... every chemical combination is wholly and solely dependent on two opposing forces, positive and negative electricity, and every chemical compound must be composed of two parts combined by the agency of their electrochemical reaction, since there is no third force. Hence it follows that every compound body, whatever the number of its constituents, can be divided into two parts, one of which is positively and the other negatively electrical.

[The compass needle] as the guide of Vasco de Gama to the East Indies, and of Columbus to the West Indies and the New World, it was pre-eminently the precursor and pioneer of the telegraph. Silently, and as with finger on its lips, it led them across the waste of waters to the new homes of the world; but when these were largely filled, and houses divided between the old and new hemispheres longed to exchange affectionate greetings, it removed its finger and broke silence. The quivering magnetic needle which lies in the coil of the galvanometer is the tongue of the electric telegraph, and already engineers talk of it as speaking.

A first step in the study of civilization is to dissect it into details, and to classify these in their proper groups. Thus, in examining weapons, they are to be classed under spear, club, sling, bow and arrow, and so forth; among textile arts are to be ranged matting, netting, and several grades of making and weaving threads; myths are divided under such headings as myths of sunrise and sunset, eclipse-myths, earthquake-myths, local myths which account for the names of places by some fanciful tale, eponymic myths which account for the parentage of a tribe by turning its name into the name of an imaginary ancestor; under rites and ceremonies occur such practices as the various kinds of sacrifice to the ghosts of the dead and to other spiritual beings, the turning to the east in worship, the purification of ceremonial or moral uncleanness by means of water or fire. Such are a few miscellaneous examples from a list of hundreds … To the ethnographer, the bow and arrow is the species, the habit of flattening children’s skulls is a species, the practice of reckoning numbers by tens is a species. The geographical distribution of these things, and their transmission from region to region, have to be studied as the naturalist studies the geography of his botanical and zoological species.

All known living bodies are sharply divided into two special kingdoms, based upon the essential differences which distinguish animals from plants, and in spite of what has been said, I am convinced that these two kingdoms do not really merge into one another at any point.

Biology can be divided into the study of proximate causes, the study of the physiological sciences (broadly conceived), and into the study of ultimate (evolutionary) causes, the subject of natural history.

Consider the eighth category, which deals with stones. Wilkins divides them into the following classifications: ordinary (flint, gravel, slate); intermediate (marble, amber, coral); precious (pearl, opal); transparent (amethyst, sapphire); and insoluble (coal, clay, and arsenic). The ninth category is almost as alarming as the eighth. It reveals that metals can be imperfect (vermilion, quicksilver); artificial (bronze, brass); recremental (filings, rust); and natural (gold, tin, copper). The whale appears in the sixteenth category: it is a viviparous, oblong fish. These ambiguities, redundances, and deficiencies recall those attributed by Dr. Franz Kuhn to a certain Chinese encyclopedia entitled Celestial Emporium of Benevolent Knowledge. On those remote pages it is written that animals are divided into (a) those that belong to the Emperor, (b) embalmed ones, (c) those that are trained, (d) suckling pigs, (e) mermaids, (f) fabulous ones, (g) stray dogs, (h) those that are included in this classification, (i) those that tremble as if they were mad, (j) innumerable ones, (k) those drawn with a very fine camel's hair brush, (l) others, (m) those that have just broken a flower vase, (n) those that resemble flies from a distance.

Events in the past may be roughly divided into those which probably never happened and those which do not matter. This is what makes the trade of historian so attractive.

Exper. I. I made a small hole in a window-shutter, and covered it with a piece of thick paper, which I perforated with a fine needle. For greater convenience of observation I placed a small looking-glass without the window-shutter, in such a position as to reflect the sun's light, in a direction nearly horizontal, upon the opposite wall, and to cause the cone of diverging light to pass over a table on which were several little screens of card-paper. I brought into the sunbeam a slip of card, about one-thirtieth of an inch in breadth, and observed its shadow, either on the wall or on other cards held at different distances. Besides the fringes of colour on each side of the shadow, the shadow itself was divided by similar parallel fringes, of smaller dimensions, differing in number, according to the distance at which the shadow was observed, but leaving the middle of the shadow always white. Now these fringes were the joint effects of the portions of light passing on each side of the slip of card and inflected, or rather diffracted, into the shadow. For, a little screen being placed a few inches from the card, so as to receive either edge of the shadow on its margin, all the fringes which had before been observed in the shadow on the wall, immediately disappeared, although the light inflected on the other side was allowed to retain its course, and although this light must have undergone any modification that the proximity of the other edge of the slip of card might have been capable of occasioning... Nor was it for want of a sufficient intensity of light that one of the two portions was incapable of producing the fringes alone; for when they were both uninterrupted, the lines appeared, even if the intensity was reduced to one-tenth or one-twentieth.

