Solved Sentence Examples

She had hoped it solved all her issues.

This expedient seems to have solved the problem.

He thus admits that to philosophize is to systematize, but holds that every systematization is narrowly circumscribed, and is therefore to be solved and completed with ever new systematization.

The problem was not solved, but the inadequate solutions were excluded, and the data to be considered in any adequate solution were affirmed.

Swedenborg knew that the machine would not fly, but suggested it as a start and was confident that the problem would be solved.

East of Bhutan, amongst the semi-independent hill states which sometimes own allegiance to Tibet and sometimes assert complete freedom from all authority, the geographical puzzle of the course of the Tsanpo, the great river of Tibet, has been solved by the researches of Captain Harman, and the explorations of the native surveyor "K.

In point of fact this problem had been partially solved in the early days of the zgth century, thanks to the sagacious guesses of the German philologist Grotefend.

He proposed the problem of the catenary or curve formed by a chain suspended by its two extremities, accepted Leibnitz's construction of the curve and solved more complicated problems relating to it.

One of these projects, on which an elaborate report had actually to be submitted to the Emperor, was a device for which it was claimed that it had solved the problem of perpetual motion.

The contradiction is solved in a higher synthesis, which takes up into itself the two opposites.

He had no profound insight into the problem of Judaism, and there was no lasting validity in his view that the problem - the thousands of years' old mystery - could be solved by a retrogression to local nationality.

Archytas of Tarentum (c. 430 B.C.) solved the problems by means of sections of a half cylinder; according to Eutocius, Menaechmus solved them by means of the intersections of conic sections; and Eudoxus also gave a solution.

These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836-901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola.

This was solved by using pairs of colored plastic bobbins instead.

Sudoku is a game of pure logic, an addictive brainteaser that can be solved by lateral.. .

The demand for more secondary armament - 15 cm - was solved by using twin casemates.

However it wasn't fully solved in a way sailors could use at sea for some 150 years, when accurate chronometers became available.

He said he was confident it could be solved painlessly and economically, if only concerted action was taken.

I couldn't decide whether it was a general purpose solver, or just has a large database of solved cryptograms.

A protein structure solved by X-ray crystallography is regarded as the gold standard to which all other structures are compared.

We solved any disagreement by discussing with each other.

He solved problems such as pairs of simultaneous quadratic equations.

Thus, in total there are six partial differential equations to be solved.

When (with her assistance) they solved it, he provided their prize of thirty festal garments by killing thirty men of Ashkelon.

That is the dilemma and, with respect, it will not be solved by questions posed in a somewhat glib way.

It gives even the most experienced helmsman and crew plenty of excitement and problems to solved.

The Professor unlocked the door, and seeing a natural hesitation among us for various reasons, solved the difficulty by entering first himself.

In the end an air raid in 942 solved one problem when the old thatched inn proved a vulnerable target.

Disputes which once seemed totally intractable have been solved.

The set of linear equations is then solved by means of a matrix inversion.

It can be solved analytically in terms of the statistical mechanics of spin lattices.

This problem was solved by adding whole linseeds (flaxseeds) to his diet.

In my experience arguments which are about money usually get solved in the end; it is arguments about principle which prove most obstinate.

The problem of national partiality is solved by the impossibility of impartiality.

This problem can be formulated and solved as an integer programming problem.

The structure was solved by molecular replacement using the same protein solved in a different space group.

An investigator may fancy his problem solved when it is merely restated in a new form.

This problem is solved by simply typing the missing semicolon on the next line of input.

All of these problems are solved by using sh instead of cpp.

But now they feel quite sheepish Those scientists unwary, One problem solved, but what to do With Mary, Mary, Mary.

The problems of the world cannot possibly be solved by skeptics or cynics whose horizons are limited by the obvious realities.

The structure was solved by molecular replacement using the same protein solved by molecular replacement using the same protein solved in a different space group.

This problem was solved by using the data buffer output enables to disable the appropriate column address strobe.

They can be solved by lateral thinking alone and have been making quite an impact around the world.

They can be solved using Venn diagrams and thinking in a logical way.

