in the other. Dr. Peacock {Algebra, p. 309.) remarks, that there is no geometrical definition of ratio by which the equivalence of different modes of representation may be ascertained as nece ary consequences; and for this reason, ratios in geometry are only considered in connection with each other, as constituting, or not constituting, a proportion. In arithmetic and algebra, a ratio may be defined as the fraction whose numerator is the antecedent, and denominator the consequent of the ratio; and hence, in those sciences, the theory of ratios become identified with the theory of fractions. ( For an accoimt of what has been written on the subject of geometrical 1024 RATTLESNAKE. ratios, see Camerer's Euclid, Excursus ad lib. v. Berlin, 1825.) [s. 1037]