## Equations Sentence Examples

- The
**equations**to the asymptotes are = t y/b and x = =y respectively. - 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. - But the bulk of the work consists of problems leading to indeterminate
**equations**of the second degree, and these universally take the form that one or two (and never more) linear or quadratic functions of one variable x are to be made rational square numbers by finding a suitable value for x. - A few problems lead to indeterminate
**equations**of the third and fourth degrees, an easy indeterminate equation of the sixth degree being also found. - Often assumptions are made which lead to
**equations**in x which cannot be solved "rationally," i.e. - Laplace (1801); Traite analytique des courbes et des surfaces du second degre (1802); Recherches sur l'integration des
**equations**differentielles partielles et sur les vibrations des surfaces (1803); Traite de physique (1816); Recueil d'observations geodesiques, astronomiques et physiques executees en Espagne et Ecosse, with Arago (1821); Memoire sur la vraie constitution de l'atmosphere terrestre (1841); Traite elementaire d'astronomie physique (1805); Recherches sur plusieurs points de l'astronomie egyptienne (1823); Recherches sur l'ancienne astronomic chinoise (1840); Etudes sur l'astronomie indienne et sur l'astronomie chinoise (1862); Essai sur l'histoire generale des sciences pendant la Revolution (1803); Discours sur Montaigne (1812); Lettres sur l'approvisionnement de Paris et sur le commerce des grains (1835); Mélanges scientifiques et litteraires (1858). - Since the distance of a body from the observer cannot be observed directly, but only the right ascension and declination, calling these a and 6 we conceive ideal
**equations**of the form a = f (a, b, c, e, f, g, t) and 5=0 (a, b, c, e, f, g, t), the symbols a, b,. - If the values ofa and 6, defining the position of the body on the celestial sphere, are observed at three different times, we may conceive six
**equations**like the above, one for each of the three observed values of a and S. - Then by solving these
**equations**, regarding the six elements as unknown quantities, the values of the latter may be computed. - For Tartaglia's discovery of the solution of cubic
**equations**, and his contests with Antonio Marie Floridas, see Algebra (History). - His largest work,Trattato generale di numeri e misure, is a comprehensive mathematical treatise, including arithmetic, geometry, mensuration, and algebra as far as quadratic
**equations**(Venice, 1556, 1560). - This section treats of such subjects as nomenclature, formulae, chemical
**equations**, chemical change and similar subjects. - We cannot deal with
**equations**that big—but a computer will solve for that in a minute if it has enough data. - Why, I can do long, complicated quadratic
**equations**in my head quite easily, and it is great fun! - Only then, expressing known historic facts by
**equations**and comparing the relative significance of this factor, can we hope to define the unknown. - And by bringing variously selected historic units (battles, campaigns, periods of war) into such
**equations**, a series of numbers could be obtained in which certain laws should exist and might be discovered.