This is divisible into the districts of Samaria and Judaea.
(a) It is clear that every integer is divisible by I!.
The white population is broadly divisible into the British and Dutch elements, the percentage of other whites in 1904 being but 8.6.
This latter, which is his "capital," is divisible into the two classes of "fixed" and "circulating."
Therefore, if (n-i) 1P+11 is divisible by (p+I)!, 'n 1P+11 is divisible b y (p +i) !.
The body is often divisible into regions.
Solutions of colloids in solvents such as water and alcohol seem to be divisible into two classes.
The inhabitants are roughly divisible into two types - Arabs in the plains and Nubas in the hills.
The body is divisible into a proboscis and a trunk with sometimes an intervening neck region.
Smith conceived the entire subject he had to treat in his public lectures as divisible into four heads, the first of which was natural theology, the second ethics, the third jurisprudence; whilst in the fourth "he examined those political regulations which are founded upon expediency, and which are calculated to increase the riches, the power, and the prosperity of a state."
But while the banner was square the pennon, which resembled it in other respects, was either pointed or forked at its extremity, and the pencel, which was considerably less than the others, always terminated in a single tail or streamer.6 If indeed we look at the scale of chivalric subordination from another point of view, it seems to be more properly divisible into four than into three stages, of which two may be called provisional and two final.
Caimi the present Jewish communities of Greece are divisible into five groups: (r) Arta (Epirus); (2) Chalcis (Euboea); (3) Athens (Attica); (4) Volo, Larissa and Trikala (Thessaly); and (5) Corfu and Zante (Ionian Islands).
In the first, all affection phenomena are primarily divisible into those which are pleasurable and those which are the reverse.
The family is divisible into two sub-families, of which the first, or Sminthinae, is represented only by the genus Sminthus, containing a few species which range from Denmark into Western Asia, Kashmir and China.
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.
Then the assumption is that, whatever positive integral value n may have, n [P] is divisible by p!.
" The atomists assert that after a certain number of such divisions the parts would be no longer divisible, because each of them would be an atom.
The Arachnida are divisible into two grades of structure - according to the fixity or non-fixity of the number of somites building up the body: - Grade A (of the Arachnida).
According to his phenomenalism, the external stimulus and the physiological stimulus are both parallels of the same psychical process; the external body, as well as my body, is merely an object abstracted from an idea of my experience; and what is really known in every case is a unitary experience; divisible, but not separable, into body and soul, physical and psychical factors of one and the same unitary experience.
The colonial budgets totalled in 1907 some 16,760,000, being divisible into six categories: Algeria 4,120,000; Tunisia 3,640,000; Indo-China3 about 5,000,ooo; West Africa 1,600,000; Madagascar 960,000; all other colonies combined 1,440,000.
The mouth leads at once into the true digestive cavity, divisible into an oesophageal region in the manubrium and a more dilated cavity, the stomach (st.), occupying the centre of the umbrella.
Rather we may say with Maine, "Sovereignty is divisible, but independence is not."
It is divisible into two well-marked periods - the first extending to the end of the 12th century and embracing as its chief names Roscellinus, Anselm, William of Champeaux and Abelard, while the second extended from the beginning of the 13th century to the Renaissance and the general distraction of men's thoughts from the problems and methods of Scholasticism.
no number of the form 4n+3, or 4n - I, can be the sum of two squares), and goes on to a d, practically, the condition stated by Fermat, "and the double of it [n] increased by one, when divided by the greatest square which measures it, must not be divisible by a prime number of the form 4n - 1," except for the omission of the words "when divided.
On the North American continent, as in Europe, the Cambrian system is divisible into three series: (i) the lower or "Georgian," with Olenellus fauna; (2) the middle or "Acadian," with Paradoxides or Dikelocephalus fauna; (3) the upper or "Potsdam," with Olenus fauna (with Saratogan or St Croix as synonyms for Potsdam).
Meanwhile, the same considerations had not been applied to time, so that in the days of Zeno of Elea time was still regarded as made up of a finite number of ` moments,' while space was confessed to be divisible without limit.
Now, As The Year Consists Of 365 Days And A Fraction, And 365 Is A Number Not Divisible By 12, It Is Impossible That The Months Can All Be Of The Same Length And At The Same Time Include All The Days Of The Year.
