# Solving Sentence Examples

- I don't care about
**solving**cases. - I want to be able to focus on
**solving**this problem, not worrying about what might be said or done to you. - The method of
**solving**equations geometrically was considerably developed by Omar Khayyam of Khorassan, who flourished in the 1 r th century. **Solving**a current murder was difficult enough—a forty-year-old case was near impossible.- In pure algebra Descartes expounded and illustrated the general methods of
**solving**equations up to those of the fourth degree (and believed that his method could go beyond), stated the law which connects the positive and negative roots of an equation with the changes of sign in the consecutive terms, and introduced the method of indeterminate coefficients for the solution of equations.' - But such a hypothetical simplicity is the necessary step for
**solving**the more complex problems of nature. - Yet by his very mode of
**solving**the problem he is led on to consider the nature of the world-process. - During the first years of the French Revolution Catherine's sympathy with philosophic liberalism rapidly evaporated, and the European sovereigns to the democratic movement; but she carefully abstained from joining the Coalition, and waited patiently for the moment when the complications in western Europe would give her an opportunity of
**solving**independently the Eastern Question in accordance with Russian interests. - Then by
**solving**these equations, regarding the six elements as unknown quantities, the values of the latter may be computed. - Another civic improvement was the plan that a permanent committee of citizens should be engaged in the
**solving**of the housing problem, and that the chamber of commerce, cooperating with the state, should employ a director in charge of the Americanization programme in which the public schools and corporations cooperate. - When, therefore, the latter, on the 22nd, marched southward to reopen his communications by the defeat of the enemy's army, always the surest means of
**solving**this difficulty, he actually reached the neighbourhood of Eckmuhl with a sufficient numerical superiority had he only been prompt enough to seize his opportunity. - The methods which Leonardo made use of in
**solving**those problems fill the Liber quadratorum, the Flos, and a Letter to Magister Theodore. - = 0, we find that, eliminating x, the resultant is a homogeneous function of y and z of degree mn; equating this to zero and
**solving**for the ratio of y to z we obtain mn solutions; if values of y and z, given by any solution, be substituted in each of the two equations, they will possess a common factor which gives a value of x which, corn bined with the chosen values of y and z, yields a system of values which satisfies both equations. - By
**solving**k linear equations we similarly express the latter functions as linear functions of the former, and this table will also be symmetrical. - By
**solving**the equations of transformation we obtain rE1 = a22x1 - a12x1, r = - a21x1 + allx2, aua12 where r = I = anon-anon; a21 a22 r is termed the determinant of substitution or modulus of transformation; we assure x 1, x 2 to be independents, so that r must differ from zero. - Hence,
**solving**the cubic, R 2 j = (S -m i a) (S - m 2 a) (S - m3a) wherein m 1 m2, m 3 are invariants. **Solving**the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The Jacobian Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.- The difficulties in the way of
**solving**it are very great, and up to the present time the best authorities are not agreed as to the result, the effect of half a century of research having been merely to reduce the uncertainty within continually narrower limits. - In algebra he discovered the method of approximating to the real roots of an equation by means of continued fractions, and imagined a general process of
**solving**algebraical equations of every degree. - (iii.) In
**solving**a quadratic equation by the method of ï¿½ 38 (viii.) we may be led to a result which is apparently absurd. - This author questioned the possibility of
**solving**cubics by pure algebra, and biquadratics by geometry. - His first contention was not disproved until the 15th century, but his second was disposed of by Abul Wefa (940-998), who succeeded in
**solving**the forms x 4 =a and x4-%ax3=b. - Although the foundations of the geometrical resolution of cubic equations are to be ascribed to the Greeks (for Eutocius assigns to Menaechmus two methods of
**solving**the equation x 3 = a and x 3 = 2a 3), yet the subsequent development by the Arabs must be regarded as one of their most important achievements. - The Greeks had succeeded in
**solving**an isolated example; the Arabs accomplished the general solution of numerical equations. - This contest over, Tartalea redoubled his attempts to generalize his methods, and by 1541 he possessed the means for
**solving**any form of cubic equation. - Cardan or Cardano, who was at that time writing his great work, the Ars Magna, could not restrain the temptation of crowning his treatise with such important discoveries, and in 1 545 he broke his oath and gave to the world Tartalea's rules for
**solving**cubic equations. - He improved the methods for
**solving**equations, and devised geometrical constructions with the aid of the conic sections. - During the late summer the authorities in Vienna and Budapest keenly debated rival plans for
**solving**the southern Slav question - in every case, however, in accordance with Austrian or Hungarian rather than Yugoslav interests. - Another important conception connected with the preceding is the infinity of philosophy, which arises out of history and is as it were a reflection from history, varying at every moment and always
**solving**a problem by placing alongside its solution the premise of a new history and therefore of a new problem and a new philosophy. - That Roger Bacon was acquainted with the principle of the camera obscura is shown by his attempt at
**solving**Aristotle's problem stated above, in the treatise De Speculis, and also from his references to Alhazen's experiments of the same kind, but although Dr John Freind, in his History of Physick, has given him the credit of the invention on the strength of a passage in the Perspectiva, there is nothing to show that he constructed any instrument of the kind. - His first notable work was a proof of the impossibility of
**solving**the quintic equation by radicals. - Instead of discoursing on the corporate conscience of the state and the endowments of the Church, the importance of Christian education, and the theological unfitness of the Jews to sit in parliament, he is
**solving**business-like problems about foreign tariffs and the