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triangle

She stopped in front of a small mural depicting a triangle with a form at each of the points.

Surprisingly, Fred O'Connor, arch fan of any hint of mystery, remained uninterested in the Donald Ryland-Edith Shipton-Jerome Shipton triangle.

His shoulders and hips formed a triangle that rippled with movement.

the order in which they occur in the triangle) round a circle.

One of these areas is defined by the three fortresses, La Fre, Laon and Reims, the other by the triangle, LangresDijonBesancon.

The kasbah forms the apex of a triangle of which the quays form the base.

the big drum, cymbals and triangle, was used by Haydn in his Military Symphony, and Mozart in his Entfilhrung, for reasons of "local colour"; it appears as an extreme means of climax in the finale of Beethoven's 9th symphony.

Triangle and cymbals.

Triangle.

If there were such a thing as a triangle contained by absolutely straight lines, its three angles would no doubt measure what Euclid says; but straight lines and true triangles nowhere exist in reruns natura.

It may be asked, Why can God not create a triangle whose three angles shall not be equal to two right angles?

We reach similar conclusions when we recognize that the laws of nature are general or hypothetical; not in Mill's sense (" If you had such a non-existent thing as three perfectly straight lines united in a triangle "), but in a sense noted in F.

The district of Bugey occupies the triangle formed by the Rhone in the south-east of the department.

A third reflecting plate is sometimes employed, the cross-section of the three forming an equilateral triangle.

Two lines may be drawn from this point, one to each of the two rails, in a plane normal to the rails, and the ends of these lines, where they meet the rails, may be joined to complete a triangle, which may conveniently be regarded as a rigid frame resting on the rails.

Its form is approximately that of an isosceles triangle, with the sharp angle extending into Lower California, W.

Turning, therefore, to a globe, Asia, viewed as a whole, will be seen to have the form of a great isosceles spherical triangle, having its north-eastern apex at East Cape (Vostochnyi), in Bering Strait; its two equal sides, in length about a quadrant of the sphere, or 6500 m., extending on the west to the southern point of Arabia, and on the east to the extremity of the Malay peninsula; and the base between these points occupying about 60° of a great circle, or 4 500 m., and being deeply indented by the Arabian Sea and the Bay of Bengal on either side of the Indian peninsula.

He has little to say of the inner history and policy of the kingdom of Theodoric: his interests lie, as Mommsen says, within a triangle of which the three points are Sirmium, Larissa and Constantinople.

In plan it is a triangle, protected by a double moat, and has round towers at the angles.

Its superficial extent is seen when the folds covering the shell are cut away and the shell removed; the external surface forms a triangle with its base bordering the pericardium, and its apex directed posteriorly and reaching to the lefthand posterior corner of the shell-chamber.

Since, however, the steppe edge on the east is somewhat indefinite, some early Moslem and other geographers have included all the Hamad in Syria, making of the latter a blunt-headed triangle with a base some 700 m.

The marching band had one percussion player who played the triangle.

Since the area of the triangle FPP' is one half the product of FP into the perpendicular p from P on FP', it follows that if these perpendiculars were equal all round the orbit, the areas described during the infinitesimal time would be smallest at the pericentre and continually increase during the passage of the body to B.

the hypothetical radicals of acids, were denoted by squares enclosing the initial letter of the base; an alkali was denoted by a triangle, and the particular alkali by inserting the initial letter.

The problem then resolves itself in the solution of a spherical triangle.

If both places have the same latitude we have to deal with an isosceles triangle, of which two sides and the included angle are given.

This triangle, for the convenience of calculation, we divide into two right-angled triangles.

If the latitudes differ, we have to solve an oblique-angled spherical triangle, of which two sides and the included angle are given.

In general outline it is an irregular triangle, with apex at Cape Guardafui.

For when a triangle "moves," the points do not move with it.

So what is it that keeps unaltered in the moving triangle ?

From this triangle they harried the French communications with Berlin, and to secure a winter's rest for his men Napoleon determined to bring them to action.

Bennigsen, now commanding the whole Russian army which with Lestocq's Prussians amounted to 100,000, also moved into winter quarters in the triangle Deutsch-Eylau-Osterode-Allenstein, and had every intention of remaining there, for a fresh army was already gathering in Russia, the 1st corps of which had reached Nur about 50 m.