The section is divisible into the families Equidae and Palaeotheriidae, of which the latter is extinct.
In order that a monomial containing a m as a factor may be divisible by a monomial containing a p as a factor, it is necessary that p should be not greater than m.
According to him, we begin with an experience of ideas, in which object and idea are originally identical (V orstellungsobject); we divide this unitary experience into its subjective and objective factors; and especially in natural science we so far abstract the objects as to believe them at last to be independent things; but it is the office of psychology to warn us against this popular dualism, and to teach us that there is only a duality of psychical and physical, which are divisible, not separable, factors of one and the same content of our immediate experience; and experience is our whole knowledge.
(v.) Since (r) is an integer, (r) is divisible by r!; i.e.
The ego and non-ego limit one another, or determine one another; and, as limitation is negation of part of a divisible quantum, in this third act, the divisible ego is op-posed to a divisible non-ego.
These particles, however, would be still divisible by their own nature, because the Deity cannot diminish his own power, and therefore must retain his power of dividing them.
A school committee consisting of any number of members divisible by three is chosen, one-third each year, at the annual town-meeting or at a special meeting which is held in the same month.
The country is divisible, broadly, into three zones running parallel with the coast: (I) the delta, (2) forest region, giving place to (3) the plateau region.
The population is generally divisible into I The fellahin or peasantry and the native townsmen.
The ectoderm rarely consists of more than one layer of cells: these are divisible by structure and function into nervous, muscular and secretory cells, supported by interstitial cells.
When the net product of the ceded revenues amounts to £T2,157,375, the surplus is divisible as to 75% to the Turkish government and 25% to the public debt administration.
is of the form a p b e c r d s, where p, q, r, s have the least possible values consistent with the condition that a P PC'd s shall be divisible by each of the given expressions.
This was the state of opinion when the celebrated arguments against the possibility of motion, of which that of Achilles and the tortoise is a specimen, were propounded by Zeno, and such, apparently, continued to be the state of opinion till Aristotle pointed out that time is divisible without limit, in precisely the same sense that space is.
word meaning "some," "so many"), a term generally occurring in the phrase "aliquot part," and meaning that one quantity is exactly divisible into another; thus 3 is an aliquot part of 6.
On the continent of Europe it is customary to consider coal as divisible into two great classes, depending upon differences of colour, namely, brown coal, corresponding to the term "lignite" used in England and France, and black or stone coal, which is equivalent to coal as understood in England.
Even in external view, careful inspection will show that the body is divisible into four regions, namely, cephalic, atrial, abdominal and caudal.
This conception of matter, as infinitely divisible and continuous, was taught by Anaxagoras more than four centuries before the Christian era, and in the philosophy of Aristotle the same ideas are found.
To hold sovereignty not to be divisible is for juridical purposes not a working theory; states part, permanently or temporarily, with few or many of the rights and powers comprehended in sovereignty; to speak of it as undivided in the case of Crete, Egypt or Tibet is to do violence to facts.
Therefore n 1P+11 -(n-I) (P+11 is divisible by p!.
But, by hypothesis, n 1P1 is divisible by p!.
The colonies are divisible into two classes, (I) those possessing considerable powers of local self-government, (2) those in which the local government is autocratic. To this second class may be added the protectorates (and some colonies) where the native form of government is maintained under the supervision of French officials.
is then an expression of the form a p b e c r d s, where p, q, r, s have the greatest possible values consistent with the condition that each of the given expressions shall be divisible by a p b e c r d s .
With This Correction The Rule Of Intercalation Is As Follows: Every Year The Number Of Which Is Divisible By 4 Is A Leap Year, Excepting The Last Year Of Each Century, Which Is A Leap Year Only When The Number Of The Century Is Divisible By 4; But 4000, And Its Multiples, 8000, 12,000, 16,000, &C. Are Common Years.
There is no doubt but that in the Maccabean times and onward 218 was the shekel; but the use of the word darkemon by Ezra and Nehemiah, and the probabilities of their case, point to the daragmaneh, 1/60 maneh or shekel of Assyria; and the mention of 1/3 shekel by Nehemiah as poll tax nearly proves that the 129 and not 218 grains is intended, as 218 is not divisible by 3.
A president and vice-president are voted for every fourth year, in the years divisible by four, on the first Tuesday following the first Monday of November.