I have solved the problem of the rickshaw wallahs.

These manifestations of the divine spirit again cannot be traced and understood by reducing (as Hegel did) the growth of the human mind in the individual, in society and in history to the monotonous rhythm of a speculative schematism; the essence and worth which is in them reveals itself only to the student of detail, for reality is larger and wider than philosophy; the problem, "how the one can be many," is only solved for us in the numberless examples in life and experience which surround us, for which we must retain a lifelong interest and which constitute the true field of all useful human work.

In the view of Hobbes, the difficulty of the genesis of conscious minds is solved by saying that sensation and thought are part of the reaction of the organism on external movement.

In Australia, however, where sacrifice of the ordinary type is unknown, the ritual killing of a child is practised in connexion with the initiation of a magician; it is therefore by no means axiomatic that animals were offered before human beings; the problem of priority is one to be solved for each area separately, but probably no solution is possible; in the absence of Aztec traditions it would hardly have seemed probable that two centuries had seen so great a transformation.

The pioneer in this field was August Kekule, who, in 1865 (Ann., 137, p. 129; see also his Lehrbuch der organischen Chemie), submitted his well-known formula for benzene, so founding the " benzene theory " and opening up a problem which, notwithstanding the immense amount of labour since bestowed upon it, still remains imperfectly solved.

Some have supposed that certain chemical properties of which the Nile water was possessed acted as a glue or cement to cause the two layers to adhere; others, with more reason, that glutinous matter contained in the material itself was solved by the action of water, whether from the Nile or any other source; and others again read in Pliny's words an implication that a paste was actually used.

On the other hand, Wayland Vaughan (see Annual Report of the Smithsonian Institution, 1917) has shown clearly that the problem is essentially a biochemical one and may finally be solved by the methods of the latter science.

As early as 1539 Cardan had solved certain particular cases, but it remained for his pupil, Lewis (Ludovici) Ferrari, to devise a general method.

All the hypotheses about the causation of new growths seek to explain the secret of this individuality or " autonomy," as they recognize that the mystery of the origin of the great majority of tumours would be solved if we could trace how or why the tissue elements in which they develop first took on this abnormal growth.

A vivid new light is shed by him upon certain problems, such for instance as those of the imagination or intuition, the source of Art and the theme of the Aesthetic, upon pure will, the source of Economic of Rights and of Politics, treated by Economic. The more precise determination and configuration of the categories and their mode of acting, by means of which is negated and solved the concept of an external reality and of nature placed outside the spirit and opposed to it, led Croce to an absolute spiritualism, widely different from the pan-logicism of Hegel and his school, which only seemed to solve the dualism of spirit and nature and really opened the door to the notion of a transcendental God, as became clear in the development of Hegel's theory at the hands of the right wing of his school.

He was wont to mention the following as the two incidents in his life which had afforded him the greatest pleasure, - that a stranger, whom he had met as a travelling companion in his youth, made to his declaration "I am Daniel Bernoulli" the incredulous and mocking reply, "And I am Isaac Newton"; and that, while entertaining Kdnig and other guests, he solved without rising from table a problem which that mathematician had submitted as difficult and lengthy.

A solution by means of the parabola and hyperbola was given by Dionysodorus of Amisus (c. 1st century B.c), and a similar problem - to construct a segment equal in volume to a given segment, and in surface to another segment - was solved by the Arabian mathematician and astronomer, Al Kuhi.

Some of these are exceedingly difficult, but Cherubini solved the whole of them.

How far such adaptations are produced afresh in each generation, whether or no their effects are transmitted to descendants and so directly modify the stock, to what extent adaptations characteristic of a species or variety have come about by selection of individuals capable, in each generation, of responding favourably, or how far by the selection of individuals fortuitously suitable to the environment, or, how far, possibly by the inheritance of the responses to the environment, are problems of biology not yet definitely solved.

There were two strong candidates whose claims were so nearly equal that it was difficult to elect either; the difficulty was solved by a unanimous invitation to Maine to accept the post.