The French army was thus disposed almost in an equilateral triangle with sides of about 570 m., with 95,000 men at the apex at Moscow opposed to 120,000, 30,000 about Brest opposite ioo,000, and 17,000 about Drissa confronted by 40,000, whilst in the centre of the base at Smolensk lay Victor's corps, about 30,000.

The sides of the triangle slope down abruptly towards the west, more gradually towards the east; at the base stands the cone of Ayala Hill, the last outpost of the Rudnik Mountains, which extend far away to the south; and, at the apex, a cliff of Tertiary chalk, 200 ft.

In somewhat sensational and affected but prophetic words Gaj compared Illyria to a lyre, " a triangle between Skutari, Varna and Villach.

The Treaty of Trianon satisfied the most essential claims of Yugoslavia, by dividing the whole Banat (save a small Magyar triangle opposite the city of Szeged) between her and Rumania, and by assigning to her the whole Backa (except Baja and district), part of the Baranya (forming the angle between Drave and Danube) and the Medjumurje (between Drava and Mur).

The northern part of Natal presented two faces of a triangle to the two enemies, the short base being formed by the Tugela river.

Close to the head of the triangle at Dundee and Glencoe was posted a small British force under Major-General Sir W.

It is in this book that Hero proves the expression for the area of a triangle in terms of its sides.

If the section of the finished tube is to be a triangle, with the enamel and bore at the base, the molten mass is pressed into a V-shaped mould before it is pulled out.

Take any two arbitrary directions in the plane of the paper, and draw a small isosceles triangle abc, whose sides are perpendicular to the two directions, and consider the equilibrium of a small triangular prism of fluid, of which the triangle is the cross section.

A scalene triangle abc might also be employed, or a tetrahedron.

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.

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.

Inside an equilateral triangle, for instance, of height h, - 2Ra/3y/h, (8) where a, 13, y are the perpendiculars on the sides of the triangle.

(to) Integrating over the base, to obtain one-third of the kinetic energy T, 3T = 2 pf '3 4R2(3x4-h4)dx/h 3 = pR2h4 / 1 35 V 3 (II) so that the effective k 2 of the liquid filling the trianglc is given by k 2 = T/Z p R 2 A = 2h2/45 = (radius of the inscribed circle) 2, (12) or two-fifths of the k 2 for the solid triangle.

The cities of Shanghai, Hangchow and Suchow form the three points of a triangle, each being connected with the other by canal, and trade is now open by steam between all three under the inland navigation rules.

8) be an equilateral triangle, the angular points corresponding to the three pure metals A, B, C. C Then the composition of any alloy can be FIG.

If now we wish to represent the variations in some property, such as fusibility, we determine the freezing-points of a number of alloys distributed fairly uniformly over the area of the triangle, and, at each point corresponding to an alloy, we erect an ordinate at right angles to the plane of the paper and proportional in length to the freezing temperature of that alloy.

If now we cut the freezing-point surface by planes parallel to the base ABC we get curves giving us all the alloys whose freezing-point is the same; these isothermals can be projected on to the plane of the triangle and are seen as dotted lines in fig.

projected on to the plane of the triangle as Ee, E'e and E"e.

Since the potential rises proportionately to the quantity in the conductor, the ends of these ordinates will lie on a straight line and define a triangle whose base line is a length equal to the total quantity Q and V height a length equal to the final potential V.

The triangle pennant on the ship signalled that the ship was in trouble.

Pascal treated these numbers in his Traite du triangle arithmetique (1665), using them to develop a theory of combinations and to solve problems in proba-, bility.

" a triangle is a three-sided rectilineal figure."

A triangle is a rectilineal figure; i.e.

quadrilaterals, hexagons, &c., all of which are rectilineal figures, a triangle is "differentiated" as having three sides.

To say, for instance, that the area of a right-angled triangle is half the area of the rectangle contained by the two sides, is not to say what the area is, but what it is the half of.

For fuller discussion reference should be made to Geometry and Trigonometry, as well as to the articles dealing with particular figures, such as Triangle, Circle, &C.

(iii) Right-angled triangle: sides a and b, enclosing the right angle.

(v) Triangle: one side a, distant h from the opposite angle.

If, for instance, the data for the triangle are sides a and b, enclosing an angle C, the area is lab sih C.

In the case of the triangle, for instance, b is zero, so that the area is lha.

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.

the lateral) faces being a triangle with an angular point in one end of the figure and its opposite side in the other.