Finally in a large population, divided and subdivided into partially isolated local races of small size, there is a continually shifting differentiation among the latter (intensified by local differences in selection but occurring under uniform and static conditions) which inevitably brings about an indefinitely continuing, irreversible, adaptive, and much more rapid evolution of the species. Complete isolation in this case, and more slowly in the preceding, originates new species differing for the most part in nonadaptive parallel orthogenetic lines, in accordance with the conditions. It is suggested, in conclusion, that the differing statistical situations to be expected among natural species are adequate to account for the different sorts of evolutionary processes which have been described, and that, in particular, conditions in nature are often such as to bring about the state of poise among opposing tendencies on which an indefinitely continuing evolutionary process depends.

I could clearly see that the blood is divided and flows through tortuous vessels and that it is not poured out into spaces, but is always driven through tubules and distributed by the manifold bendings of the vessels... [F]rom the simplicity Nature employs in all her works, we may conclude... that the network I once believed to be nervous [that is, sinewy] is really a vessel intermingled with the vesicles and sinuses and carrying the mass of blood to them or away from them... though these elude even the keenest sight because of their small size... From these considerations it is highly probable that the question about the mutual union and anastomosis of the vessels can be solved; for if Nature once circulates the blood within vessels and combines their ends in a network, it is probable that they are joined by anastomosis at other times too.

If a mixture of different kinds of electrified atoms is moving along in one stream, then when electric and magnetic forces are applied to the stream simultaneously, the different kinds of atoms are sorted out, and the original stream is divided up into a number of smaller streams separated from each other. The particles in any one of the smaller streams are all of the same kind.

If an event can be produced by a number n of different causes, the probabilities of the existence of these causes, given the event (prises de l'événement), are to each other as the probabilities of the event, given the causes: and the probability of each cause is equal to the probability of the event, given that cause, divided by the sum of all the probabilities of the event, given each of the causes.

If E is considered to be a continuously divisible quantity, this distribution is possible in infinitely many ways. We consider, however—this is the most essential point of the whole calculation—E to be composed of a well-defined number of equal parts and use thereto the constant of nature h = 6.55 ×10^-27 erg sec. This constant multiplied by the common frequency ν of the resonators gives us the energy element ε in erg, and dividing E by ε we get the number P of energy elements which must be divided over the N resonators.
[Planck’s constant, as introduced in 1900; subsequently written e = hν.]

If the world has begun with a single quantum, the notions of space and would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time. I think that such a beginning of the world is far enough from the present order of Nature to be not at all repugnant. It may be difficult to follow up the idea in detail as we are not yet able to count the quantum packets in every case. For example, it may be that an atomic nucleus must be counted as a unique quantum, the atomic number acting as a kind of quantum number. If the future development of quantum theory happens to turn in that direction, we could conceive the beginning of the universe in the form of a unique atom, the atomic weight of which is the total mass of the universe. This highly unstable atom would divide in smaller and smaller atoms by a kind of super-radioactive process.

If we view mathematical speculations with reference to their use, it appears that they should be divided into two classes. To the first belong those which furnish some marked advantage either to common life or to some art, and the value of such is usually determined by the magnitude of this advantage. The other class embraces those speculations which, though offering no direct advantage, are nevertheless valuable in that they extend the boundaries of analysis and increase our resources and skill. Now since many investigations, from which great advantage may be expected, must be abandoned solely because of the imperfection of analysis, no small value should be assigned to those speculations which promise to enlarge the field of anaylsis.

