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.

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.

Mention is also made of a work by Clement on the Prophet Amos, and another on Definitions.

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.

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.

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.

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.

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.

Andrewes declares against the invocation of saints, the apparent examples in patristic literature are "rhetorical outbursts, not theological definitions."

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.

That world of the learned offers us non-dogmatic definitions, drawn up from the outside; definitions which do not share the root assumptions either of Catholicism or of post-Reformation Protestant orthodoxy.

Hence Catholic, and scientific or historical, definitions of dogma are on different planes.

Its meaning varies (a) according to the various definitions of deity, and especially (b) according as it is (i.) deliberately adopted by a thinker as a description of his own theological standpoint, or (ii.) applied by one set of thinkers to their opponents.

Many of these definitions describe an ideal state of things rather than realities.

Some of the definitions would apply to the authority of powerful religious bodies in certain periods of history, or of illegal associations, such as the Mafia, which have terrorized the community.

Being called upon to arrange the plants in the garden, he necessarily had to consider the best method of doing so, and, following the lines already suggested by his uncle, adopted a system founded in a certain degree on that of Ray, in which he embraced all the discoveries in organography, adopted the simplicity of the Linnean definitions, and displayed the natural affinities of plants.

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.

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 definitions of the logarithmic and exponential functions may be extended to complex values of x.

Out of this mist of contradictions scholastic thought strove to emerge by means of clear-cut definitions.

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."

He appears to have joined the Homoean party, which took shape and acquired influence before the council of Constantinople in 360, where he adhered with the rest of the council to the creed of Ariminum, with the addendum that in future the terms inroTTao-cs and oucla should be excluded from Christological definitions.

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.

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).

He attached no value to mere scholarship; scholastic disputations he utterly ignored and despised - and especially the discussions on medical topics, which turned more upon theories and definitions than upon actual practice.

Besides his great work, Malthus wrote Observations on the Effect of the Corn Laws; An Inquiry into the Nature and Progress of Rent; Principles of Political Economy; and Definitions in Political Economy.

During the seven years which he passed in the drudgery of penning definitions and marking quotations for transcription, he sought for relaxation in literary labour of a more agreeable kind.

The definitions show so much acuteness of thought and command of language, and the passages quoted from poets, divines and philosophers are so skilfully selected, that a leisure hour may always be very agreeably spent in turning over the pages.

It seemed unlikely that the author of these definitions would himself be pensioned.

He was absent from the important sitting of the 18th of June 1870, and did not send in his submission to the decrees until 1871, when he explained in a pastoral letter that the dogma "referred only to doctrine given forth ex cathedra, and therein to the definitions proper duly, but not to its proofs or explanations."

The difference between the two definitions, however, is of small practical concern.

He is variously styled Byzantinus, Hierosolymitanus (as an inmate of the monastery of St Saba near Jerusalem) and Scholasticus (the first "schoolman," as the introducer of the Aristotelian definitions into theology; according to others, he had been an advocate, a special meaning of the word scholasticus).

Thus the first and second definitions represent the founders of the sophistry of culture, Protagoras and Prodicus, from the respective points of view of the older Athenians, who disliked the new culture, and the younger Athenians, who admired it; the third and fourth definitions represent imitators to whom the note of itinerancy was not applicable; the fifth definition represents the earlier eristics, contemporaries of Socrates, whom it was necessary to distinguish from the teachers of forensic oratory; the sixth is framed to meet the anomalous case of Socrates, in whom many saw the typical sophist, though Plato conceives this view to be unfortunate; and the seventh and final definition, having in view eristical sophistry fully developed, distinguishes it from SfµoXoyuci, i.e.

The first four definitions represent the period of Protagoras, Prodicus, and their immediate successors, when the object sought was " virtue," " excellence," " culture," and the means to it was literature.

The fifth and sixth definitions represent the close of the 5th century, when sophistry handled eristically, and perhaps, though Plato demurs to the inclusion, dialectically, questions of justice, injustice and the like, Su

The two definitions are identical, provided that the thermal capacity of unit mass of water, at a standard temperature, is taken as the unit of heat.

Among the dialecticians, Socrates had used inductive arguments to obtain definitions as data of deductive arguments against his opponents, and Plato had insisted on the processes of ascending to and descending from an unconditional principle by the power of giving and receiving argument.

Erdmann propose new moods of syllogism with convertible premises, containing definitions and equations.

