We frequently meet with cogredient and contragedient quantities, and we have in general the following definitions:-(i) " If two equally numerous sets of quantities x, y, z,...
But admitting the validity of this criticism, and even going so far as to question the possibility of ever devising absolutely inclusive and, at the same time, exclusive definitions, no sufficient reason is adduced for giving up all attempt at morphological analysis.
He is not prepared to exclude the great medieval pronouncements, or the modern Roman Catholic definitions, from the list of dogmas; but on the whole he prefers to keep in view " one historical species " - Loofs suggests that he ought perhaps rather to say one individual type - that greatest group of Christian dogmas which " was created by the Greek spirit upon the soil of the gospel " (Hist.
A discussion of these concepts and the various definitions of angles in Euclidean geometry is to be found in W.
It was simply a case of differing definitions of quid pro quo.
The only reservation which the most advanced Gallicans dared to formulate, in the terms of the celebrated declaration of the clergy of France (1682), had as its object the irreformable character of the pontifical definitions, which, it was claimed, could only have been acquired by them through the assent of the Church.
It doubtless arose from the proposed forms for the definitions of the primacy and the pontifical magisterium.
The same definitions occur also in the Canonis Descriptio (1614), p. 5: "Logarithmos sinuum, qui semper majores.
There are many genera and species of leeches, the exact definitions of which are still in need of a more complete survey.
With these definitions it is now possible to prove the following six premisses applying to finite cardinal numbers, from which Peano 2 has shown that all arithmetic can be deduced i.
The definitions of the finite ordinals can be expressed without use of the corresponding cardinals, so there is no essential priority of cardinals to ordinals.
Contrasting the above definitions of number, cardinal and ordinals, with the alternative theory that number is an ultimate idea incapable of definition, we notice that our procedure exacts a greater attention, combined with a smaller credulity; for every idea, assumed as ultimate, demands a separate act of faith.
The arithmetic of rational numbers is now established by means of appropriate definitions, which indicate the entities meant by the operations of addition and multiplication.
These entities are not created by mathematicians, they are employed by them, and their definitions should point out the construction of the new entities in terms of those already on hand.
The arithmetic of real numbers follows from appropriate definitions of the operations of addition and multiplication.
But an indefinite number of definitions of the product of two complex numbers yield interesting results.
The second includes definitions of technical terms in common use, together with so much of the elementary theory as is necessary for understanding the experimental work described in subsequent portions of the article; a number of formulae and results are given for purposes of reference, but the mathematical reasoning by which they are obtained is not generally detailed, authorities being cited whenever the demonstrations are not likely to be found in ordinary textbooks.
To say, for instance, that X is equal to A -B, is the same thing as to say that X is a quantity such that X and B, when added, make up A; and the above five statements of necessary connexion between two statements of equality are in fact nothing more than definitions of the symbols -, m of, =,, and loga.
The deductions follow directly from the definitions, and such mechanical processes as "clearing of fractions " find no place (ï¿½ 21 (ii.)).
., or (by analogy with the definitions of 2, 3, 4,.
They are (a+b)-?-c=a+(b+c) (A) (aXb)Xc=aX(bXc) (A') a+b=b+a (c) aXb=bXa (c') a(b c) =ab-Fac (D) (a - b)+b=a (I) (a=b)Xb=a (I') These formulae express the associative and commutative laws of the operations + and X, the distributive law of X, and the definitions of the inverse symbols - and =, which are assumed to be unambiguous.
Z considerable use of anatomical characters in his definitions of larger groups, and may thus be considered as the father of modern zoology.
- Special mention may be made of `Ananisho` of Hedhaiyabh (middle of 7th century) well known as the author of a new recension of the Paradise of Palladius, and also the author of a volume on philosophical divisions and definitions; Romanus the physician 0-896), who wrote a medical compilation, a commentary on the Book of Hierotheus, a collection of Pytha - gorean maxims and other works; Moses bar Kepha, the voluminous writer above referred to; the famous physician Honain ibn Islhn See O.
