In the country along the diagonal line.
It hadn't come from the sky but from one of the buildings across the street, diagonal to her.
Two blocks away, the patrol car struck a van backing out from its diagonal parking space in front of the toy store.
The faces of the cube are striated parallel to one diagonal, and alternate corners are sometimes replaced by faces of a tetrahedron.
Hence the product determinant has the principal diagonal elements each equal to A and the remaining elements zero.
Thus a bar of glass of sufficient thickness, placed in the diagonal position between a crossed polarizer and analyser and bent in a plane perpendicular to that of vision, exhibits two sets of coloured bands separated by a neutral line, the double refraction being positive on the dilated and negative on the compressed side.
Machines used for lifting only are not called cranes, but winches, lifts or hoists, while the term elevator or conveyor is commonly given to appliances which continuously, not in separate loads, move materials like grain or coal in a vertical, horizontal or diagonal direction.
For example, what is a safe speed at a given curve for an engine, truck or coach having the load equally distributed over the wheels may lead to either climbing or overturning if the load is shifted to a diagonal position.
The (r+ i) th number in the nth diagonal row, is n(n-}-1).
For (4) may (ï¿½ 43 (iv.)) be written (n - i) [71 = n [r] - n[r_1], and this leads to relations of the form 1 +2x+3x2+..ï¿½ i (I -x) (I +3x+6x2+Iox3+...) (30), each set of coefficients being the numbers in a downward diagonal of the table.
Diagonal bracing or strutting is nowhere to be found, and in many cases mortises and other joints are such as very materially to weaken the timbers at their points of connection.
This is an upright frame, usually made in wrought iron or steel strutted by diagonal thrust beams against the engine-house wall or other solid abutments, the height to the bearings of the guide pulleys being from 80 to 1 00 ft.
The statement that, if the adjacent sides of a rectangle are represented numerically by 3 and 4, the diagonal is represented by 5, is as much a matter of mensuration as the statement that the area is represented by 12.
The quadrilateral, for instance, consists of two triangles, and its area is the product of half the length of one diagonal by the sum of the perpendiculars drawn to this diagonal from the other two angular points.
Are called the offsets from the diagonal to the angular points.
During his second and more important journey in Central Asia (1899-1902), Sven Hedin left Charkhlik, on the edge of the Taklamakan desert, in May 1901, intending to cross Tibet in a diagonal direction to the sources of the Indus.
The diagonal telescope nn is provided with cross hairs, and is used fcr the final centring of the instrument over an object.
The mirror mm is attached to the framework pafe, the members of which are parallel to the incident and reflected rays SO, OR, and the diagonal pf is perpendicular to the mirror.
Further, at any one of the centres of load let PL represent the magnitude and direction of the gross load, and Pa, Pb the two resistances by which the piece to which that load is applied is supported; then wifl those three lines be respectively the diagonal and sides of a parallelogram; or, what is the same thing, they will be equal to the three sides of a triangleS and they must be in the same plane, although the sides of the polygon of resistances may be in different planes.
By what precedes it appears that there exists a function of the n 2 elements, linear as regards the terms of each column (or say, for shortness, linear as to each column), and such that only the sign is altered when any two columns are interchanged; these properties completely determine the function, except as to a common factor which may multiply all the terms. If, to get rid of this arbitrary common factor, we assume that the product of the elements in the dexter diagonal has the coefficient + 1, we have a complete definition of the determinant, and it is interesting to show how from these properties, assumed for the definition of the determinant, it at once appears that the determinant is a function serving for the solution of a system of linear equations.
Moreover, representing the remaining three lines by a" b" c" d" e" b /r c a, d N, e"' a " c 'N d"N err" it is further seen that the factor which multiplies the determinant formed with any two columns of the first set is the determinant of the third order formed with the complementary three columns of the second set; and it thus appears that the determinant of the fifth order is a sum of all the products of the form ' a b c" d" e" a, b"c"'dN, ear the sign being in each case such that the sign of the term .c"d"'e" obtained from the diagonal elements of the component determinants may be the actual sign of this term in the determinant of the fifth order; for the product written down the sign is obviously +.
With a biaxal plate perpendicular to the optic axis in the diagonal position, the hyperbolic brush becomes an hyperbolic line and the rings are expanded or contracted on its concave side, with a positive plate, according as the plane of the optic axes is parallel or perpendicular to the axis of the quarter-wave plate, the reverse being the case with a negative plate.
Angles formed by the lateral and median planes are the diagonal planes and in these flowers the petals which alternate with the sepals are cut by the diagonal planes.
With the exception of the top squares, every square is divided into two parts by a diagonal, the units being written on one side and the tens on the other, so that when a multiple consists of two figures they are separated by the diagonal.
Claus (Theoretische Betrachtungen and deren Anwendung zur Systematik der organischen Chemie) proposed his diagonal formula (III), and two years later, A.
Reduction to hexamethylene compounds necessitates the disruption of three of the edges of the octahedron, the diagonal linkings remaining intact, or, in the plane projection, three peripheral linkages, the hexamethylene ring assuming the form (III); In 1888 J.
Marsh also devised a form closely resembling that of Thomsen, inasmuch as the carbon atoms occupied the angles of a regular octahedron, and the diagonal linkages differed in nature from the peripheral, but differeng from Thomsen's since rupture of the diagonal and not peripheral bonds accompanied the reduction to hexamethylene.
Except that the elements of the leading diagonal are not all zero.
In the irregular crystalline aggregates branching and moss-like forms are most common, and in Transylvania thin plates or sheets with diagonal structures are found.