Much of the Principia consists of synthetical deductions from definitions and axioms. But the discovery of the centripetal force of the planets to the sun is an analytic deduction from the facts of their motion discovered by Kepler to their real ground, and is so stated by Newton in the first regressive order of Aristotle - P-M, S-P, S-M.

The ideal of science or demonstrative knowledge is to exhibit as flowing from the definitions and postulates of a science, from its special principles, by the help only of axioms or principles common to all knowledge, and these not as premises but as guiding rules, all the properties of the subject-matter, i.e.

Where they are not derivative they clearly are definitions or immediate transcripts from definitions.

There remain, then, primary definitions and the postulates of their realization, and the axioms or common principles, " which he must needs have who is to reach any knowledge."

Spinoza's philosophy is expounded ordine geometrico and with Euclidean cogency from a relatively small number of definitions, axioms and postulates.

The philosophies which are " redargued " are divided into three classes, the sophistical, of which the best example is Aristotle, who, according to Bacon, forces nature into his abstract schemata and thinks to explain by definitions; the empirical, which from few and limited experiments leaps at once to general conclusions; and the superstitious, which corrupts philosophy by the introduction of poetical and theological notions.

Amongst the numberless definitions of religion that have been suggested, those that have been most frequently adopted for working purposes by anthropologists are Tylor's and Frazer's.

Such definitions, then, are to be accepted, if at all, as definitions of type, selective designations of leading but not strictly universal features.

Distrusting tradition, he took a few of the finest dialogues as his standard, and from internal evidence denounced as spurious not only those which are generally admitted to be so (Epinomis, Minos, Theages, Arastae, Clitophon, Hipparchus, Eryxias, Letters and Definitions), but also the Meno, Euthydemus, Charmides, Lysis, Laches, First and Second Alcibiades, Hippias Major and Minor, Ion, Euthyphro, Apology, Crito, and even (against Aristotle's explicit assertion) The Laws.

All definitions of suzerainty are of little use.

The Orthodox Greek Church adopts the doctrinal decisions of the seven oecumenical councils, together with the canons of the Concilium Quinisextum or second Trullan council (692); and they further hold that all these definitions and canons are simply explanations and enforcements of the Nicaeo-Constantinopolitan creed and the decrees of the first council of Nicaea.

The metaphysical & roplac of Theophrastus which have come down to us show that he was fully alive to the difficulties that beset many of the Aristotelian definitions.

It may be pointed out here that these expressions are defined by the act, the effect of the definitions being shortly that a drain is a conduit for the drainage of one building or of several within the same curtilage, while a sewer comprises every kind of drain except that which is covered by the definition of a drain as above stated.

But, if we desire to keep by older landmarks and maintain a distinction between the two disciplines, a ground for doing so may be found in the fact that all the main definitions of logic point to the investigation of the laws of thought in a subjective reference - with a view, that is, by an analysis of the operation, to ensure its more correct performance.

It is, indeed, only from the standpoint of such a theory that the definitions and divisions of the different philosophical disciplines adopted in this article can be said to hold good.

But the expression is most frequently used to designate disciplinary laws, in which case canons are distinguished from dogmatic definitions.

With regard to form, the decisions of councils, even when dogmatic, are called canons; thus the definitions of the council of Trent or of the Vatican, which generally begin with the words " Si quis dixerit," and end with the anathema, are canons; while the long chapters, even when dealing with matters of discipline, retain the name of chapters or decrees.

The above definitions of logarithms, &c., relate to cases in which n and p are whole numbers, and are generalized later.

Obviously the number of such geometrical or kinematical definitions is infinite.

It is possible, and (not so much for any application thereof as in order to more fully establish the analogy between the two kinds of co-ordinates) important, to give independent quantitative definitions of the two kinds of co-ordinates; but we may also derive the notion of line-co-ordinates from that of point-coordinates; viz.

Why should theology labour at definitions?

Western Christendom wishes to call Christ God; even the Ritschlian school uses the wonted language in the light of its own definitions.

It is a more obvious, if perhaps a more vulgar, criticism of the great development to say that it was too simply intellectual - seeking clear-cut definitions and dogmas without measuring the resources at the command of Christians or the urgency of their need for such things.

But ultimately they persuaded themselves to accept these definitions as normal and biblical, and as presuppositions of Christ's saving work.

Thus, by the aid of his famous " dialectic," Socrates arrived first at the negative result that the professed teachers of the people were as ignorant as he himself claimed to be, and in a measure justified the eulogy of Aristotle that he rendered to philosophy the service of " introducing induction and definitions."

