## Linear Sentence Examples

- Is a large tree remarkable for the variability in the shape of its leaves, which are
**linear**in young trees and vigorous shoots, and broad and ovate on older branches. - In Crete, had given way entirely to a
**linear**system by Period III. - Hence it is impossible to form a satisfactory
**linear**series. - For the few cases where data are available - data, however, belonging to engines representing standard practice in their construction and in the design of cylinders and steam ports and passages - the law connecting p and v is approximately
**linear**and of the form p=c - bv (28) where b and c are constants. - There is evidence that the use in Crete of both
**linear**and pictorial signs existed in the Early Minoan period, contemporary with the first Egyptian dynasties. - A theory of matrices has been constructed by Cayley in connexion particularly with the theory of
**linear**transformation. - Simspon concluded that for a given wind velocity dissipation is practically a
**linear**function of ionization. - The metasternum is without the transverse
**linear**impression that is found in most families of Adephaga. - Schlafli 1 this equation may be directly formed and exhibited as the resultant of two given equations, and an arbitrary
**linear**non-homogeneous equation in two variables. - Serratifolia, having
**linear-lanceolate**sharply serrulate leaves, and B. - Explorations carried out by him in Crete from 1894 onwards, for the purpose of investigating the prehistoric civilization of the island, fully corroborated this belief, and showed that a
**linear**as well as a semi-pictorial form of writing was diffused in the island at a very early period (" Cretan Pictographs and PraePhoenician Script," Journ. - In 1895 he obtained a libation-table from the Dictaean cave with a
**linear**dedication in the prehistoric writing (" Further Discoveries," &c., J.H.S. - Foot narrow; dorsal papillae
**linear**or fusiform, in several - series. - This is equally true both of the pictographic and the
**linear**Aegean systems. Its nearest affinities are with the "Asianic" scripts, preserved to us by Hittite, Cypriote and south-west Anatolian (Pamphylian, Lycian and Carian) inscriptions. - The regions of this cuticle have a markedly segmental arrangement, and the definite hardened pieces (sclerites) of the exoskeleton are in close contact with one another along
**linear**sutures, or are united by regions of the cuticle which are less chitinous and more membranous, so as to permit freedom of movement. - Peirce, "Mathematics is the science which draws necessary conclusions" (
**Linear**Associative Algebra, § i. - Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "
**Linear**Substitutions," with the topics determinants, &c.,**linear**substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers. - Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "
**Linear**Substitutions," with the topics determinants, &c.,**linear**substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers. - Organization and tactics did not affect the issue directly, for the conduct of the men and their junior officers gave abundant proof that in the hands of a competent leader the "
**linear**" principle of delivering one shattering blow would have proved superior to that of a gradual attrition of the enemy here, as on the battlefields of the Peninsula and at Waterloo, and this in spite of other defects in the training of the Prussian infantry which simultaneously caused its defeat on the neighbouring field of Auerstadt. - Arithmetical groups, connected with the theory of quadratic forms and other branches of the theory of numbers, which are termed "discontinuous," and infinite groups connected with differential forms and equations, came into existence, and also particular
**linear**and higher transformations connected with analysis and geometry. **Linear**Equations.-It is of importance to study the application of the theory of determinants to the solution of a system of**linear**equations.**Linear**Equations.-It is of importance to study the application of the theory of determinants to the solution of a system of**linear**equations.- For further information concerning the compatibility and independence of a system of
**linear**equations, see Gordon, Vorlesungen fiber Invariantentheorie, Bd. - Resultant Expressible as a Determinant.