Hence area of triangle ACB = twice area of triangle aTb.

Repeating the process with the arcs AC and CB, and continuing the repetition indefinitely, we divide up the required area and the remainder of the triangle ATB into corresponding elements, each element of the former being double the corresponding elements of the latter.

Hence the required area is double the area of the remainder of the triangle, and therefore it is two-thirds of the area of the triangle.

If we draw a line at right angles to TCV, meeting TCV produced in M and parallels through A and B in K and L, the area of the triangle ATB is KL.

to) than the area of the trapezium Kabl by two-thirds of the area of the triangle ATB (§ 34).

constructing a square of twice the area of a given square (which follows as a corollary to the Pythagorean property of a right-angled triangle, viz.

Nask and Kamna) within the triangle they form.

The Russians, then, at the beginning of June, were divided into three groups, the Southern, or offensive group (3 5,000), in the triangle Neuchwang-Haicheng-Kaiping; the Eastern or defensive group (30,000), the main body of it guarding the passes right and left of the Wiju-Liao-Yang road, the left (Cossacks) in the roadless hills of the upper Aiho and Yalu valleys, the right (Mishchenko's Cossacks and infantry supports) guarding Fenshuiling pass and the road from Takushan; the reserve (42,000) with Kuropatkin at Liao-Yang; the " Ussuri Army " about Vladivostok; and Stessel's two divisions in the Kwantung peninsula.

For the position shown the distribution of bending moment due to W 1 is given by ordinates of the triangle 000 A'CB'; that due to W2 by ordin al, W, WW1 W„ ates of A'DB'; and that due to W3 by ordinates of A EB'.

The total moment at WI, due to three loads, is the sum mC-Fmn--Emo of the intercepts which the triangle sides cut off from the vertical under W 1.

Then the triangle YXE is the reciprocal FIG.

The direction of YX, being a thrust upwards, shows the direction in which we must go round the triangle YXE to find the direction of the two other forces; doing this we find that the force XE must act down towards the point YXE, and the force EY away from the same point.

In the triangle FDC, let FD be tangent to the curvelFC vertical, and Dqhorizontal; these three sides will necessarily be proportional respectively.to_the FIG.

the shape of an irregular triangle, and occupy a position of great natural strength between two valleys.

The best known of these, which is called Legendre's theorem, is usually given in treatises on spherical trigonometry; by means of it a small spherical triangle may be treated as a plane triangle, certain corrections being applied to the angles.

The most considerable areas over 3000 fathoms are the Aldrich deep, an irregular triangle nearly as large as Australia, situated to the east of New Zealand, in which a sounding of 5155 fathoms was obtained by H.M.S.

The territory occupied by the Basque Provinces forms a triangle bounded on the west and south by the provinces of Santander, Burgos and Logrono, on the east by Navarre, on the north by France and the Bay of Biscay.

The triangle is here an irregular one, consisting of a narrow base to which one end of the string was fixed, while the second side, forming a slightly obtuse angle with the base, consisted of a wide and slightly curved sound-board pierced with holes through which the other end of the strings passed, being either knotted or wound round pegs.

The third side of the triangle was formed by the strings themselves, the front pillar, which in modern European harps plays such an important part, being always absent in these early Oriental instruments.

The island of Kotlin, or Kettle (Finn., Retusari, or Rat Island) in general outline forms an elongated triangle, 72 m.

(I) the North Atlantic division~down to New Jersey and Pennsylvania; (2) the South Atlantic divisionfrom Delaware to Florida (including West Virginia); (3) the North Central divisionincluding the states within a triangle tipped by Ohio, Kansas and North Dakota; (4) the South Central division -covering a triangle tipped by Kentucky, Alabama and Texas; and (5) the Western divisionincluding the Rocky Mountains and Pacific states.

The iron-producing area of the country may be divided, with regard to natural geographic, historic and trade considerations, into four districts: (1) the Lake Superior district, embracing the states of Minnesota, Michigan and Wisconsin; (2) the southern district, embracing the triangle tipped by Texas, Maryland and Georgia; (3) the northern district, embracing the triangle tipped by Ohio, New Jersey and Massachusetts, plus the states of Iowa and Missouri; (4) the western district, which includes the states of the Rocky Mountain region and Pacific coast.