In old age, you realise that while you're divided from your youth by decades, you can close your eyes and summon it at will. As a writer it puts one at a distinct advantage.

In the beginning God created the heaven and earth. And the earth was waste and void; and darkness was upon the face of the deep: and the spirit of God moved upon the face of the waters. … God said, “Let there be a vault in the waters to divide the waters in two.” And so it was. God made the vault, and it divided the waters above the vault from the waters under the vault. God called the vault “heaven.”

It is customary to connect Medicine with Botany, yet scientific treatment demands that we should consider each separately. For the fact is that in every art, theory must be disconnected and separated from practice, and the two must be dealt with singly and individually in their proper order before they are united. And for that reason, in order that Botany, which is, as it were, a special branch of Natural Philosophy [Physica], may form a unit by itself before it can be brought into connection with other sciences, it must be divided and unyoked from Medicine.

It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination.

It is not strictly demonstrated that atoms are indivisible; but it appears that they are not divided by the laws of nature.

Literature has her quacks no less than medicine, and they are divided into two classes; those who have erudition without genius, and those who have volubility, without depth; we shall get second-hand sense from the one, and original nonsense from the other.

Natural bodies are divided into three kingdoms of nature: viz. the mineral, vegetable, and animal kingdoms. Minerals grow, Plants grow and live, Animals grow, live, and have feeling.

Nature vibrates with rhythms, climatic and diastrophic, those finding stratigraphic expression ranging in period from the rapid oscillation of surface waters, recorded in ripple-mark, to those long-deferred stirrings of the deep imprisoned titans which have divided earth history into periods and eras. The flight of time is measured by the weaving of composite rhythms- day and night, calm and storm, summer and winter, birth and death such as these are sensed in the brief life of man. But the career of the earth recedes into a remoteness against which these lesser cycles are as unavailing for the measurement of that abyss of time as would be for human history the beating of an insect's wing. We must seek out, then, the nature of those longer rhythms whose very existence was unknown until man by the light of science sought to understand the earth. The larger of these must be measured in terms of the smaller, and the smaller must be measured in terms of years.

Newton was probably responsible for the concept that there are seven primary colours in the spectrum—he had a strong interest in musical harmonies and, since there are seven distinct notes in the musical scale, he divided up the spectrum into spectral bands with widths corresponding to the ratios of the small whole numbers found in the just scale.

Nonmathematical people sometimes ask me, “You know math, huh? Tell me something I’ve always wondered, What is infinity divided by infinity?” I can only reply, “The words you just uttered do not make sense. That was not a mathematical sentence. You spoke of ‘infinity’ as if it were a number. It’s not. You may as well ask, 'What is truth divided by beauty?’ I have no clue. I only know how to divide numbers. ‘Infinity,’ ‘truth,’ ‘beauty’—those are not numbers.”

Number is divided into even and odd. Even number is divided into the following: evenly even, evenly uneven, and unevenly uneven. Odd number is divided into the following: prime and incomposite, composite, and a third intermediate class (mediocris) which in a certain way is prime and incomposite but in another way secondary and composite.

Ordinarily logic is divided into the examination of ideas, judgments, arguments, and methods. The two latter are generally reduced to judgments, that is, arguments are reduced to apodictic judgments that such and such conclusions follow from such and such premises, and method is reduced to judgments that prescribe the procedure that should be followed in the search for truth.

Petr Beckmann has divided the men who made history into two classes, the thinkers and the thugs. The Greeks were the thinkers and the Romans were the thugs. The general law seems to be that the thugs always win, but the thinkers always outlive them.

So far as I have been able to observe thus far, the series of strata which compose the earth’s visible crust, seem to me to be divided into four general or successive, orders, without taking into consideration the sea. These four orders can be thought of as being four enormous strata ... which, wherever they are found, are seen to be placed one above the other, in a consistently uniform manner.

That the master manufacturer, by dividing the work to be executed into different processes, each requiring different degrees of skill or of force, can purchase precisely the precise quantity of both which is necessary for each process; whereas, if the whole work were executed by one workman, that person must possess sufficient skill to perform the most difficult, and sufficient strength to execute the most laborious, of the operations into which the art is divided.

