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.
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.
R represented by the diagonal OC of the parallelogram determined by OA, OB.
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.
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.
The mechanical idea, named the parallelogram of velocities, permits a ready and easy graphical representation of these facts.
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.
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.
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.
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.
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.
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.
M., and forms a parallelogram 45 m.
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.
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.
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.
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.
VC, VW = (i - 0 2) VC; curved area ACB = a of parallelogram Afgb = 3kl.
Then the section of the pyramid by this plane is the parallelogram Pqrs.
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.
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.
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.
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.
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.
Complete the parallelogram ~
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.
Sylvester discovered that this property of the parallelogram is not confined to points lying in one line with the fixed point.