In various systems of triangular co-ordinates the equations to circles specially related to the triangle of reference assume comparatively simple forms; consequently they provide elegant algebraical demonstrations of properties concerning a triangle and the circles intimately associated with its geometry.

It may be shown to be the locus of the vertex of the triangle which has for its base the distance between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the two circles.

Since the area of a circle equals that of the rectilineal triangle whose base has the same length as the circumference and whose altitude equals the radius (Archimedes, KIKXou A ir, prop.i), it follows that, if a straight line could be drawn equal in length to the circumference, the required square could be found by an ordinary Euclidean construction; also, it is evident that, conversely, if a square equal in area to the circle could be obtained it would be possible to draw a straight line equal to the circumference.

6, ABC is an isosceles triangle right D FIG.

It is easily shown that the areas of the lune Adbea and the triangle ABC are equal.

7, ABC is any triangle 1 Eisenlohr, Ein math.

right angled at C, semicircles are described on the three sides, thus forming two lunes Afcda and Cgbec. The sum of the areas of these lunes equals the area of the triangle ABC.] As for Euclid, it is sufficient to recall the facts that the original author of prop. 8 of book iv.

2-}-cos B It is readily shown that the latter gives the best approximation to 0; but, while the former requires for its application a knowledge of the trigonometrical ratios of only one angle (in other words, the ratios of the sides of only one right-angled triangle), the latter requires the same for two angles, 0 and 3B.

The base of the triangle is upward, and at each lateral angle one of the Fallopian tubes opens.

Hawaii Island, from which the group and later the Territory was named, has the shape of a rude triangle with sides of 90 m., 75 m.

p. 157); (2) the angles at the base of an isosceles triangle are equal (Id.

25) that he perfected the things relating to the scalene triangle and the theory of lines.

24, that he was the first person to describe a right-angled triangle in a circle.

To the former belong the theorems (t), (2), and (3), and to the latter especially the theorem (4), and also, probably, his solution of the two practical problems. We infer, then, [t] that Thales must have known the theorem that the sum of the three angles of a triangle are equal to two right angles.

32 was first proved in a general way by the Pythagoreans; but, on the other hand, we learn from Geminus that the ancient geometers observed the equality to two right angles in each kind of triangle - in the equilateral first, then in the isosceles, and lastly in the scalene (Apoll.

Beta (13) iron, an unmagnetic, intensely hard and brittle allotropic form of iron, though normal and stable only in the little triangle GHM, is yet a state through which the metal seems always to pass when the austenite of region 4 changes into the ferrite and cementite of regions 6 and 8.

in the triangle between Catania, Nicolosi and Acireale.

" It is from the idea of a triangle that we discover the relation of equality which its three angles bear to two right ones; and this relation is invariable, so long as our idea remains the same " (i.

The properties of this individual subject, the idea of the triangle, are, according to him, discovered by observation, and as observation, whether actual or ideal, never presents us with more than the rough or general appearances of geometrical quantities, the relations so discovered have only approximate exactness.

BAY OF BENGAL, a portion of the Indian Ocean, resembling a triangle in shape, lying between India and Burma.

These two mountain ranges unite at their northern extremities with the Vindhya chain of mountains, and thus is formed a vast triangle supporting at a considerable elevation the expanse of table-land which stretches from Cape Comorin to the valley of the Nerbudda.

It appears that Pascal contemplated publishing a treatise De aleae geometria; but all that actually appeared was a fragment on the arithmetical triangle (Traite du triangle arithmetique, " Properties of the Figurate Numbers"), printed in 1654, but not published till 1665, after his death.

The Piedmontese company takes over from the government the control of all the irrigation within a triangle between the left bank of the Po and the right bank of the Sesia.

It also follows that a line half-way between a point and its polar and parallel to the latter touches the parabola, and therefore the lines joining the middle points of the sides of a self-conjugate triangle form a circumscribing triangle, and also that the ninepoint circle of a self-conjugate triangle passes through the focus.

Expressing this condition we obtain mb = 1/ nc = o as the relation which must hold between the co-efficients of the above equation and the sides of the triangle of reference for the equation to represent a parabola.

Try = o to be a parabola is lbc+mca+nab = o, and the conic for which the triangle of reference is self-conjugate la 2 +143 2 +n7 2 =o is a 2 inn--+b 2 nl+c 2 lm=o.

It is a large triangle, having its corners at Jenin, Jebel et-Tur, and the outlet of the Wadi Mukatta`, by which last it communicates with the sea-coast.