Whether the two families have a common ancestor in the negritos of Malaysia and the Indian archipelago, or whether Papuan and Negrito are alike branches of an aboriginal African race, is a problem yet to be solved.

The problem involved in this double name has not yet been definitely solved.

Thus palaeontology has brought to light an entirely new nomenclatural problem, which can only be solved by resolutely adopting an entirely different principle.

For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.

Halley added in his edition (1710) a restoration of Book viii., in which he was guided by the fact that Pappus gives lemmas "to the seventh and eighth books" under that one heading, as well as by the statement of Apollonius himself that the use of the seventh book was illustrated by the problems solved in the eighth.

Aristotle did not altogether solve the question, What is, and scarcely solved at all the question, How do we know the external world?

But has Haeckel solved the problems of mind ?

The mystery of the Hyksos has not yet been solved; but it is not impossible that they had relations with Mesopotamia.

Next year, having solved, as he thought, another ancient crux, the duplication of the cube, he had his solution brought out anonymously at Paris in French, so as to put Wallis and other critics off the scent and extort a judgment that might be withheld from a work of his.

Pascal solved the hitherto refractory problem of the general quadrature of the cycloid, and proposed and solved a variety of others relating to the centre of gravity of the curve and its segments, and to the volume and centre of gravity of solids of revolution generated in various ways by means of it.

It is by means of the cytological evidence, however, that this problem will finally be solved.

The conflict is usually solved for practical purposes by an understanding which is approximately general, namely that, in cases not provided for by treaty, no state shall protect those whom it claims as its nationals while residing in the territory of another state which claims them as its own nationals by any title, whether jus soli, jus sanguinis, naturalization, or the refusal to allow expatriation.

John Wallis utilized the intersections of this curve with a right line to solve cubic equations, and Edmund Halley solved sextic equations with the aid of a circle.

In his De Quadratura Circuli he professed to have solved the problem; and in his Conjectura de novissimis diebus he prophesied that the world would come to an end in 1734.

In his Saggiatore Galileo states that he solved the problem of the construction of a telescope the first night after his return to Padua from Venice, and made his first telescope next day by fitting a convex lens in one extremity of a.

No doubt the problem has been in a measure solved in England by that useful incentive to industry, the mark system.

Hence also induction is a real process, because, when we know that this individual magnet attracts iron, we are very far from knowing that all alike do so similarly; and the question of inductive logic, how we get from some similars to all similars, remains, as before, a difficulty, but not to be solved by the fallacy that inference is identification.

A situation involving a need of adaptation to environment arises and the problem it sets must be solved that the will may control environment and be justified by success.

Temporary financial embarrassment followed, but when the Federal government had taken upon itself half the burden and established the economic administration of the commissioners, the problem of beautifying the nation's capital was solved.

These equations can be at once solved for H, H, H,.

The force F acts in this line, and thus the problem is completely solved.

Humanism, as it actually appeared in Italy, was positive in its conception of the problems to be solved, pagan in its contempt for medieval mysticism, invigorated for sensuous enjoyment by contact with antiquity, yet holding in itself the germ of new religious aspirations, profounder science and sterner probings of the mysteries of life than had been attempted even by the ancients.

The problems to be solved were the frontier difficulty with Argentina, the question of the possession of Tacna and Arica with Peru, and the necessity of fulfilling the obligation contracted with Bolivia to give that country a seaport on the Pacific coast.

There were also urgent economic problems to be solved.

Others hold the problem to be insoluble, and not needing to be solved.

He solved the problem of finding the point in a convex mirror at which a ray coming from one given point shall be reflected to another given point.

The Broken Hill Proprietary Company owns the principal mine, and at Port Pixie in the neighbouring colony of South Australia erected a complete smelting plant; the problem of the recovery of the zinc contents of the ore having been satisfactorily solved, the company made extensive additions to the plant already erected, and in 1906 the manufacture of spelter was undertaken.

A terrestrial habitat is less common, but the widely-distributed land Isopoda or woodlice and the land-crabs of tropical regions have solved the problem of adaptation to a subaerial life.

This problem was solved independently by Vicenzo Viviani in Italy.

