It will be noticed that under the old system the queens could never meet each other, for they operated on diagonals of different colours.
Arrangements connected with Claus' formula are obtained by placing six tetrahedra on the six triangles formed by the diagonals of a plane hexagon.
I); a plane projection gives a hexagon withdiagonals (II).
Squares that have many more summations than in rows, columns and diagonals were investigated by A.
The diagonals of cells which follow each other passing once only through each zone and section, form similar and equal closed curves passing once quite round the circular axis of the ring and once quite round the centre of the ring.
The diagonals of the square are the two equatorial axes.
In the Quadrilonchida it becomes a square double pyramid, the two equatorial axes of which (or the diagonals of the square) are constantly longer than all other axes.
A quadrilateral, one of whose diagonals is an axis of symmetry.
The sides and thediagonals of the Square do not symmetrically represent degrees of incompatibility, or opposition in the ordinary sense.
Sidenote: Full Vertical Surface Enrichment] Inceptive Axes: Diameters or diagonalsof the area.
These diagonalsand center lines are the building lines or leading axes of the pattern.
The diagonals of each quarter should be drawn before proceeding with the details of the design.
For making diagonals the warp is divided into four sheds; the uppermost one of these is provided with a shed-rod, the others are supplied with healds.
Dishonour not your Mothers: now attest, That those whom you call'd Fathers, did beget you.
The stresses in the flanges were taken out, as shown in the figure, keeping separate those caused by diagonals inclined to the left from those caused by diagonals inclined to the right.
Stress caused by diagonals Length of ver- Depth of parallel | | leaning to right.
Thus the horizontal component of the stress in D= | Stress caused bydiagonals Length of right Depth of parallel | | leaning to left.
In the same way the horizontal and vertical components of the stresses in each of the other bays of the flanges of the bowstring were found; and the stresses in the verticals and diagonals were found by addition, subtraction, and reduction.
That every one of the diagonals is subjected to compression at some point or other in the passage of the live load over the bridge, c.
That the maximum horizontal component of the stresses in each of the diagonals is a constant quantity, not only for tension and compression, but for all the diagonals.
This is crossed by a series of diagonals sloping downward to the right, with a little solid filling triangle in the acute angle made by the diagonal with the border of the band.
Of course, some of the very sharp boys who read this will at once exclaim, "Why, they are the only diagonals a square can have, for a rectangular figure can only have two diagonals.
Similarly, to say that five diagonals make exactly seven sides does not involve an error of the 84th part of the diagonal.
The earth has passed through thediagonals of these three parallelograms, in the space of three months, and has performed one quarter of a circle; and on the same principle it will go on till it has completed the whole of the circle.
What portion of a year is represented by the three diagonals in the figure?
The pyramid of Illahoun, like the northern pyramid of Dashour and others, is built of brick; its masonry was additionally strengthened by walls of stone, the thickest being upon the diagonals of the plan.
The diagonals of these different terraces were not directly above one another, the steps being 9 m.
The Square, the Oblong, and their Diagonals 125 LXXV.
It will also intersect the two diagonals at the four points o (Fig.
Draw diagonals BD and AC, and produce the latter till it cuts the horizon in G.
In this figure I have first drawn the pavement by means of the diagonals GA, Go, Go, &c.
To draw the smaller square K we simply draw a smaller parallel square h h h h, and within that, guided by the intersections of the diagonals therewith, we obtain the four points through which to draw square K.
From A measure off on the base line the divisions required, say five of 1 foot each; from each division draw diagonals to point of distance D, and where these intersect the line AC the corresponding divisions will be found.
How to Draw Lines which shall Meet at a Distant Point, by Means of Diagonals 121 LXXI.
The two fives are marked or scored separately, and the diagonals thus form a series of alternations, which, when repeated, form a scale of ten, the tally of the coalwhippers.
The notched ends of the diagonals should be lashed with thread to keep them from splitting.
Next determine and mark on each spar except the diagonals the places where other spars cross it.