Its form is that of a great triangle, with its base resting upon the Himalayan range and its apex running far into the ocean.

The length of India from north to south, and its greatest breadth from east to west, are both about 1900 m.; but the triangle tapers with a pear-shaped curve to a point at Cape Comorin, its southern extremity.

The other two sides of the elevated southern triangle are known as the Eastern and Western Ghats.

The drift went on until April 9 1916 when the floe, reduced to a triangle zoo yds.

Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.

Deduction is synthesis when it is progressive from real ground to consequence, as when we start from these two results of analysis as principles and deduce synthetically the proposition that therefore the angles of a triangle are equal to two right angles, in the order familiar to the student of Euclid.

A formula such as the equality of the interior angles of a triangle to two right angles is only scientifically known when it is not of isosceles or scalene triangle that it is known, nor even of all the several types of triangle collectively, but as a predicate of triangle recognized as the widest class-concept of which it is true, the first stage in the progressive differentiation of figure at which it can be asserted.° Three points obviously need development, the nature of definition, its connexion with the syllogism in which the middle term is cause or ground, and the way in which we have assurance of our principles.

It should be added that the proper names in the inscriptions show the regular Italic system of gentile nomen preceded by a personal praenomen; and that some inscriptions show the interesting feature which appears in the Tables of Heraclea of a crest or coat of arms, such as a triangle or an anchor, peculiar to particular families.

Nicaragua forms an irregular equilateral triangle with its base stretching for 280 m.

(a) In 1880 was discovered between the Quirinal and Viminal hills a little earthenware pot of a curious shape, being, as it were, three vessels radiating from a centre, each with a separate mouth at the top. 6 Round the sides of the triangle formed by the three vessels and under the mouths runs an inscription of considerable length.

At Corchiano itself, however, similar walls may be traced, and the site is a strong and characteristic one - a triangle between two deep ravines, with the third (west) side cut off by a ditch.

the particular case of three forces it reduces to the triangle of forces, viz.

If three forces acting on a particle are represented as to magnitude and direction by the sides of a triangle taken in order, they are in equilibrium.

if three forces acting on a particle be in equilibrium, and any triangle be constructed whose sides are respectively parallel to the forces, the magnitudes of the forces will be to ope another as the corresponding sides of the triangle.

The relations between this force P, the gravity W of the body, and the reaction S of the plane are then determined by a triangle of forces HKL.

The relation between the three forces acting on any particle, viz, the extraneous force and the tensions in the two adjacent portions of the string can be exhibited by means of a triangle of forces; and if the successive triangles be drawn to the same scale they can be fitted together so as to constitute a single force-diagram, as shown in fig.

16) represent the two forces, AD their resultant; we have to prove that the sum of the triangles OAB, OAC is D equal to the triangle OAD,

to the sides of a triangle at the middle points will be in equilibrium provided they are proportional to the respective sides, and act all inwards or all outwards.

Thus if the three lines form a triangle ABC, and if the given force F meet BC in H, then F can be resolved into two components acting in HA, BC, respectively.

Hence in trilinear co-ordinates, with ABC as fundamental triangle, its equation is Pa+Q/1+R7=o.

The two diagrams being supposed constructed, it is seen that each of the given systems of forces can be replaced by two components acting in the sides of the funicular which meet at the corresponding vertex, and that the magnitudes of these components will be given by the corresponding triangle of forces in the force-diagram; thus the force 1 in the figure is equivalent to two forces represented by 01 and 12.

The consequent displacement of any point P will then be at right angles to the plane PAB, its amount will be represented by double the area of the triangle PAB, and its sense will depend on the cyclical order of the letters P, A, B.

The two forces at B will cancel, and we are left with a couple of moment P.AC in the plane AC. If we draw three vectors to represent these three couples, they will be perpendicular and proportional to the respective sides of the triangle ABC; hence the third vector is the geometric sum of the other two.

Hence these three forces will be concurrent, and their ratios wifi be given by a triangle of forces.

Since PNS is a triangle of forces for the portion AP of the chain, we have wx/To=PN/NS, or yW.Xu/2T5, (14)

be situate at the vertices of a triangle ABC, the mass-centre of ~ and y is at a point A in BC, such that ~.