According to Hittorf he was the first who saw the three lines of the hydrogen spectrum, which a few months after his death were recognized in the spectrum of the solar protuberances, and thus solved one of the mysteries of modern astronomy.

He refused to tell how he became aware of the secret articles, and the mystery has never been fully solved.

At first Livingstone thought the Nile problem had been all but solved by Speke, Baker and Burton, but the idea grew upon him that the Nile sources must be sought farther south, and his last journey became in the end a forlorn hope in search of the "fountains" of Herodotus.

He received a scanty education; worked as a carpenter in Syracuse and as a machinist in Ithaca; became interested (about 2842) in the development of the electric telegraph; and after unsuccessful or over-expensive attempts to ground the telegraph wires in 1844 solved the difficulty by stringing them on poles.

Newton received this problem about 5 o'clock in the afternoon as he was returning from the mint, but, though he was fatigued with business, he solved the problem the same evening.

How far and in what sense this ground of necessity renders them personal are of course questions still to be solved.

And whether the laws of our reason are the laws of all intelligence and being - whether and how we are to relate our fundamental, intellectual and moral conceptions to what is beyond our experience, or to an infinite being - are problems which Cousin cannot be regarded as having solved.

The problems met and solved by Governor Morton, however, were not only the comparatively simple ones of furnishing troops as required.

Palaeontology, so far as it goes, is a sure guide, but some of the oldest fossiliferous rocks yield remains of distinctly differentiated crinoids, asteroids and echinoids, so that the problem is not solved merely by collecting fossils.

There was now a problem of some difficulty to be solved.

However the domestic problems in the United Kingdom might be solved, the future of the greatness of the English throne lay with its headship of an empire, loyal to the core, over which the sun never sets.

As the indisputable facts became known, the world recognized that the two astronomers had independently solved the problem of Uranus, and ascribed to each equal glory.

By means of this instrument questions in navigation, trigonometry, &c., are solved with the aid of a pair of compasses.

They were quite sure they had attained a certain ' gnosis ' - had more or less successfully solved the problem of existence; while I was quite sure that I had not, and had a pretty strong conviction that the problem was insoluble.

He pointed out that the principle of the greatest happiness of the greatest number is a principle without any definite meaning, since men are nowhere unanimous in their standard of happiness, but regard the conception of happiness rather as a problem to be solved than a test to be applied.

When the subject was taken up by the continental mathematicians, using the analytical method, the question naturally arose whether the motions of three bodies under their mutual attraction could not be determined with a degree of rigour approximating to that with which Newton had solved the problem of two bodies.

The longitudes, latitudes and radii vectores of a planet, being algebraically expressed as the sum of an infinite periodic series of the kind we have been describing, it follows that the problem of finding their co-ordinates at any moment is solved by computing these expressions.

The problem of measuring from an axis perpendicular to this plane is solved on the principle that the incident and reflected rays of light make equal angles with the perpendicular to a reflecting surface.

Although the precision of the mathematical solution has been placed beyond serious doubt, the problem of completely reconciling this solution with the observed motions of the moon is not yet completely solved.

These researches incidentally solved the constitution of coumarin, the odoriferous principle of woodruff.

They also investigated certain hydrocarbons occurring in the high boiling point fraction of the coal tar distillate and solved the constitution of phenanthrene.

This latter problem received the attention of the Arabian astronomer Abul Wefa (loth century A.D.), who solved it with a single opening of the compasses.

Another "social" measure of less importance, which formed part of the Chamberlain programme, was the Small Houses Acquisition Act of 18 9 9; but the problem of old age pensions was less easily solved.

At present the manufacture of artificial camphor may be considered a solved problem, although it is doubtful whether such camphor will be able to compete in price with the natural product in the future.

Quite apart from the genuineness of a sample, its special aroma constitutes the value of an oil, and in this respect the judging of the value of a given oil may, apart from the purity, be more readily solved by an experienced perfumer than by the chemist.

Poncelet, how all problems of the second order can be solved by aid of the straight-edge alone without the use of compasses, as soon as one circle is given on the drawing-paper.