It admits of several definitions framed according to the aspect from which the curve is considered.

The definitions given above reflect the intimate association of these curves, but it frequently happens that a particular conic is defined by some special property (as the ellipse, which is the locus of a point such that the sum of its distances from two fixed points is constant); such definitions and other special properties are treated in the articles Ellipse, Hyperbola and Parabola.

Later investigations, whilst confirming the general validity of Huxley's conclusions, have slightly altered the limits and definitions of his groups.

Kant is not always in his language faithful to his view of the sense-manifold, but the theory as a whole, together with his own express definitions, is unmistakable.

The site is used to quickly compare dictionary definitions.

Here the material covered is precisely defined, but these definitions appear arbitrary.

It will promote definitions of achievement to which all learners can realistically aspire, and are relevant to them.

Institutions may have different definitions of dormant account, lost account or unclaimed assets.

Such definitions include many people with milder immune deficiency, which is generally not fatal.

Alternatively, all glossary definitions can be seen on the ' Glossary ' page in the ' Resources ' section.

The new versions have facilities that greatly ease the task of updating the virus definitions on a regular basis.

Resource definitions like " fisheries " or " aquatic ecology " could encompass the entire globe.

Key terms are linked to definitions in an accompanying glossary.

Some variable declarations and lex definitions might be needed in more than one lex source file.

Unlike most modern lexicographers, Johnson introduced humor or prejudice into many of his definitions.

I don't think you could call the mirror neuron system a model under these definitions.

Of the five students interviewed over two 10 week terms, none were able to make the definitions operable.

The use of various assays to detect serum antibodies and differing definitions of antibody positivity limits the ability to compare antigenicity among different products.

The default file includes definitions for all familiar units, abbreviations and metric prefixes.

Ultimately she did not succeed in broadening definitions of femininity to include rationalism and mathematical accomplishment.

It also examines the changing definitions of social need these reflected and asks why welfare states have experienced retrenchment in recent years.

Physical Activity Within the definitions used in the survey, 25% of people aged 16 and over can be classed as sedentary.

Definitions Obligatory set-aside This covers the area of compulsory set-aside designated for any year, 10% for 2003.

It has a manual stepper for constructing plans and dynamically testing domain definitions.

Restricted definitions of this kind are essential in qualitative arms control, however, without which the whole enterprise would become vacuous.

In current web ser vices standards, the notion of sequencing is handled by the workflow definitions provided by proposals such as BPEL4WS.

For definitions of the groups see below.

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.

We have seen how his classification of substances into elements and compounds, and the definitions which he assigned to these species, have similarly been retained; and how Lavoisier established the law of the "conservation of mass," overthrew the prevailing phlogistic theory, and became the founder of modern chemistry by the overwhelming importance which he gave to the use of the balance.

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.

His favourite expression for the universal is "quod de pluribus natum est praedicari " (a translation of Aristotle, Dc interpretatione, 7), which would seem to point to a real or objective counterpart of the products of our thought; and the traditional definitions of Boetius, whom he frequently quotes, support the same view of the concept as gathered from a number of individuals in virtue of a real resemblance.

The effect of these definitions is that the sum and the product of two quaternions are also quaternions; that addition is associative and commutative; and that multiplication is associative and distributive, but not commutative.

These definitions being thus various, the Eleate notes that the sophist, in consideration of a fee, disputes, and teaches others to dispute, about things divine, cosmical, metaphysical, legal, political, technical - in fact, about everything - not having knowledge of them, because universal knowledge is unattainable; after which he is in a position to define the sophist (7) as a conscious impostor who, in private, by discontinuous discourse, compels his interlocutor to contradict himself, in opposition to the Sn,uoXoyucos, who, in public, by continuous discourse, imposes upon crowds.

In the former book he still makes large additions and alterations, but there is less scope for his prolixity than before; and in the latter, where he is no longer dealing with generalities, but making actual definitions, the Constitutions of necessity become more precise and statutory in form.

Thus, on the denary system (§ 16) we can give independent definitions to the numbers up to ten, and then regard (e.g.) fifty-three as a composite number made up of five tens and three ones.

Helen acquired language by practice and habit rather than by study of rules and definitions.

We show how such definitions can be used to automatically derive schema transformation operators for the higher-level data models.

There are currently two schemes in the UK which provide definitions of verbal descriptors of the nutrient content of foods.

The subsequent list is a dictionary of potential Muslim baby names with their definitions.