It possesses thi property that the radius of gyration about any diameter is half thi distance between the two tangents which are parallel to that diameter, In the case of a uniform triangular plate it may be shown that thi momental ellipse at G is concentric, similar and similarly situatec to the ellipse which touches the sides of the triangle at their middle points.

Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.

Then from the proportionality and parallelism sides of a triangle, there results the following of the load and the two resistances applied to each piece of the structure to the three theorem (originally due to Rankine): If from the angles of the polygon of loads there be drawn lines (Ri, R2, &c.), each of which is parallel to the resistance (as Pi F2, &c.) exerted FIG.

Should K be inconveniently far off, draw any triangle with its sides respectively parallel to CiT~, CiT2 and TiTi; the ratio of the twiJ sides first mentioned will be the velocity ratio required.

and if these ends be not in one straight line with that axis, then S, L R, and L+R, are the three sides of a triangle, having the angle opposite S at that axis; so that, if 0 be the supplement of the arc between the dead-points, Si=2(L2+Ri)_2(Li_R~ cos0,)

The ventral side of the body in the atrial region is broad and convex, so that the body presents the appearance of a spherical triangle in transverse section, the apex being formed by the dorsal fin and the angles bordered by two hollow folds, the metapleural folds, each of which contains a continuous longitudinal lymph-space, the metapleural canal.

The Mesozoic beds form an irregular triangle extending from Lisbon and Torres Novas on the south to Oporto on the north.

For if in the triangle abc the side ab is taken so as to represent on a given scale the tension of the surface of contact of the fluids a and b, and if the other sides be and ca are taken so as to represent on the same scale the tensions of the surfaces between b and c and between c and a respectively, then the condition of equilibrium at 0 for the corresponding tensions R, P and Q is that the angle ROP shall be the supplement of abc, POQ of bca, and, therefore, QOR of cab.

If no one of these tensions is greater than the sum of the other two, the drop will assume the form of a lens, the angles which the upper and lower surfaces of the lens make with the free surface of A and with each other being equal to the external angles of the triangle of forces.

But when the surface-tension of A exceeds the sum of the tensions of the surfaces of contact of B with air and with A, it is impossible to construct the triangle of forces, so that equilibrium becomes impossible.

If the three fluids can remain in contact with one another, the sum of any two of the 3 quantities must exceed the third, and T 31 I by Neumann's rule the directions of the interfaces at the common edge must be parallel to the sides of a triangle, taken proportional to T12, T23, T31.

If the above-mentioned condition be not satisfied, the triangle is imaginary, and the three fluids cannot rest in contact, the two weaker tensions, even if acting in full concert, being incapable of balancing the strongest.

Marangoni, van der Mensbrugghe, Quincke, have all arrived at results inconsistent with the reality of Neumann's triangle.

We are thus led to the important conclusion that according to this hypothesis Neumann's triangle is necessarily imaginary, that one of three fluids will always spread upon the interface of the other two.

The following is Pettigrew's description of wings and wing movements published in 1867: " The wings of insects and birds are, as a rule, more or less triangular in shape, the base of the triangle being directed towards the body, its sides anteriorly and posteriorly.

long, the total triangle.

The base of the triangle runs from the South Foreland to Land's End W.

It extends from the eastern extremity of Wiltshire in a widening triangle to the sea, which it meets along an irregular line from Deal to Cromer.

The Hampshire Basin forms a triangle with Dorchester, Salisbury and Worthing near the angles, and the rim of Chalk to the south appears in broken fragments in the Isle of Purbeck, the Isle of Wight, and to the east of Bognor.

along the line of 9° N., and resembles in shape a triangle with its apex to the north.

The addition of the triangle west of that line-the so-called Platte Purchase-violated the Missouri Compromise.

As the pressure of water is nil at the surface and increases in direct proportion to the depth, the overturning moment is as the cube of the depth; and the only figure which has a moment of resistance due to gravity, varying also as the cube of its depth, is a triangle.

It can be shown, for example, that for masonry having a density of 3, water being 1, the figure of minimum section is a right-angled triangle, with the water against its vertical face; while for a greater density the water face must lean towards the water, and for a less density away from the water, so that the water may lie upon it.