(2) But 11P+11=(p+i)!, which is divisible by (p+I)!.
According To The Gregorian Rule Of Intercalation, Therefore, Every Year Of Which The Number Is Divisible By Four Without A Remainder Is A Leap Year, Excepting The Centurial Years, Which Are Only Leap Years When Divisible By Four After Omitting The Two Ciphers.
They cling tenaciously to their native language, which is closely allied to the Finnish, and divisible into two, or according to some authorities into three, principal dialects - Dorpat Esthonian and Reval Esthonian, with Pernau Esthonian.
In fact, so far as the direct evidence of our senses tells us, matter appears to be indefinitely divisible.
divisible into two different types of structural region.
Conversely, he argues that corporeal things, however small, are always divisible.
Tax tips are divisible into two main categories: procedural and content.
(3) Therefore n1P+11 is divisible by (p+ I) !, whatever positive integral value n may have.
the product of any r consecutive integers is divisible by r!
(b) Let us assume that the product of every set of p consecutive integers is divisible by p!, and let us try to prove that the product of every set of p+ I consecutive integers is divisible by (p+i)!.
The body proper is usually divisible into two regions to which the names thorax and abdomen are applied.
Sometimes also, when a charge upon a commodity is not of such a figure as to be easily divisible among the ordinary units of retail consumption, so that it can be passed on to a consumer of the articles in the form of an increased price, it may remain fixed upon those who first pay it, at least for a time.
8), the colony looks like a feather having a stem divisible into an upper moiety or rachis, bearing lateral central leaflets (pinnae), and a lower peduncle, which is sterile and imbedded in sand or mud.
Its body is divisible into three portions, an upper capitulum bearing the mouth and tentacles, a median scapus covered by a friable cuticle, and a terminal physa which is rounded.
The remaining forms, the Actiniidea, are divisible into the Malacactiniae, or soft-bodied sea-anemones, which have !already been described sufficiently in the course of this article, and the Scleractiniae (= Madreporaria) or true corals.
When now we pass to geometrical measurement, each " one " is a thing which is itself divisible, and it cannot be said that at any moment we are counting it; it is only when one is completed that we can count it.
The number is divisible (i) by io if it ends in o; (ii) by 5 if it ends in o or 5; (iii) by 2 if the last digit is even; (iv) by 4 if the number made up of the last two digits is divisible by 4; (v) by 8 if the number made up of the last three digits is divisible by 8; (vi) by 9 if the sum of the digits is divisible by 9; (vii) by 3 if the s l um of the digits is divisible by 3; I 3=31 2 9 =32 3 27=33 481 =34 (viii) by II if the difference between the sum of the 1st, 3rd, 5th,.
is zero or divisible by I i.
(ix) To find whether a number is divisible by 7, II or 13, arrange the number in groups of three figures, beginning from the end, treat each group as a separate number, and then find the difference between the sum of the 1st, 3rd,.
Then, if this difference is zero or is divisible by 7, II or 13, the original number is also so divisible; and conversely.
For example, 31521 gives 521 -31 = 49 0, and therefore is divisible by 7, but not by II or 13.
They are divisible into two groups, an African and an Asiatic, both of which are generally included in the sub-genus, or genus, Bubalus, although the latter are sometimes separated as Buffelus.
The field we have defined is divisible into at least two parts, that of Astronomy proper, or " Astrometry," which treats of the motions, mutual relations and dimensions of the heavenly bodies; and that of Astrophysics, which treats of their physical constitution.
The former should be regarded as asserting that the whole is, not temporally, but logically, subsequent to the part, and that therefore there is an infinite regress in the notion of a whole which is infinitely divisible - a view which at any rate demands a serious refutation.
Finally, the last paradox may be interpreted as a valid refutation of the doctrine that space and time are not infinitely divisible.
divisible points, or in other words, the conception of Continuity.'
They are divisible into two great series, according to their mode of origin in the sea or in fresh-water.
The various states are politically divisible into four groups: (1) those west of the Niger; (2) those between the Niger and Lake Chad; (3) those between Lake Chad and the basin of the Nile; (4) those in the upper Nile valley.
Fermat's Theorem, if p is prime and a is prime to p then a p-1 -1 is divisible by p, was first given in a letter of 1640.