That the area of a parallelogram is equal to the area of a rectangle on the same base and between the same parallels, or that the volume of a cone is one-third that of a cylinder on the same base and of the same height, may be established by a proof which is admitted to be rigorous, or be accepted in good faith without proof, and yet fail to be a matter of conviction, even though there may be a clear conception of the relative lengths of the diagonal and the side of a square or of the relative contents of two vessels of different shapes.
The sum of two such lines (formed by adding together the real and the imaginary parts of two such expressions) can, of course, be expressed as a third directed line) - the diagonal of the parallelogram of which they are conterminous sides.
R represented by the diagonal OC of the parallelogram determined by OA, OB.
The intersections of the diagonal streets left a number of small, triangular parks, which, as well as the larger ones, are well shaded.
The cloth is woven "one end up and two ends down," and as there are more picks of weft per inch than ends of warp the diagonal lines pass from selvage to selvage at an angle of less than 45 degrees.
Jeanette is the converse of jean, being a twill of "two ends up to one down"; the diagonal passes from selvage to selvage at a greater angle than 45 degrees and the warp makes the wearing surface.
The diagonal line shows the average price per lb of all Indian tea sold in the London public auctions.
On stones too large for facing-plates a diagonal draft was run, so as to avoid any wind in the plane (P.T.
OA1EA2 the diagonal OET will be the ~
D, Diagonal sc, Sulcus.
The island has the form of an irregular rhomboid, the largest diagonal of which, from Torr Head in the north-east to Mizen Head in the south-west, measures 302 m.
Constructed in this way, the successive diagonal rows, commencing with the first, give the figurate numbers of the first, second, third,.
Thus if a lacquer box in the form of a parallelogram is the object, Japanese artists will not divide it in two equal parts by a perpendicular line, but by a diagonal, as offering a more pleasing line and division.
He winds it on bobbins with a rapid reciprocating motion, so as to lay the fibre in diagonal lines.
It is an advance on this when Heraclitus 2 opposes to the eyes and ears which are bad witnesses " for such as understand not their language " a common something which we would do well to follow; or again when in the incommensurability of the diagonal and side of a square the Pythagoreans stumbled upon what was clearly neither thing nor image of sense, but yet was endowed with meaning, and henceforth were increasingly at home with symbol and formula.
As a simple example, take the case of a light frame, whose bars form the slides of a rhombus ABCD with the diagonal BD, suspended from A and carrying a weight W at C; and let it be required to find the stress in BD.
Through any point 0 in this common perpendicular draw 0A1 parallel to B~C~ and OAi parallel to B2C,; make those lines pro B1 C2 portional to the angular velocities D ~ about the axes to which they are P respectively paiallel; complete the ~ B2 parallelogram OA1 EA2, and draw the diagonal OE; divide BiBf in D into C, two parts, inversely proportional to the angular velocities about the axes which they respectively adjoin; A2 through D parallel to OE draw DT.
The capsules are incised vertically, or in some districts vertical cuts with diagonal branches are made.
This begets a twisting diagonal movement of the wing on its long axis, which, but for the elasticity referred to, would break the wing into fragments.
The bracing is accomplished by the introduction at the angles of the columns and girders or beams of gusset plates or knee braces, or by diagonal straps or rods properly attached by rivet or pin connexions.
It may be added, that if the lines are converted into columns, and the columns into lines, in such a way as to leave the dexter diagonal unaltered, the value of the determinant is unaltered; the determinant is in this case said to be transposed.
A determinant is symmetrical when every two elements symmetrically situated in regard to the dexter diagonal are equal to each other; if they are equal and opposite (that is, if the sum of the two elements be = o), this relation not extending to the diagonal elements themselves, which remain arbitrary, then the determinant is skew; but if the relation does extend to the diagonal terms (that is, if these are each = o), then the determinant is skew symmetrical; thus the determinants a, h, g a, v, - µ 0, v, - h, b, f - v, h, - v, 0, g,f,c c 12, - X, o are respectively symmetrical, skew and skew symmetrical: =0; a,b,c,d a' b' c' d'a" b c d" a, b, c, d a' b' c' d'a", b N' c N' dN,, , c d The theory admits of very extensive algebraic developments, and applications in algebraical geometry and other parts of mathematics.
With a crossed polarizer and analyser the rings are interrupted by a dark hyperbolic brush that cuts the plane of the optic axes at right angles, if this plane be at 45° to the planes of polarization and analysation - the so-called diagonal position - and that becomes a rectangular cross with its arms parallel and perpendicular to the plane of the optic axes when this plane coincides with the plane of primitive or final polarization - the normal position.
The leading member of the determinant is alla22a33ï¿½ï¿½ï¿½ann, and corresponds to the principal diagonal of the matrix.
We may therefore form an orthogonal transformation in association with every skew determinant which has its leading diagonal elements unity, for the Zn(n-I) quantities b are clearly arbitrary.
The pillars are strengthened against lateral yielding by horizontal and diagonal bracing.
The diagonal AD of the parallelogram, of which AB and AC are adjacent sides, will represent, both in direction and magnitude, the motion of the rain as apparent to the observer.
The distance between joists should be limited to 5 or 6 ft.; horizontal bracing by means of diagonal rods is sometimes used, but should be avoided.
In compression boom, 7 o tons in tension boom, 5 o tons in vertical struts, 6.5 tons in diagonal ties, 8 o tons in wind bracing, and 6.5 tons in cross and rail girders.
The fan has eight arms, framed together of wrought iron bars, with diagonal struts, so as to obtain rigidity with comparative lightness, carrying flat close-boarded blades at their extremities.