exportation of machinery; waxing eloquent over the regulation of railways, and a graduated tax on corn; subtle on the monetary merits of half-farthings, and great in the mysterious lore of quassia and cocculus indicus. - Putting the values of F in (1) and
**solving**for f max ., we get for the breaking stress of a bar subjected to repetition of varying stress, f max. - By a far-reaching policy an attempt has been made towards
**solving**the housing problem. - New and unheard-of orders of amphibians, reptiles and mammals came to the surface of knowledge, revolutionizing thought, demonstrating the evolution theory, and
**solving**some of the most important problems of descent. - Mainly in view of the condition of things in Belgium, for
**solving**the social question on Christian lines. - It will probably be sufficient to indicate the problem as conceived by Hume, and the relation of the method he adopts for
**solving**it to the fundamental doctrine of his theory of knowledge. **Solving**that the sunset of his life should be even more splendid than its dawn he decided to go on crusade, and in 1189 he started with a great army for the Holy Land.- Of writing a letter or a report on a particular subject with a particular object in view, of translating from or into a foreign language, of
**solving**a mathematical problem, of criticizing a passage from a literary work, of writing an essay on an historical or literary subject with the aid of books in a library, of diagnosing the malady of a patient, of analysing a chemical mixture or compound; and (the highest form under the rubric) of making an original contribution to learning or science as the result of personal investigation or experiment. - It was in the pressing to its extreme consequences of the conception of uncompromising identity which is to be found in Leibnitz, that the contradictions took their rise which Herbart aimed at
**solving**, by the method of relations and his doctrine of the ultimate plurality of " reals," The logic of relations between conceptual units, themselves unaltered by the relation, seems a kind of reflection of his metaphysical method. - Doubt as to the use of the higher efforts, or as to the possibility of
**solving**the great mysteries of life. - General conventions, to which most of the European states are parties, were signed in 1883 at Paris for the protection of industrial, and in 1886 at Bern for the protection of literary and artistic, property, and, from 1899 onwards, a series of general treaties, to none of which is Great Britain a party, have been signed at the Hague, as the result of conferences, invited by the government of the Netherlands, for
**solving**some of the more pressing questions arising out of " the conflict of laws." - Stearn in England, succeeded in completely
**solving**the practical problems. From and after that date incandescent electric lighting became commercially possible, and was brought to public notice chiefly by an electrical exhibition held at the Crystal Palace, near London, in 1882. - 12 in the Metropolitan Museum of New York, remains the largest series of Cypriote antiquities in the world, the accounts which have been given of its origin are so inadequate, and have provoked so much controversy, 13 that its scientific value is small, and a large part of subsequent excavation has necessarily been directed to
**solving**the problems suggested by its practically isolated specimens. - The king himself perceived in the compromise a means of
**solving**the conflicting questions, and warmly approved it. - Johnson, Anthony,
**Solving**Stonehenge: The New Key to an Ancient Enigma. - This man was born of a Saivite family about 1825, but in early manhood grew dissatisfied with idolworship. He undertook many pilgrimages and studied the Vedic philosophy in the hope of
**solving**the old problem of the Buddha, - how to alleviate human misery and attain final liberation. - In determining the dimensions of corresponding drums of cone pulleys it is evident that for a crossed belt the sum of the radii of each pair remains a constant, since the angle a is constant, while for an open belt a is variable and the values of the radii are then obtained by
**solving**the equations r 1 = l/ir - c(a sin a + cos a) + 2c sin a, r 2 = l/7r - c(a sin a +cos_a) - lc sin a. - His life was one of incessant eager questioning of nature on all sides, and his many and varied works all bear the stamp of a fresh and original genius, capable of stating and
**solving**problems in all departments of science - at one time finding the true explanation of "ducks and drakes" (formerly attributed to the elasticity of water) and at another helping to lay the foundations of our modern vulcanology and meteorology. - In this position he acquired a wide knowledge of Chinese religion and civilization, and especially of their mathematics, so that he was able to show that Sir George Homer's method (1819) of
**solving**equations of all orders had been known to the Chinese mathematicians of the 14th century. - This way of
**solving**, or passing over, the ultimate problems of thought has had many followers in cultured circles imbued with the new physical science of the day, and with disgust for the dogmatic creeds of contemporary orthodoxy; and its outspoken and even aggressive vindication by physicists of the eminence of Huxley had a potent influence upon the attitude taken towards metaphysics, and upon the form which subsequent Christian apologetics adopted. - Analytically the elements are determined from these data by
**solving**the four equations just given, regarding a, b, c and d as unknown quantities, and x, y, x', y' and t as given quantities. **Solving**for cot e i we obtain 2 cot 2 i= (p 2 -1) 2 {(p2 - tan2 (7r - A)/4) {p - cot2 - A)/411, and since tan { (ir - A)/4-} is less than unity, p must exceed cot {Or - A)/41 if cot 2 i is to be real.- The Internet is not unique in
**solving**for this access to information. - He was himself always occupied: writing his memoirs,
**solving**problems in higher mathematics, turning snuffboxes on a lathe, working in the garden, or superintending the building that was always going on at his estate. - She sat awhile, wondering what the meaning of it all having happened before could be, and without
**solving**this problem, or at all regretting not having done so, she again passed in fancy to the time when she was with him and he was looking at her with a lover's eyes. - She added, "Leland Anderson's wife Marian says you're a schmuck for not
**solving**the Byrne thing and causing her to lose her bet." - Catherine had conceived an ambitious plan of
**solving**radically the Eastern Question by partitioning Turkey as she and her allies had partitioned Poland, and she had persuaded the emperor Joseph II.