Knowledge is regarded as a mechanical product, part furnished by the subject, part given to the subject, and is thus viewed as mechanically divisible into a priori and a posteriori, into pure and empirical, necessary and contingent.
The materials used in the construction of furnaces are divisible into two classes, namely, ordinary and refractory or fire-resisting.
NOTE: Sometimes the desired azimuth is not exactly divisible by three, causing an option of rounding up or rounding down.
Parity and ECC memory modules have a chip count divisible by three or five.
divisible by the number of teeth on the blue gear.
divisible by n.
divisible by each fraction denominator.
Now we are looking for squares of all numbers divisible by 4, hence squares of even numbers.
divisible by the size of a tile, including the thickness of the walls of the pond.
Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible into parts that are infinitely divisible.
divisible into four units.
divisible into three groups, described in the foregoing table.
divisible balance available for profit and rent.
divisible incomplete block designs.
divisible 4-berth bedroom inners split by a 2.8m x 3.5m living area.
The geometric continuum is infinitely divisible; segments, no matter how small or how large, can arise.
A data unit is properly aligned if its address is evenly divisible by the data unit's size in bytes.
Where the proposed numbers are not easily divisible the lower number of double rooms will normally be acceptable " .
In the above example the number of teeth on the orange gear is not divisible by the number of teeth on the blue gear.
It might therefore be divisible into two kinds: adherent free goodwill and separable free goodwill.
find the least palindrome which is divisible by 13, and find any palindrome which is divisible by 54.
Their view was that "matter is not indefinitely divisible, but that all substances are formed of indivisible particles or atoms which are eternal and unchangeable, that the atoms are separated from one another by void, and that these atoms, by their combinations, form the matter we are conscious of."
This method of classification, though formally accurate, has slight value in the exact sciences, partly because at every step one of the two groups is merely negatively characterized and therefore incapable of real subdivision; it is useful, however, in setting forth clearly the gradual descent from the most inclusive genus (summum genus) through species to the lowest class (infima species), which is divisible only into individual persons or things.
The polyp usually has the body distinctly divisible into hydranth, hydrocaulus and hydrorhiza, and is usually clothed in a perisarc. The medusae may be set free or may remain attached to the polyp-colony and degenerate into a gonophore.
They are divisible into the Haplodrili or Archiannelida, the Polychaeta containing the marine worms, the Oligochaeta or terrestrial and fresh-water annelids (see Earthworm), the Hirudinea or leeches (see Leech), and a small group of parasitic worms, the 11-Tyzostomida (q.v.).
For we may in any product interchange a and b without altering its signification; therefore (ab) 2m+1 4) 1 = - (ab) 2 " 4)2, where 4,1 becomes by the interchange, and hence (ab)2m+14)1= Z (ab) 2m+1 (4) 1 - 02); and identity (I.) will always result in transforming 01-02 so as to make it divisible by (ab).
In correspondence with these four aspects of its subject, biology is logically divisible into four chief subdivisions - I.
They are divisible into three parts, the Lower Coal Measures, the middle or Pennant, a mass of sandstone containing some coals, and the Upper Coal Measures, also containing workable coal.
The Suidae are divisible into the true Old World swine (Suinae) and the American peccaries (Dicotylinae).
Under the influence of Leibnitz, Boscovich, Kant and Herbart, he supposed that bodies are divisible into punctual atoms, which are not bodies, but centres of forces of attraction and repulsion; that impenetrability is a result of repulsive force; and that force itself is only law - taking as an instance that Newtonian force of attraction whose process we do not understand, and neglecting that Newtonian force of pressure and impact whose process we do understand from the collision of bodies already extended and resisting.
The best charities are divisible into eleven categories: animals, children, education and literacy, the environment, housing, hunger, international affairs, mental illness, physical illness, poverty and veterans and their families.
It is indeed difficult to understand how so acute a thinker should confound that which is infinitely divisible with that which is infinitely great, as in (I), (2), (5), and (6); that he should identify space and 'magnitude, as in (3); that he should neglect the imperfection of the organs of sense, as in (4); that he should deny the reality of motion, as in (7); and that he should ignore the relativity of speed, as in (8): and of late years it has been thought that the conventional statements of the paradoxes, and in particular of those which are more definitely mathematical, namely (5), (6), (7), (8), do less than justice to Zeno's acumen.
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