The colors of the squares and diagonals in combination with those of the fields, run in the order that is so natural to us all, viz.
So Jim ranged at large indiagonals having a good time, while the man enjoyed himself by watching the animal.
In Sketch C diagonals are drawn and pathways sent along them to the center.
Connect the ends of the diagonals to get a square.
A square is said to be on its diameters when one of its diameters is vertical and the other horizontal; it is said to be on its diagonals when the diagonals are in this position.
To draw a square in the position of Sketch C, use your test square, and draw the diagonals first, dividing them into inch spaces.
In the plan for the border design in Sketch C, connect the outer points on the diagonals to form the space for a border decoration.
They have also provided an impost for the diagonals which are themselves of the broken type, and in fact the form of the vaults is practically perfected except in the matter of the transverse arches.
In fact, judging from the awkward manner in which the diagonals rise from their [Illustration: FIG.
As in Lombardy, the crown is highly domed up while to facilitate the construction of the web of the vault with the least possible centering, pointed diagonals and enclosing arches are employed.
The form of the diagonals is in any case displeasing, as they spring from the shafts at an awkward angle and, furthermore, render the thrusts of the vault excessive.
Wall ribs were, for example, omitted, and the diagonals were made of segmental section, thus rendering unnecessarily severe the thrusts of the vaults.
The diagonals of many vaults in France and Spain and especially in England had been decorated with carving, particularly in the early Gothic period.
Every turning must be made on a star, and the lines must be parallel to the sides and diagonals of the square, as shown.
For example, you would find little difficulty in merely placing a different number in each of the nine cells in the illustration so that the rows, columns, and diagonals shall all add up 15.
The second example is a Semi-Nasik, which has the additional property that the opposite short diagonals of two cells each together sum to 34.
Nearly everybody knows that a "magic square" is an arrangement of numbers in the form of a square so that every row, every column, and each of the two long diagonals adds up alike.
And it is well here to state that when we speak of "diagonals" in connection with the chessboard, we do not limit ourselves to the two long diagonals from corner to corner, but include all the shorter lines that are parallel to these.
You must so arrange yourselves in the sixteen cells that the numbers on your backs shall form a magic square in which every column, every row, and each of the two diagonals shall add up the same.
Now, the puzzle is to cut these strips into the fewest possible pieces so that they may be placed together and form a magic square, the seven rows, seven columns, and two diagonals adding up the same number.
I shall give the best answer that I have been able to obtain, in which there is a slight error in the diagonals alone.
While waiting for a train we noticed that the hands of the clock were pointing in opposite directions, and were parallel to one of the diagonals of the wall.
Note "row of four cards," so that the only diagonals we have here to consider are the two long ones.
We are not here considering the diagonals at all, and every different six squares occupied makes a different solution, so we have not to exclude reversals or reflections.
Note that in every one of the sixteen smaller squares the two diagonals sum to 65.
Draw, in each half of the square, the diagonals E F, G H.
For tenths of inches there would require to be but six horizontal lines, the diagonals being drawn as before.
Draw also the diagonal lines A 1, a 2, B 3, and so on; then the distances from the line A C to the points of intersection of the diagonals with the horizontal lines represent hundredths of an inch.
When the diagonals are exactly alike the corners will also be right angles.
Before nailing on the back test the squareness of the frame in this way (unless your eye is very accurate; even then it is a good thing to get in the habit of measuring exactly): measure the diagonals from the opposite corner.
The Bishop can operate along either of the diagonals of which the square on which he is standing forms part.
Two Bishops are, generally speaking, of greater value than two Knights, because together they also act on all the squares, and their command of long diagonals is a clear advantage.
Black has succeeded in eliminating the White centre pawn, and sweeps long diagonals with his Bishops, but the advantage cannot be maintained.
White has open files and diagonals for all his forces, whilst Black's pieces are immobilised.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "diagonals" in a variety of sentences. We hope that you will now be able to make sentences using this word.