Alberti solved the problem with marvellous skill, blending the old architecture with the new style of the Renaissance, and giving it variety without destroying its unity of effect.

You're smart enough to know that having sex wouldn't have solved any problems for Edith Shipton, and probably not stopped her from taking her own life.

To be perfectly honest, shouldn't this kind of dispute be solved by the Gatekeeper?

Necessary algorithmic problems are then solved by converting types to finite tree automata.

Mysteries are not meant to be solved, they are meant to strike awe.

The emancipation was not merely a humanitarian question capable of being solved instantaneously by imperial ukaz.

Having obtained the set of instantaneous centres for a chain, suppose a is the fixed link of the chain and c any other link; then O,,,is the instantaneous centre of the two links and may be considered for the instant as the trace of an axis fixed to an extension of the link a about which c is turning, and thus problems of instantaneous velocity concerning the link c are solved as though the link c were merely rotating for the instant about a fixed axis coincident with the instantaneous axis.

No European race confronted with the problem of an immense coloured population has solved it more successfully than the Portuguese and their kinsmen in Brazil; in both countries intermarriage was freely resorted to, and the offspring of these mixed unions are superior in character and intelligence to most half-breeds.

His work constitutes the oldest commentary in the world on Genesis and part of Exodus, an enlarged Targum on these books, in which difficulties in the biblical narration are solved, gaps supplied, dogmatically offensive elements removed and the genuine spirit of later Judaism infused into the primitive history of the world.

But as regards the first of these, it is rather a case of condensed citation than of misinterpretation; the second is explained by the writer's carelessness as shown in other passages, and all are solved if a considerable interval of time elapsed between the compilation of the Constitutions and the spurious Ignatian epistles.

In 1953, James Watson and Francis Crick announced to the scientific world that they had solved the puzzle.

So these former farmers got jobs in factories, learned to repair equipment, solved problems, became line managers, suggested improvements to processes, and got paid for their effort.

A bright idea, however, shot into my mind, and the problem was solved.

Then the hunter came forward and stood in their midst, and the mystery was solved.

Without changing his careless attitude, Pierre looked at them over his spectacles unable to understand what they wanted or how they could go on living without having solved the problems that so absorbed him.

The question that had perturbed Pierre on the Mozhaysk hill and all that day now seemed to him quite clear and completely solved.

Yes, one must harness them, must harness them! he repeated to himself with inward rapture, feeling that these words and they alone expressed what he wanted to say and solved the question that tormented him.

Themis in anger at the riddle being solved sent a wild beast to ravage the countryside.

After the normal form for the equations has been derived, the extent to which the equations may be solved analytically is covered.

We also feel that the issue should be solved peacefully and diplomatically.

These two hurdles, for which separate solutions exist, must, however, be solved simultaneously for developing improved vaccines.

This however might be solved easily in future releases.

The problem cant be solved when there is no such thing.

Cutting a longer slot in the socket end of the coupling solved the speed hump problem.

Spreadsheet templates are included to illustrate how each problem is solved.

Incidentally I solved the business of the stilettos shoes damaging the floor.

The gentleman in question solved this delicate social problem by requesting a rope in a strangulated tone.

Over time we hope to provide details of all structures solved within the SBG.

If you do, it can be solved by using a surge suppressor plug at the mains socket where you plug the player in.

They can be solved using venn diagrams and thinking in a logical way.

Jenny said she knew a simple tactic for us to follow as we solved the murder-mystery game.

Nursery gliders have solved this problem with a simple design.

Classic Detective - is identified as an investigator who solved mysteries through observation and logical deduction.

For many people, their problems have been solved by popular rent to own businesses.

This problem has been solved with modern lenses, as the plastic can be melted and poured into a mold in which the polarizing film has been suspended.

There are also extra features like the math alarm - which requires a math problem to be solved before dismissing an alarm - and the nap alarm clock that works like a timer rather than like a conventional alarm.

I'm sure his sweet personality makes up for some of these things, so let's see if we can get some of these issues solved for you.