A child's dictionary has pictures and word definitions geared toward children.

Specialty dictionaries deal with jargon of the medical profession, business, industry or science and are helpful in determining working definitions.

There are many definitions of renewable resources, however the main principle is that what ever is used can be replaced in a sustainable fashion.

In understanding climate change, definitions are crucial because they're the only way we can begin to take real action.

These are very simplistic definitions for complex diseases, but the description provides the basis for understanding the purposes of primrose oil.

From there, additional definitions, quotes, references, timelines, and translations have been and continue to be added.

Webster's Dictionary offers more than just definitions.

The Merriam Webster online dictionary is an efficient way to look up definitions, the phonics and synonyms of words.

The online dictionary uses the print edition as a basis for delivering definitions and quotes through the Internet.

Search. You can search definitions for various parts of speech the word is involved in.

You can also choose to have only English definitions appear.

It provides definitions, translations, and auditory single words.

Both of the sources will return dozens of results with definitions, sentence results and more.

This website also uses various dictionaries like the Oxford Pocket Dictionary of Current English, A Dictionary of Psychology and nutrition definitions from A Dictionary of Food Nutrition.

When you feel ready to hit the stores, take a minute to jot down a list of the features you prefer as well as any terminology and definitions you still find confusing.

Leave room on each page of notes for information you may need to add later - like definitions or examples.

I had to put definitions on a whole lot of things in sobriety, because everything was new and it was like I was just born and aware of everything around me.

By common definitions, Securitas distance learning isn't a formal education.

The dog food industry has its own definitions for many of the terms used on their labels, and you may be surprised to learn what they actually mean.

By these definitions, many commercial formulas may not be as healthy, tasty and nutritious as the label might suggest.

Definitions of nudity, which are subject to historical and cultural variation, rely on assumptions about what counts as clothing.

Full sunlight is six hours or more of direct sunlight per day; partial shade or partial sun definitions vary, but usually mean morning or afternoon-only light.

Not all countries use the same size definitions therefore being able to 'translate' between sizes and measurements will help.

The stereotype of the cowboy casanova has even made its way into internet slang, with the official definition coined by the Urban Dictionary, which has two definitions.

As you can see from this handful of shops, there are a lot of different definitions of what counts as sustainable that may not intersect with your ideas about organic products.

It is necessary to understand organic certification definitions in order to understand what is said in the Organic Foods Production Act.

For a complete list of terms read the USDA Definitions list.

At the end of the month, quiz seniors on words and definitions to see who can remember.

Different definitions can lead to significant differences in AHI values, which makes a standard desirable for many patients and professionals.

Three hypopnea definitions were used in the study, and each one was acquired from the American Academy of Sleep Medicine (AASM).

Of course, as with all videogame definitions, what constitutes a MMOG is somewhat vague.

The video game industry evolves quickly, and the standard definitions have to adapt and expand periodically.

Definitions of what is or is not moral are in a state of upheaval within individual societies.

Most children wet the bed occasionally, and definitions of the age and frequency at which bed-wetting becomes a medical problem vary somewhat.

However, these definitions are simplified, as both medical and behavioral causes often appear together.

Before considering pain management, a review of pain definitions and mechanisms may be useful.

First is the general problem that there are no universally accepted definitions of creativity.

Exotic swimwear appears to meet both of these definitions, and then some.

These days, the definitions of what's what in the fashion world have blurred.

Players take turns reading aloud words and the other players make up fake definitions.

All those definitions, including the right one, are said aloud and the players must pick which one they think is the correct one.

Depending on whom you ask and where you look, there are many definitions of self esteem, both positive and negative.

You can do this using sidebars, lists and definitions.

Experts agree that the best tarot card readings are a result of letting the cards speak in their own way and not adhering strictly to literal definitions.

This is a listing of general card definitions.

This site devotes most of their articles to definitions, so you won't be able to ask a question if you need some clarification on an article, but you will discover the meaning of each of the numbers.

Different symbols may be applied to identify these energies, but overall, when you delve further into the zodiac symbols of certain cultures, you will see patterns in their definitions.

The definitions are simple and the print is large enough to be comfortable and engaging for children.

Intermediate dictionaries are perfect for the more mature learner who is seeking a user-friendly set-up but more sophisticated definitions.

Dictionaries are also available on a CD-ROM, but these are becoming more and more unpopular as most definitions can be easily found by searching via Google, Yahoo, or visiting numerous dictionary websites.