Tumours Or New Growths The various definitions of the term " new growth " leave us with a definite conception of it as a new formation of tissue which appears to originate and to grow independently.
To us at the present time it seems merely a dialectical construction, having its beginning and end in definitions: the words power, stimulus, &c., being used in such a way as not to correspond to any precise physical conceptions, still less to definite material objects or forces.
The province of reverent theology is to aid accurate thinking by the use of metaphysical or psychological terms. Its definitions are no more an end in themselves than an analysis of good drinking water, which by itself leaves us thirsty but encourages us to drink.
In later memoirs Reynolds followed up this subject by proceeding to establish definitions of the velocity and the momentum and the energy at an element of volume of the molecular medium, with the precision necessary in order that the dynamical equations of the medium in bulk, based in the usual manner on these quantities alone, without directly considering thermal stresses, shall be strictly valid - a discussion in which the relation of ordinary molar mechanics to the more complete molecular theory is involved.
Since the weights used in conjunction with a balance are really standard masses, the word "weight" may be substituted for the word "mass" in the preceding definitions; and we may symbolically express the relations thus: - If M be the weight of substance occupying a volume V, then the absolute density O = M/V; and if m, m 1 be the weights of the substance and of the standard substance which occupy the same volume, the relative density or specific gravity S = m/m l; or more generally if m i be the weight of a volume v of the substance, and m l the weight of a volume v l of the standard, then S = mv l /m l v.
The sciences, for example, all seek to define their own species; dialectic, on the other hand, sets forth the conditions which all definitions must satisfy whatever their subject matter.
The new view of faith is bracketed with the old, and practically neutralized by it; as was already the case in Melanchthon's theological definitions in the 1552-1553 edition of Loci Communes, also printed in other works by him.
Finally we have to glance at a new list of definitions which perhaps in some cases seek more or less to formulate modern Protestant ideas, but which in general represent rather the world of disinterested historical scholarship.
It is an elementary introduction to the study of Hebrew, the first of its kind, in which only the most indispensable definitions and rules have a place, the remainder being almost wholly occupied by paradigms. Moses Kimhi was the first who made the verb paqadh a model for conjugation, and the first also who introduced the now usual sequence in the enumeration of stem-forms. His handbook was of great historical importance as in the first half of the 6th century it became the favourite manual for the study of Hebrew among non-Judaic scholars (1st ed., Pesaro, 1508).
Zygospores, oospores, brand-spores, aecidiospores, ascospores, basidiospores, &c. Little or nothing is gained by these definitions, however, which are especially physiological.
According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was utilized by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
Number in arithmetic, magnitude in geometry, stars in astronomy, a man's good in ethics; concentrates itself on the causes and appropriate principles of its subject, especially the definition of the subject and its species by their essences or formal causes; and after an inductive intelligence of those principles proceeds by a deductive demonstration from definitions to consequences: philosophy is simply a desire of this definite knowledge of causes and effects.
In the succeeding three definitions the centre, diameter and the semicircle are defined, while the third postulate of the same book demands the possibility of describing a circle for every " centre " and " distance."
The definitions of the logarithmic and exponential functions may be extended to complex values of x.
Of the metric units international definitions have been stated as follows:
In 1899, with a view to the many modifications exhibited by parasitic and semi-parasitic species, the definitions, stripped of a too hampering precision, took a different form: (a) Ampharthrandria.
The class is divisible into two main divisions or sub-classes, Hydromedusae and Scyphornedusae, of which definitions and detailed systematic accounts will be found under these headings.
The anathema of the Roman Church had fallen upon all the fundamental doctrines for which the Reformers had contended and died; the right of free discussion within the limits of the creeds, which had given room for the speculations of the medieval philosophers, was henceforth curtailed and confined; and the definitions of the schoolmen were for ever exalted by the authority of Rome into dogmas of the Church.
It may truly be said that the ideas for which Nestorius and the Antiochene school strove "won the day as regards the doctrinal definitions of the church.