The problems seem to be solved, and Taste of the Wild was not one of the products that had been recalled.

Look at each day as an adventure, a crazy puzzle to be solved, a game where, if everyone plays fair, everyone wins.

Rather than spend money on an expensive hotel or have someone spend an uncomfortable night on the floor, simply unfold the bed and your problems are solved.

Martha Stewart and Kmart report that they have solved the problem that was causing the shattering.

In addition, online hunting games offer more than shooting games; games range from arcade formats to specific missions solved with logic and skill.

My neighbor added a gate to keep the dog away from our shared fence, and a major problem was solved.

If only all barking dog problems were solved so easily!

This can be solved by softening the walls with decorative drapes.

Flooding can often be solved by installing a sump pump.

Anyone who uses a CPAP or BiPAP machine is invited to visit their free monthly clinic to get their questions answered and fitting problems solved.

The physician can help determine whether the condition is caused by problems that can be solved with a few simple lifestyle changes.

Ideally, you learn to sleep on your side and your snoring problem is solved or at least lessened.

There are many different dream theories, but dreaming is a mystery, like sleep, that hasn't completely been solved.

Use the steps outlined above as a reference point and you should have your inquiry answered, or problem solved, in no time!.

Puzzles can be solved with single solutions, but novices should not fear since contextual clues abound.

When all the stones on the board have been eliminated, the puzzle's solved.

If more consumers become gamers, the problem is solved.

Place the Golden Child in the "magical" garden created when you solved puzzle 9.

This problem can be solved by taping programs for later viewing after children are asleep.

According to Erikson, the socialization process of an individual consists of eight phases, each one accompanied by a "psychosocial crisis" that must be solved if the person is to manage the next and subsequent phases satisfactorily.

The more equations that are solved, the more ingrained the concept can become.

While many of these problems are solved by two-piece suits, parents and girls alike can feel uncomfortable about them.

Those who cut into the figure or bit into to it solved the mystery, but lost the ability to make the figure stretch when the gel inside escaped.

If your problem isn't solved by basic troubleshooting measures, contacting Bunn customer service is the next step you should take.

Often, a problem with a microwave oven be easily diagnosed and solved.

Fortunately, most issues with a Braun shaver are common and can be solved at home.

This can be solved by visiting local stores and viewing similar rings prior to making an online purchase.

Most of the common backpack problems can be solved or avoided with a bit of common sense and attention to the body.

Just when you think you have the puzzle solved, she'll toss in another piece.

Clues may be riddles that must be solved, map coordinates to be worked out, or simple directions that only need to be followed.

With this kind of anecdotal evidence, the question becomes whether or not the problems are actually being solved by the uniform policies.

If they are being solved, are they also causing more problems?

At the end, the mystery was solved, and the ghosts were able to RIP.

Perhaps one day, the mystery will be solved to everyone's satisfaction.

In 1975, debunker Larry Kusche published The Bermuda Triangle Mystery - Solved, where he tried to explain as many cases as possible and debunk many of [Urban Legends Hoaxes and Rumors the rumors].

In many cases, your crisis might be solved through alternative means that won't cost you any money at all.

The spoilers are often worded in teasing fashion as though they are a puzzle that must be solved.

The secret is out, the suspense is gone, the mystery solved.

The problem of matching your skin tone is solved by mixing various colors together.

Like many companies during the Depression Era, Ingersoll-Waterbury had been struggling along, barely able to make ends meet, but the Mickey Mouse wrist watch solved the firm's cash flow problems.

The many facets of autism continue to present a mystery that has only been solved in bits and pieces.

Try to get a rep to become one of your trusted contacts, thereby assuring you that any problems you develop will be the first to be solved.

Not all digestive problems can be solved through diet changes.

It is very rewarding to receive the phone calls, e-mails and letters from women who tell me that I have solved a problem they have endured for years.

She solved the trim problem by using white ribbon and a lot of sewing -- but that is a skill that not all cosplayers have to draw on.

Blogging sites have solved this scarcity of good names through the use of subdomains, but these don't really have the power of an actual full-fledged URL.