Learning the definitions of parenting styles may help generate an awareness of how your behaviors and attitudes affect your children.

All of the definitions above include the caveat that the person demonstrating these abilities is not using his or her five senses.

Look up words and definitions in online dictionaries like YourDictionary or read informative articles about history subjects at Encylopedia.com.

The soap clichés link includes definitions of some of the greatest clichés to play out on the small screen from amnesia to who's the daddy.

This extensive site includes subculture slang, definitions of specific practices and relevant medical information.

This essential reference book/CD set contains over 200 asanas and 300 Sanskrit definitions and pronunciations.

There are a few definitions associated with Kriya yoga.

Here are some of the various definitions of Namaste you may encounter.

He feels his ASD is an asset, rather than a disability, and recommends that people on the spectrum create their own goals and definitions of success.

One of the Merriam-Webster dictionary definitions of culture describes it as a collection of customary traits, characteristic features, beliefs and social forms shared by a group of people.

Healthcare environments and industrial environments are two examples of work environments with unique definitions for professional attire.

Some leagues have rules about how short the skirt can be, along with definitions of how the shell must cover the midriff when the arms are raised.

Emily Smith's website offers definitions for faux painting techniques, but no projects.

Different diet plans, such as the Atkins Diet and the The South Beach Diet, have different definitions of what constitutes low carb, and those definitions change as you work your way through the diet.

Truth is, practically any activity is good for you; the definitions above are merely how to make it more of a targeted effort.

Though there are many other definitions of the word exercise in the Merriam-Webster, this is the definition that pertains to physical exercise for the sake of pursuing and maintaining a fit body.

All of these definitions of connaître are commonly used.

Insurers do not have such specific definitions when deeming a car to be considered a classic.

Depending on your definitions, you could trace reality TV all the way back to the advent of television itself, with shows like Candid Camera, which hit the airwaves in 1948.

Definitions of science fiction vary as much as the myriad of subgenres it encompasses.

On her website you will find definitions of common skincare ailments such as Rosacea.

A list of definitions of SEO words and concepts - which coincidentally happen to be popular search-engine queries for anyone looking for higher page rankings.

What this means is that Microsoft Word will use individual font tags and definitions for each part of the page, and put in many more properties and definitions than needed.

Astute designers will note that this basic HTML cheat sheet, along with the similar one at PSA Cake, don't include things like DOCTYPE definitions and other validating tags.

The definitions of basic HTML tags like

and

(header) tags are constructed using a combination of the original language and "selectors" and "classes".

It was simply a case of differing definitions of quid pro quo.

It doubtless arose from the proposed forms for the definitions of the primacy and the pontifical magisterium.

There are many genera and species of leeches, the exact definitions of which are still in need of a more complete survey.

It is impossible here to give even a list of the names of the many observers who in recent times have made empirical study of the effects of growth-forces and of the symmetrical limitations and definitions of growth.

It is urged that the various parts are, as a matter of fact, organs; and that it is therefore inadmissible to ignore their functions, as is done in the foregoing definitions.

It is also urged against these definitions that they are not of universal applicability; that there are exceptional structures which cannot be brought within the limits of any one of them.

It is a plain, straightforward description of the globe, and of the various phenomena of the surface, dealing only with definitely ascertained facts in the natural order of their relationships, but avoiding any systematic classification or even definitions of terms.

It is to be noted that often no absolute line of demarcation can be drawn in regard to these regions, their definitions being rather convenient than morphological.

The assumptions, the definitions, the reasoning, the conclusions of the classical writers have been ruthlessly overhauled.

Herein the author first assigned anatomical reasons for rearranging the order Anseres of Linnaeus and Natatores of Illiger, who, so long before as 1811, had proposed a new distribution of it into six families, the definitions of which, as was his wont, he had drawn from external characters only.

These definitions provide a basis on which the calibration of amperemeters can be conducted.

As will have been seen, they hold an exalted view of the divinity and work of Christ as the Word become flesh and the Saviour of the world; but they have always shrunk from rigid Trinitarian definitions.

Such definitions, however, are not universally accepted.

The Eastern bishops subscribed, these edicts, and even Pope Vigilius yielded, in spite of the protests of the Western bishops, and at the 5th General Council (Constantinople, 553) agreed to the condemnation of the "three chapters" 1 and the anathematizing of any who should defend them by an appeal to the Definitions of Chalcedon.

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.

What many children think of with dread, as a painful plodding through grammar, hard sums and harder definitions, is to-day one of my most precious memories.

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.