The geometry of the rectangular hyperbola is simplified by the fact that its principal axes are equal.
In point of fact, as we look to history, we find that theism has been much simplified and cut down.
In fresh-water Hydromedusae the life-cycle is usually secondarily simplified, but in marine forms the life-cycle may be extremely complicated, and a given species often passes in the course of its history through widely different forms adapted to different habitats and modes of life.
It is quite possible that some of these medusae will be found to be truly hypogenetic, that is to say, with a life-cycle secondarily simplified by suppression of metagenesis.
These courts were convenient, since it was the custom to appoint delegates resident in the neighbourhood, and the power of sub-delegation, general or limited, simplified questions of distance.
It is more nearly related to modern Siamese than to modern Shan, but possesses many groups of consonants which have become simplified in both.
(d) The problem of Christian apologetic has been simplified in the past by the prevalence of the Christian ethics and temper even among many non-Christians (e.g.
The interesting little Rhodope veranyii, which has no odontophore, has been associated by systematists both with these simplified Opisthobranchs and with Rhabdocoel Planarians.
He regulated and simplified the whole system of taxation, encouraged agriculture by differential duties in favour of the farmers, and promoted trade by a systematic improvement of the ways of communication.
Some of Laplace's results in the theory of probabilities are simplified in S.
He introduced the terms multinomial, trinomial, quadrinomial, &c., and considerably simplified the notation for decimals.
Yugoslavia's relations with Albania, though simplified by this decision, have been affected by the Albanian counterclaim to Pee, Djakovo and the plain of Kosovo, where since the middle of last century the Albanian element had grown steadily stronger at the expense of the Serbs.
A simplified exposition has been given by Horace Lamb (Prot.
Finance In addition to the provisions that have been mentioned above (Section VII.), the London Government Act 1899 simplified administration in two respects.
These equations may be simplified slightly, using the equation of continuity (5) § for dpu dpu 2 dpuv dpuw dt dx + dy + dz =p Cat +uax+vay+waz?
The Hatton defecator, which is employed for working it, has been already described, but it may be mentioned that the regulation of the admission of steam is now simplified and secured.
The bodywall is greatly simplified in the Gymnolaemata, in correlation with the functional importance of the skeletal part of the wall.
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 task of the chronologer was thus simplified and reduced to a study and comparison of dates in a few leading systems.
Passing through found its task much simplified, and before nightfall had carried the Hindenburg reserve line on practically the whole of its front, taking a further Boo men and 20 guns in its advance.
The third form is the outflow or reversing thermometer, first introduced by Aime, who used a very inconvenient form in the Mediterranean in 1841-1845, but greatly improved and simplified by Negretti and Zambra in 1875.
The introduction of these special methods has considerably simplified the problem of sinking through water-bearing strata.
There is no unreduced material, and the process is considerably simplified, while less expensive plant is required.
The position was simplified when, in 1220, Albert van Cuyck, the last of the hereditary burgraves, sold his rights to the bishop. These ecclesiastical princes were churchmen in little but name, and their desire to be absolute rulers found itself confronted by the determination of the burghers to secure greater independence.
The complexity of administrative areas, though far less than in England, was simplified, and the census compilation proportionately facilitated, by the passing of the Local Government Act for Scotland, in 1889.
The calculation of this last expression is simplified by noticing that we are only concerned with the mutual ratios of Xo, X 1, ...
The process is simplified by writing down the general formula first and then substituting the values of u.
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, ..
In the second half of the 17th century the rules of grammar and rhetoric were simplified, and the time withdrawn from the practice of composition (especially verse composition) transferred to the explanation and the study of authors.
In the 18th century Rollin, in his Traits des etudes (1726), agreed with the Port - Royalists in demanding that Latin grammars should be written in French, that the rules should be simplified and explained by a sufficient number of examples, and that a more important place should be assigned to translation than to composition.
To meet that dissatisfaction, the teachers had accepted new subjects of study, had improved their methods, and had simplified the learning of the dead languages.
14 each cherub has four faces, a view tastefully simplified in the Johannine Apocalypse (Rev. iv.
In his history of the Arietidae Hyatt points out that toward the close of the Cretaceous this entire group of ammonites appears to have been affected with some malady; the unrolled forms multiply, the septa are simplified, the ornamentation becomes heavy, thick, and finally disappears in the adult; the entire group ends by dying out and leaving no descendants.
This system again was simplified, and as the supreme secret was taught in a single name or a single formula, by means of which the happy possessor was able to penetrate through all the spaces of heaven (cf.
Other reforms. followed in quick succession during the next five or six years: army and navy organization, a new judicial administration on the French model, a new penal code and a greatly simplified system of civil and criminal procedure, an elaborate scheme of local self-government for the rural districts and the large towns, with elective assemblies possessing a restricted right of taxation, and a new rural and municipal police under the direction of the minister of the interior.
Copernicus (1473-1543) employed the same system, and greatly simplified the application of it, especially by regarding the earth as rotating and the sun as the centre of the solar system.
The deliberations follow a simplified procedure, which is founded more on equity than on the more strictly legal forms, and decisions are given in the shortest possible form, in answer to carefully formulated questions or dubia.
Wenzel, one of his pupils, edited in 1883 from his MS. a Simplified Tibetan Grammar.
The mediae have become aspirate tenues with a low intonation, which also marks the words having a simple initial consonant; while the former aspirates and the complex initials simplified in speech are uttered with a high tone, or, as the Tibetans say, " with a woman's voice," shrill and rapidly.
The original Deville process for obtaining pure alumina from bauxite was greatly simplified in 1889 by K.
If we are to credit a 9th century biographer, Gregory abbreviated and otherwise simplified the Sacramentary of Gelasius, producing a revised edition with which his own name has become associated, and which represents the groundwork of the modern Roman Missal.
A comparative judgment is simplified into an isolated perception of a peculiar form, and a series of similar facts are grouped under a single symbol, representing a particular perception, and only by the accident of custom treated as universal (see i.
This system of execution was simplified by an act of 1837 (Personal Diligence Act), and execution is now usually by diligence (see Execution).
The system was, on the advice of an Anglo-Indian official (Sir John Scott), modified and simplified in 1891, but its essential character remained unaltered.
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.
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.
The question is greatly simplified when two of the principal moments are equal, say A=B.
To apply the equations (11) to the case of the top we start with the expression (15) of 22 for the kinetic energy, the simplified form (i) of 20 being for the present purpose inadmissible, since it is essential that the generalized co-ordinates employed should be competent to specify the position of every particle.
(pope 1073-1085), too, simplified the liturgy as performed at the Roman court, and gave his abridgment the name of Breviary, which thus came to denote a work which from another point of view might be called a Plenary, involving as it did the collection of several works into one.
The services were at the same time simplified and shortened, and the use of the whole Psalter every week (which had become a mere theory in the Roman Breviary, owing to its frequent supersession by saints' day services) was made a reality.