They brought problems to the forum which were quickly solved by other users, much more quickly (if not always as accurately) as a customer support desk.

Clarity of purpose is essential, though, and with that solved, putting your site on the web can be as efficient and cost effective as your company hopes to be.

If your designers are working right alongside your system administrators, odds are that communication will be good, technical difficulties will be solved more quickly, and in general your site will function more smoothly.

It's tough on these old cases, especially if it's considered solved.

This seemed to satisfy the official, who was obviously embarrassed over the entire debacle and infinitely relieved that at least half their problem was solved without any accusatory newspaper headlines.

While Fred, and to a lesser extent Cynthia, had solved cryptograms in the newspaper, neither were particularly adept at it.

Duclaux stated that the yeast question as regards low fermentation has been solved by Hansen's investigations.

The ancient geometry, as we know it, is a wonderful monument of ingenuity - a series of tours de force, in which each problem to all appearance stands alone, and, if solved, is solved by methods and principles peculiar to itself.

The problem of the curves is solved by their reduction to a problem of straight lines; and the locus of any point is determined by its distance from two given straight lines - the axes of co-ordinates.

The Chinese difficulty, so far as the mining population was concerned, was solved by the exhaustion of the extensive alluvial deposits; the miners' prejudice against the race, however, still exists, though they are no longer serious competitors, and the laws of some of the states forbid any Chinese to engage in mining without the express authority in writing of the minister of mines.

To write an account of symphonic instrumentation in any detail would be like attempting a history of emotional expression; and all that we can do here is to point out that the problem which was, so to speak, shelved by the polyphonic device of the continuo, was for a long time solved only by methods which, in any hands but those of the greatest masters, were very inartistic conventions.

The problem, however, of constructing a deep-sea cable satisfactorily, with suitable inductance coils inserted at short distances apart, is a difficult one, and one which it cannot be said has been solved.

The difficulty is solved by the provision of a complete system of minute intercellular spaces which form a continuous series of delicate canals between the cells, extending throughout the whole substance of the plant.

In 1744 Alembert applied this principle to the theory of the equilibrium and the motion of fluids (Trcite de l'equilibre et du mouvement des fluides), and all the problems before solved by geometricians became in some measure its corollaries.

In 1749 he furnished a method of applying his principles to the motion of any body of a given figure; and in 1754 he solved the problem of the precession of the equinoxes, determined its quantity and explained the phenomenon of the nutation of the earth's axis.

With the suppression and absorption of the independent principalities the problem was only half solved.

The problem of obtaining a firm footing on the Baltic coast, on which Ivan the Terrible had squandered his resources to no purpose, was now solved satisfactorily.

A condition of tenure attached to this chair was that the holder should propose mathematical questions for solution, and should resign in favour of any person who solved them better than himself; but, notwithstanding this, Roberval was able to keep the chair till his death, which occurred at Paris on the 27th of October 1675.

Roberval was one of those mathematicians who, just before the invention of the infinitesimal calculus, occupied their attention with problems which are only soluble, or can be most easily solved, by some method involving limits or infinitesimals, and in the solution of which accordingly the calculus is always now employed.

This problem of religion was solved by Amos and by the prophets who succeeded him through a more exalted conception of Yahweh and His sphere of working, which tended to detach Him from His limited realm as a national deity.

So far, however, only half the problem, and from the practical point of view the less important half, had been solved.

The problem of the profitable treatment of the sulphide ores has been practically solved here.

The country was ravaged by a monster, the Sphinx; Oedipus solved the riddle which it proposed to its victims, freed the country, and married his own mother.

Even to the present day the legend has 1 It is probable that the story of the piercing of his feet is a subsequent invention to explain the name, or is due to a false etymology (from oih&o), 01St rovs in reality meaning the "wise" (from oTSa), chiefly in reference to his having solved the riddle, the syllable - irovs having no significance.

Among the great variety of problems solved are problems leading to determinate equations of the first degree in one, two, three or four variables, to determinate quadratic equations, and to indeterminate equations of the first degree in one or more variables, which are, however, transformed into determinate equations by arbitrarily assuming a value for one of the required numbers, Diophantus being always satisfied with a rational, even if fractional, result and not requiring a solution in integers.