-From the theory of
**linear**equations it can be gathered that the condition that p**linear**equations in p variables (homogeneous and independent) may be simultaneously satisfied is expressible as a determinant, viz. - Assuming then 01 to have the coefficients B1, B2,...B,, and f l the coefficients A 1, A21...A,n, we may equate coefficients of like powers of x in the identity, and obtain m+n homogeneous
**linear**equations satisfied by the m+n quantities B1, 2, ...B n, A 1, A 2, ...A m. - He first divides by the factor x -x', reducing it to the degree m - I in both x and x' where m>n; he then forms m equations by equating to zero the coefficients of the various powers of x'; these equations involve the m powers xo, x, - of x, and regarding these as the unknowns of a system of
**linear**equations the resultant is reached in the form of a determinant of order m. - ï¿½ ï¿½ P1 v2 v3...) ï¿½ For, writing as before, Xm 'Xm 2 Xm '= zzo(SQls:2s73...) xi'x12x13..., 1 2 3" 1231 2 3 = EPxi l x A2 x A3, P is a
**linear**function of separations of(/ 1 / 2 A2 / 4 3 3 ...) of specification (m"`1mï¿½2m"`3...), and if X; 1 X 3 2X8 3 ' .. - = ?P'xilx12xi 3 P' is a
**linear**1231 2312 ??? - The law of reciprocity shows that p(s) = zti (m 1te2tmtL3t) t=1 st It 2t 3t viz.: a
**linear**function of symmetric functions symbolized by the k specifications; and that () St =ti ts. - A table may be formed expressing the k expressions Pa l), P(2),...P(1) as
**linear**functions of the k expressions (m"`'smï¿½2smï¿½3s...), s =1, 2, ...k, and the numbers BSc occurring therein is 2s 3s possess row and column symmetry. - By solving k
**linear**equations we similarly express the latter functions as**linear**functions of the former, and this table will also be symmetrical. - From the above D p4 is an operator of order pq, but it is convenient for some purposes to obtain its expression in the form of a number of terms, each of which denotes pq successive
**linear**operations: to accomplish this write d ars and note the general result exp (mlodlo+moldol +... - The adjoint determinant will be seen subsequently to present itself in the theory of
**linear**equations and in the theory of**linear**transformation. - Thus to obtain the resultant of aox 3 +a i x 2 +a 2 x+a 3, 4, =box2+bix+b2 we assume the identity (Box+Bi)(aox 3 +aix 2 +a2x+a3) = (Aox 2 +Aix+ A 2) (box2+bix+b2), and derive the
**linear**equations Boa ° - Ac b o = 0, Boa t +B i ao - A 0 b 1 - A 1 bo =0, Boa t +B 1 a 1 - A0b2 - A1b1-A2b° = 0, Boa3+Bla2 - A l b 2 -A 2 b 1 =0, B 1 a 3 - A 2 b 2 =0, = = (y l, y2,...ynl `x1, x2,...xnl for brevity. - Di denotes, in fact, an operator of order s, but we may transform the right-hand side so that we are only concerned with the successive performance of
**linear**operations. - An important notion in the theory of
**linear**operators in general is that of MacMahon's multilinear operator (" Theory of a Multilinear partial Differential Operator with Applications to the Theories of Invariants and Reciprocants," Proc. Lond. - ALGEBRAIC FORMS. The subject-matter of algebraic forms is to a large extent connected with the
**linear**transformation of algebraical polynomials which involve two or more variables. - The present article is merely concerned with algebraical
**linear**transformation. - Equally exaggerated are the statements as to the
**linear**and lateral extent of the catacombs, and their intercommunication with one another. - Formerly map makers contented themselves with placing upon their maps a
**linear**scale of miles, deduced from the central meridian or the equator. - The
**linear**scale of maps can obviously be used only in the case of maps covering a small area, for in the case of maps of greater extension measurements would be vitiated owing to the distortion or exaggeration inherent in all projections, not to mention the expansion or shrinking of the paper in the process of printing. - Two cases then arise: (I) the properties may be expressed as
**linear**functions of the composition, the terminal values being identical with those obtained for the individual components, and there being a break in the curve corresponding to the absence of mixed crystals; or (2) similar to (I) except that different values must be assigned to the terminal values in order to preserve collinearity.