The absolute extent of land in the Archipelago is not greater than that contained by Western Europe from Hungary to Spain; but, owing to the manner in which the land is broken up and divided, the variety of its productions is rather in proportion to the immense surface over which the islands are spread, than to the quantity of land which they contain.

The collective IQ of the group is the lowest IQ of any member of the group, divided by the numbers of members in the group.

The experiments made on the mutual electrical relations of bodies have taught us that they can be divided into two classes: electropositive and electronegative. The simple bodies which belong to the first class, as well as their oxides, always take up positive electricity when they meet simple bodies or oxides belonging to the second class; and the oxides of the first class always behave with the oxides of the other like salifiable bases with acids.

The general public has long been divided into two parts those who think science can do anything, and those who are afraid it will.

The history of chemistry is properly divided into the mythologic, the obscure, and the certain. The first period exhibits it from its infancy, deformed by fictions, until the destruction of the library of Alexandria by the Arabs. —The second, though freed in some measure from these absurdities, yet is still clothed in numberless enigmas and allegorical expressions.— The third period commences at the middle of the seventeenth century, with the first establishment of societies and academies of science; of which the wise associates, in many places uniting their efforts, determined to pursue the study of Natural Philosophy by observation and experiments, and candidly to publish their attempts in a general account of their transactions.

The history of the knowledge of the phenomena of life and of the organized world can be divided into two main periods. For a long time anatomy, and particularly the anatomy of the human body, was the α and ω of scientific knowledge. Further progress only became possible with the discovery of the microscope. A long time had yet to pass until through Schwann the cell was established as the final biological unit. It would mean bringing coals to Newcastle were I to describe here the immeasurable progress which biology in all its branches owes to the introduction of this concept of the cell concept. For this concept is the axis around which the whole of the modern science of life revolves.

The invention of the differential calculus marks a crisis in the history of mathematics. The progress of science is divided between periods characterized by a slow accumulation of ideas and periods, when, owing to the new material for thought thus patiently collected, some genius by the invention of a new method or a new point of view, suddenly transforms the whole subject on to a higher level.

The most startling result of Faraday’s Law is perhaps this. If we accept the hypothesis that the elementary substances are composed of atoms, we cannot avoid concluding that electricity also, positive as well as negative, is divided into definite elementary portions, which behave like atoms of electricity.

The most wonderful mystery of life may well be the means by which it created so much diversity from so little physical matter. The biosphere, all organisms combined, makes up only about one part in ten billion of the earth’s mass. … Yet life has divided into millions of species, the fundamental units, each playing a unique role in relation to the whole.

The nations may be divided in everything else, but they all share a single body of science.

The strangest thing of all is that our ulama these days have divided science into two parts. One they call Muslim science, and one European science. Because of this they forbid others to teach some of the useful sciences. They have not understood that science is that noble thing that has no connection with any nation, and is not distinguished by anything but itself. Rather, everything that is known is known by science, and every nation that becomes renowned becomes renowned through science. Men must be related to science, not science to men. How very strange it is that the Muslims study those sciences that are ascribed to Aristotle with the greatest delight, as if Aristotle were one of the pillars of the Muslims. However, if the discussion relates to Galileo, Newton, and Kepler, they consider them infidels. The father and mother of science is proof, and proof is neither Aristotle nor Galileo. The truth is where there is proof, and those who forbid science and knowledge in the belief that they are safeguarding the Islamic religion are really the enemies of that religion. Lecture on Teaching and Learning (1882).

The student of palaetiological sciences is a scientist and a historian. The former tries to be as uniformitarian as possible, the latter has to recognize the contingency of events which will ever be a 'skandalon' to the scientist. Verily, the geologist 'lives in a divided world'.

The word atom signifies without parts—not to be divided. You divide it in thought; for, if you were to divide it in reality, it would no longer be an atom.

This king [Sesostris] divided the land among all Egyptians so as to give each one a quadrangle of equal size and to draw from each his revenues, by imposing a tax to be levied yearly. But everyone from whose part the river tore anything away, had to go to him to notify what had happened; he then sent overseers who had to measure out how much the land had become smaller, in order that the owner might pay on what was left, in proportion to the entire tax imposed. In this way, it appears to me, geometry originated, which passed thence to Hellas.

