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.
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.
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.
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.
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 +.
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.
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.
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.
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.
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.
The intersections of the diagonal streets left a number of small, triangular parks, which, as well as the larger ones, are well shaded.
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.
Claus (Theoretische Betrachtungen and deren Anwendung zur Systematik der organischen Chemie) proposed his diagonal formula (III), and two years later, A.
The leading member of the determinant is alla22a33ï¿½ï¿½ï¿½ann, and corresponds to the principal diagonal of the matrix.
Except that the elements of the leading diagonal are not all zero.
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 (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.
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.
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.
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.
3) so as to form a diagonal AE, and that the whole of the figure lies between A N P Q, E lines through A and E at right angles to AE.
Are called the offsets from the diagonal to the angular points.
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.
He winds it on bobbins with a rapid reciprocating motion, so as to lay the fibre in diagonal lines.
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.
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.
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.
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.
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 capsules are incised vertically, or in some districts vertical cuts with diagonal branches are made.
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.
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.
On stones too large for facing-plates a diagonal draft was run, so as to avoid any wind in the plane (P.T.
The diagonal telescope nn is provided with cross hairs, and is used fcr the final centring of the instrument over an object.
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.