Often assumptions are made which lead to equations in x which cannot be solved "rationally," i.e.

Kepler's Problem, namely, that of finding the co-ordinates of a planet at a given time, which is equivalent - given the mean anomaly - to that of determining the true anomaly, was solved approximately by Kepler, and more completely by Wallis, Newton and others.

This has taken the form of inoculating the soil with the particular organism required by the particular kind of leguminous crop. To this end the endeavour has been made to produce preparations which shall contain in portable form the organisms required by the several plants, and though, as yet, it can hardly be claimed that they have been generally successful, the work done justifies hopes that the problem will eventually be solved in a practical direction.

Origen thus solved, after his own fashion, a problem which his predecessor Clement had not even ventured to grapple with.

He solved the problem in characteristic fashion.

The problem of finding a radius vector satisfying this condition is one which can be solved only by successive approximations, or tentatively.

The problem could obviously be completely solved only when the composition of the air, and the parts played by its components, had been determined.

The first question has not yet been solved, although it has been speculated upon y ?

The laws of chemical combination were solved, in a measure, by John Dalton, and the solution expressed as Dalton's " atomic theory."

As a complete fusion between dramatic and musical movement, its very crudities point to its immense advance towards the solution of the problem, propounded chaotically at the beginning of the i 7th century by Monteverde, and solved in a simple form by Gluck.

The presentation was accompanied by a kind of mathematical performance, in which Leonardo solved several hard problems proposed to him by John of Palermo, an imperial notary, whose name is met with in several documents dated between 1221 and 1240.

These problems are, however, certain to be solved in the near future, and then probably caoutchouc may be formed in other ways than from isoprene.

The general equation of degree 5 cannot be solved algebraically, but the roots can be expressed by means of elliptic modular functions.

Cubic equations having been solved, biquadratics soon followed suit.

The determination of the O's and x's is a kinematical problem, solved as yet only for a few cases, such as those discussed above.

This solved the difficulty of military service apparently, but with decisive consequences.

But the problem of the actual origin of the Berber race has not yet been solved.

The great variety of views amongst competent critics is significant of the difficulty of the problem, which can hardly be regarded as yet solved; this divergence of opinion perhaps points to the impossibility of maintaining the unity of chs.

The nature of this element is a problem which has been provisionally, but not conclusively, solved by many psychologists; the method is necessarily experimental, and all experiments on feeling are peculiarly difficult.

But their constitution is not yet solved, there even being some divergence of opinion as to their empirical formulae.

Nevertheless, many important problems relating to the distribution of magnetic induction may be solved by methods similar to those employed for the solution of analogous problems in electricity.

The beds of these rivers, as well as that of the Danube, are continually changing, forming morasses and pools, and rendering the country near their banks marshy, Notwithstanding the work already done, such as canalizing and regulating the rivers, the erection of dams, &c., the problems of preventing inundations, and of reclaiming the marshes, have not yet been satisfactorily solved.

He also showed that every equation of an even degree must have at least one real quadratic factor, reduced the solution of linear differential equations to definite integrals, and furnished an elegant method by which the linear partial differential equation of the second order might be solved.

The particular problem - a heap (hau) and its seventh makes 19 - is solved as we should now solve a simple equation; but Ahmes varies his methods in other similar problems. This discovery carries the invention of algebra back to about 1700 B.C., if not earlier.

He solved quadratic equations both geometrically and algebraically, and also equations of the form x 2 "+ax n +b=o; he also proved certain relations between the sum of the first n natural numbers, and the sums of their squares and cubes.

Cubic equations were solved geometrically by determining the intersections of conic sections.

For the ancients these questions were solved by a belief in the direct participation of the Deity in human affairs.

Concessions were made to one side and the other; and the question of the right of " protection " was solved by the Turkish government itself undertaking the duty.

However, even if this problem were solved perfectly, it doesn't really end ignorance.

Mr. O'Hara had solved the problem without going to the police.