If the right-angled triangle abc, fig.

thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab= d in feet, the horizontal _ eL 2 pressure of water against the section of the dam, inI creasing uniformly with the depth, is properly represented by the isosceles right-angled triangle abe, in which be is the maximum water-pressure due to the Cent full depth d, while the area 2 abe = d is t h e total hor12 d3 6 If x be the width of the base, and p the density of the masonry, the weight of the masonry in terms of a cubic foot of water will be acting at its centre of gravity g, situated at 3x from the outer toe, and the moment of resistance to overturning on the outer toe, p x 2 d (2) In countries where good clay or retentive earth cannot be obtained, numerous alternative expedients have been adopted with more or less success.

- Diagram of Right-Angled cubic feet of water, acting g at one-third its depth above Triangle Dam.

of such a masonry triangle.

If, therefore, the centre of that became so far removed to the right as to make j coincident with b, the diagram of stresses would become the triangle j'l'c', and the vertical pressure at the inner face would be nil.

Thus the general curve of three bar-motion (or locus of the vertex of a triangle, the other two vertices whereof move on fixed circles) is a tricircular sextic, having besides three nodes (m = 6, 6 = 3+3+3, = 9), and having the centres of the fixed circles each for a singular focus; there is a third singular focus, and we have thus the remarkable theorem (due to S.

A more generally accepted view - especially among palaeontologists - is the tritubercular theory, according to which the most generalized type of tooth consists of three cusps arranged in a triangle, with the apex pointing inwards in the teeth of the upper jaw.

Each cusp of the primitive triangle has received a separate name, both in the teeth of the upper and of the lower jaw, while names have also been assigned to super-added cusps.

In some instances the known relation is self- Intuition evident, as when we judge intuitively that acirclecannot and de- be a triangle, or that three must be more than two.

sides, while a third forms a triangle with the S.E.

Four thousand cubits to the east the great rampart was built "mountain high," which surrounded both the old and the new town; it was provided with a moat, and a reservoir was excavated in the triangle on the inner side of its south-east corner, the western wall of which is still visible.

In Carew Triangle in the northern part of the city is a monument in honour of soldiers of the Spanish-American War.

Moreover, the English territory, a great triangle, with the Channel for base and Paris for apex, was not a really solid position.

The equilateral triangle is the basis of the tetrahedron, octahedron and icosahedron.'

If three equilateral triangles be placed at a common vertex with their covertical sides coincident in pairs, it is seen that the base is an equal equilateral triangle; hence four equal equilateral triangles enclose a space.

That the triangle could give rise to no other solid followed from the fact that six covertically placed triangles formed a plane.

V = 3rA = 2 1 4 / 3 n F tan -II cot e a = 2 I 1 3 n F cot e a cos a/ (sin' a -cos t 13) 2 R =1-/ tan IT tan 0=1/ sin 13/(sin e a-cost r =Zl tan 21 cot a= Il cot a cos 13/(sin" a -cos' (3)L 1 In the language of Proclus, the commentator: " The equilateral triangle is the proximate cause of the three elements, ` fire,' ` air ' and ` water '; but the square is annexed to the ` earth.'

(By the truncation of a vertex or edge we mean the cutting away of the vertex or edge by a plane making equal angles with all the faces composing the vertex or with the two faces forming the edge.) It is bounded by 4 triangular and 4 hexagonal faces; there are 18 edges, and 12 vertices, at each of which two hexagons and one triangle are covertical.

The section made by a plane containing the axis and perpendicular to the base is a triangle contained by two generating lines of the cone and a diameter of the basal circle.

Apollonius considered sections of the cone made by planes at any inclination to the plane of the circular base and perpendicular to the triangle containing the axis.

The points in which the cutting plane intersects the sides of the triangle are the vertices of the curve; and the line joining these points is a diameter which Apollonius named the latus transversum.

In Newton's method, two angles of constant magnitude are caused to revolve about their vertices which are fixed in position, in such a manner that the intersection of two limbs moves along a fixed straight line; then the two remaining limbs envelop a conic. Maclaurin's method, published in his Geometria organica (1719), is based on the proposition that the locus of the vertex of a triangle, the sides of which pass through three fixed points, and the base angles move along two fixed lines, is a conic section.

What remains of this once powerful sultanate is a triangular-shaped territory, the base of the triangle being represented by 80 m.

It stands on a platform forming an irregular triangle with sides about 3000 ft.

She stopped in front of a small mural depicting a triangle with a form at each of the points.

Deidre moved towards the lake, away from the center of the triangle they formed.

Surprisingly, Fred O'Connor, arch fan of any hint of mystery, remained uninterested in the Donald Ryland-Edith Shipton-Jerome Shipton triangle.