To pick a hole–say in the 2nd law of Ω^cs, that if two things are in contact the hotter cannot take heat from the colder without external agency.
Now let A & B be two vessels divided by a diaphragm and let them contain elastic molecules in a state of agitation which strike each other and the sides. Let the number of particles be equal in A & B but let those in A have equal velocities, if oblique collisions occur between them their velocities will become unequal & I have shown that there will be velocities of all magnitudes in A and the same in B only the sum of the squares of the velocities is greater in A than in B.
When a molecule is reflected from the fixed diaphragm CD no work is lost or gained.
If the molecule instead of being reflected were allowed to go through a hole in CD no work would be lost or gained, only its energy would be transferred from the one vessel to the other.
Now conceive a finite being who knows the paths and velocities of all the molecules by simple inspection but who can do no work, except to open and close a hole in the diaphragm, by means of a slide without mass.
Let him first observe the molecules in A and when lie sees one coming the square of whose velocity is less than the mean sq. vel. of the molecules in B let him open a hole & let it go into B. Next let him watch for a molecule in B the square of whose velocity is greater than the mean sq. vel. in A and when it comes to the hole let him draw and slide & let it go into A, keeping the slide shut for all other molecules.
Then the number of molecules in A & B are the same as at first but the energy in A is increased and that in B diminished that is the hot system has got hotter and the cold colder & yet no work has been done, only the intelligence of a very observant and neat fingered being has been employed. Or in short if heat is the motion of finite portions of matter and if we can apply tools to such portions of matter so as to deal with them separately then we can take advantage of the different motion of different portions to restore a uniformly hot system to unequal temperatures or to motions of large masses. Only we can't, not being clever enough.

We know only a single science, the science of history. History can be contemplated from two sides, it can be divided into the history of nature and the history of mankind. However, the two sides are not to be divided off; as long as men exist the history of nature and the history of men are mutually conditioned.

What we call man is a mechanism made up of … uncrystallized matter … all the colloid matter of his mechanism is concentrated in a countless number of small cells. … [T]hese cells [are] dwelling places, communes, a walled town within which are many citizens. ... [T]hese are the units of life and when they pass out into space man as we think we know him is dead, a mere machine from which the crew have left,so to speak. ... [T]hese units are endowed with great intelligence. They have memories, they must be divided into countless thousands of groups, most are workers, there are directing groups. Some are chemists, they manufacture the most complicated chemicals that are secreted by the glands.

When air has been freshly and strongly tainted with putrefaction, so as to smell through the water, sprigs of mint have presently died, upon being put into it, their leaves turning black; but if they do not die presently, they thrive in a most surprizing manner. In no other circumstances have I ever seen vegetation so vigorous as in this kind of air, which is immediately fatal to animal life. Though these plants have been crouded in jars filled with this air, every leaf has been full of life; fresh shoots have branched out in various , and have grown much faster than other similiar plants, growing in the same exposure in common air.
This observation led me to conclude that plants, instead of affecting the air in the same manner with animal respiration, reverse the effects of breathing, and tend to keep the atmosphere sweet and wholesome, when it is become noxious, in consequence on animals living and breathing, or dying and putrefying in it.
In order to ascertain this, I took a quantity of air, made thoroughly noxious, by mice breathing and dying in it, and divided it into two parts; one of which I put into a phial immersed in water; and to the other (which was contained in a glass jar, standing in water) I put a sprig of mint. This was about the beginning of August 1771, and after eight or nine days, I found that a mouse lived perfectly well in that part of the air, in which the sprig of mint had grown, but died the moment it was put into the other part of the same original quantity of air; and which I had kept in the very same exposure, but without any plant growing in it.

William Blake called division the sin of man; Faraday was a great man because he was utterly undivided. His whole, very harmonious, very well balanced, … and used the brain in the limited way in which it is useful…. [H]e built up his few but precious speculations. Their simplicity rivals with their forcefulness.

Writers, like teeth, are divided into, incisors and grinders.