(iv) Parallelogram: two opposite sides a and a, distance between them h.
It is in shape an irregular parallelogram, divided into two nearly equal parts by the range of the Eastern Ghats, which intersects it throughout its entire length.
The fundamental postulate of this part of our subject is that the two forces acting on a particle may be compounded by the parallelogram rule.
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.
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.
Then the section of the pyramid by this plane is the parallelogram Pqrs.
The mechanical idea, named the parallelogram of velocities, permits a ready and easy graphical representation of these facts.
This is the process adopted, for instance, for comparison of the area of a parallelogram with that of a rectangle on the same base and of the same height.
The site of the lake dwelling of Wangen, in the Untersee, Lake of Constance, forms a parallelogram more than 700 paces in length by about 120 paces in breadth.
Corner of this oblong is an elevated platform in the form of a rectangular parallelogram, some 600 yds.
The general ground-plan is a parallelogram, with irregular outlines, one side overlooking the Tweed; and the style is mainly the Scottish Baronial.
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.
On the whole, the form of a parallelogram with its longest sides in the proportion of about five to three of the shorter, and running east and west, may be considered the best form, since it affords a greater extent of south wall than any other.
Some very pleasing examples are to be met with which have the form of a parallelogram with a lightly rounded roof; others of appropriate character are square or nearly so, with a ridge-and-furrow roof.
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.
Back, showing graduations, parallelogram for measuring heights; and other tables, together with the Rule with sights (A) held by a moveable pin (B), known as the Horse or Wedge.
(4) A parallel projection of a pair of equal and parallel straight lines, or plain surfaces, is a pair of equal and parallel straight lines, or plane surfaces; whence it follows (5) That a parallel projection of a parallelogram is a parallelogram, and (6) That a parallel projection of a parallelepiped is a parallelepiped.
Curve to a scale enlarged in the ratio ab: ac. This property of the parallelogram is utilized in the construction of the pantograph, an instrument used for obtaining a copy of a map or drawing on a different scale.
The former, situated on the top of the hill, is of comparatively small extent, and forms almost a parallelogram, surrounded by ramparts of the 13th century, and, outside them, by boulevards, and entered by ancient gateways.
His map formed a parallelogram measuring 75,800 stadia from Usisama (Ushant island) or Sacrum Promontorium in the west to the mouth of the Ganges and the land of the Coniaci (Comorin) in the east, and 46,000 stadia from Thule in the north to the supposed southern limit of Libya.
A new order of battle was adopted - the troops being massed in crescent formation, with a reserve in the shape of a parallelogram ready to strengthen the weakest point.
Of temperature (o' - o") is small, the figure ABCD may be regarded as a parallelogram, and its area W as equal to the rectangle BE XEC. This is accurately true in the limit when (0' - 0") is infinitesimal, but in practice it is necessary to measure specific heats, &c., over finite ranges of temperature, and the error involved is generally negligible if the range does not exceed a few degrees.
(of which 227 are water) - forms a parallelogram of 130 m.
In E'; the case of a parallelogram, the equivalent right,, trapezium is a rectangle; in the case of a triangle, Al it is a right-angled triangle.
R represented by the diagonal OC of the parallelogram determined by OA, OB.
Complete the parallelogram ~
M., and have a great variety of forms: parallel walls, circles, semicircles, a parallelogram, an octagon, &c. About 10 m.
On the opposite side of the Vyver lies the parallelogram formed by the fine houses and magnificent avenue of trees of the Lange Voorhout, the Kneuterdyk and the Vyverburg, representing the fashionable kernel of the city.
Thus the C.P. of a rectangle or parallelogram with a side in the surface is at a of the depth of the lower side; of a triangle with a vertex in the surface and base horizontal is 4 of the depth of the base; but if the base is in the surface, the C.P. is at half the depth of the vertex; as on the faces of a tetrahedron, with one edge in the surface.
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.
Thus a fdrce can be uniquely resolved into two components acting in two assigned directions in the same plane with it by an inversion of the parallelogram construction of fig.
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.
Sylvester discovered that this property of the parallelogram is not confined to points lying in one line with the fixed point.
The combination of the parallelogram with a straight-line motion, for guiding one of the points in a straight line, is illustrated in Watts parallel motion for steam-engines.
In shape the country resembles a roughly drawn parallelogram, with its greatest length (362 m.) from N.
The town, in the shape of a rectangular parallelogram, with the corners pointing approximately toward the cardinal points of the compass, covered 741 acres of ground.
The C.P. of water lines passing through a fixed point lies on a straight line, the antipolar of the point; and thus the core of a triangle is a similar triangle of one quarter the size, and the core of a parallelogram is another parallelogram, the diagonals of which are the middle third of the median lines.
In one of his early investigations he gave an ingenious though indirect demonstration of the problem of the parallelogram of forces.
M., and forms a parallelogram 45 m.
VC, VW = (i - 0 2) VC; curved area ACB = a of parallelogram Afgb = 3kl.
It was a parallelogram 70 ft.
For the condition of equilibrium of forces not parallel is that they shall be represented in direction and magnitude by the sides and diagonals of certain parallelograms, and of parallel forces that they shall divide certain straight lines in certain ratios; and the parallel projection of a parallelogram is a parallelogram, and that of a straight line divided in a given ratio is a straight line divided in the same ratio.
They form a parallelogram 596 yds.
Vc; parallelogram Ahjb = Kl.