His shoulders and hips formed a triangle that rippled with movement.

It was just the letter "a" in a highly abstracted form, a triangle.

abstracted form, a triangle.

Unlimited assault rifle ammunition: Hold L and press X, Circle, X, R, Square, Triangle during game play.

Hiroshima mon amour (Hiroshima my Love, 1959) and Marienbad would be the other two connecting points in this triangle.

apex of the triangle.

The carapace is usually beige with a distinctive black triangle with the apex pointing toward the abdomen and the base toward the pedipalps.

bifacial working along the edges of two sides of the triangle.

place the red candleholder (with a tealight inside) in the center of the triangle of feathers.

One possible layout is shown in the artist's reconstruction of the fort, showing the triangle as primarily ceremonial.

cosine functions could have the same values that they had for the first triangle.

Study environmental criminology Scan for crime problems 9. Use the crime triangle 10.

equilateral triangle or square.

Omega Centauri makes an almost equilateral triangle with these two stars on their western side.

You should end up with a perfect triangle which totally encloses the filling.

The black craft was a perfect triangle, with no jagged edges or visible rear tail fin.

Imagine there is a triangle on the other person's forehead.

Club Triangle had many musical genres to choose from for their party.

wracked by guilt, Billie is now locked into a triangle - a kind of emotional Bermuda triangle of lost souls.

heliocentric orbits, forming a triangle of 5 million km sides.

hypotenuse of the triangle.

Figure 6: next draw a similar triangle which has the hypotenuse 4.5 units long.

Simulation with triangle input Unlike self-referenced logic, the transition has no hysteresis.

illuminative approach adopted in the Triangle report the terms became almost impossibly cumbersome and confusing.

As the Greek philanderer isosceles used to say, " There are 3 sides to every triangle " .

isosceles triangle with a altitude drawn.

Being either isosceles or scalene is inseparable from a triangle in real existence.

Back to top Germany Vehicle Requirements: Warning triangle and first-aid kit.

In our very latest work, " Marge " has mapped the whole Keble triangle.

Part of the nearby Triangle car park may be used for bus layover to facilitate the development.

In the femoral triangle the FV lies medial to the artery.

mon amour (Hiroshima my Love, 1959) and Marienbad would be the other two connecting points in this triangle.

The head viewed face on resembles a triangle tapering in straight lines to a fine muzzle.

The light nape of neck to be confined to triangle behind ears and to be as small as possible color to match flanks.

opium poppy cultivation in the Golden Triangle: Lao PDR, Myanmar, Thailand (UNODC, October 2006 ).

Taking a look at the skinny star parallax triangle above and realizing that the triangle should be over 4,500 times longer (!

Thus, any triangle of velocities could not direct a small passerine into our longitude.

He tested this intuition using two-dimensional plane figures the triangle, square, pentagon, etc. but this didn't work.

pyramid orchids were frequently seen in the central area known as the Triangle and are common all over the hill.

reroutetech firms in North Carolina's Research Triangle weathered Hurricane Floyd after days of preparation and rerouting of important online traffic.

resultant of two vectors using the vector triangle.

right-angled triangle with the longest runway being aligned with the main direction of wind for the area.

right triangle 3, 4, 5, right angle triangle on the clay tablet.

scalene triangle.

The only open aspect is the north side of the triangle, which looks out across a main road to Hackney Downs park.

During this period she appeared in the short lived shipping soap opera " Triangle " .

You have a little spaceship, a red triangle.

Take a walk along the Leeds and Liverpool Canal towpath through the Weavers ' Triangle - a well preserved Victorian industrial townscape.

On your keyboard press: Delete You should now have a right angled triangle.

Finally, we get down to our first proposition: Proposition 1. On a given straight line to construct an equilateral triangle.

Reflect, rotate and translate a triangle M5: Interactive transformation resource: drag the yellow triangle and watch the transformations.

The class work on plain paper, drawing the triangle with the help of a protractor, then writing the commands below.

The base of the equilateral triangle is the top of the wedge.

The triangle was a right-angled triangle with the longest runway being aligned with the main direction of wind for the area.

To see this, imagine an isosceles triangle with a altitude drawn.

The introduction should have roughly the shape of an inverted triangle.

There are many formulae relating the sides and angles of a spherical triangle.

triangle inequality ).

triangle symbol has been removed.

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