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The Third Servile War occurred in the Roman Republic from 73 BC to 71 BC.

3921In 58 BC, Clodius Pulcher ran on a "free grain for the poor" platform as he tried to become tribune.

129For example, rae Arenarion in one climatic or geographical region might be in~~ med an a-Arenarion and one in a different region a a-Arena- ~j1j ri, and so on (Moss, bc. cit.).

1210It consists of two branches AC and BC, which meet in a lowest point C. It will be seen that as we increase the percentage of B from nothing up to that of the mixture C, the freezing-point becomes lower and lower, but that if we further increase the percentage of B in the mixture, the freezing-point rises.

97(3) Expansion or compression at constant temperature, represented by curves called Isothermals, such as BC, AD, the form of which depends on the nature of the working sub stance.

972, let BC be a small portion of any isothermal corresponding to the temperature 0', and AD a neighbouring isothermal 0".

52Let BE be an isometric through B meeting AD in E, and EC an isopiestic through E meeting BC in C. Let BA, CD be adiabatics through B and C meeting the isothermal 0" in A and D.

53It is not necessary in this example that AB, CD should be adiabatics, because the change of volume BC is finite.

46If you look back across the span of time, you see wood plows being used in 4000 BC, then irrigation five hundred years later.

46saturated vapour), in which it occupies a volume v", the line BC represents the change of volume (v" - v').

33A cycle such as ABCD enclosed by parts of two isothermals, BC, AD, and two adiabatics, AB, CD, is the simplest form of cycle for theoretical purposes, since all the heat absorbed, H', is taken in during the process represented by one isothermal at the temperature o', and all the heat rejected, H", is given out during the process represented by the other at the temperature 0".

35We may in any relation substitute for any pair of quantities any other cogredient pair so that writing -}-d 2, -d l for x 1 and x 2, and noting that gx then becomes (gd), the above-written identity bceomes (ad)(bc)+(bd)(ca)+(cd)(ab) = 0.

36Then by relations (2) the heat, H, absorbed in the isothermal change BC, is to the work, W, done in the cycle ABCD in the ratio of o to (o' - o").

24EF is the change of volume corresponding to a change of pressure BE when no heat is allowed to escape and the path is the adiabatic BF, EC is the change of volume for the same change of pressure BE when the path is the isothermal BC. These changes of volume are directly as the compressibilities, or inversely as the elasticities.

247 let base BC=2a, and let h be the distance, measured at right angles to BC, from the middle point of BC to AD.

24Also, let angle ABC =7r - 0, angle BCD =ir - 4, angle between BC and AD = G.

24But the interval b bc" gives nearly twice as many beats and is not nearly so dissonant.

247 let base BC=2a, and let h be the distance, measured at right angles to BC, from the middle point of BC to AD.

24(ii.) By means of the commutative law we can collect like terms of a monomial, numbers being regarded as like terms. Thus the above expression is equal to 6a 5 bc 2, which is, of course, equal to other expressions, such as 6ba 5 c 2.

13Radii are drawn from the centre of the quadrant to the points of division of the arc, and these radii are intersected by the lines drawn parallel to BC and through the corresponding points on the radius AB.

1319) represent a gun at height BD above water-level DC, elevated to such an angle that a shot would strike the water at C. Draw EB parallel to DC. It is clear that under these conditions, if a tangent sight AF be raised to a height F representing the elevation due to the range BC, the object C will be on the line of sight.

13Radii are drawn from the centre of the quadrant to the points of division of the arc, and these radii are intersected by the lines drawn parallel to BC and through the corresponding points on the radius AB.

13Around 430 BC, Athens, embroiled in the Second Peloponnesian War, endured three years of epidemics that wiped out a third of its inhabitants.

13An iron plow comes three thousand years later in 500 BC, along with intensive row cultivation.

13the septal bars in bulk, bc, coelom.

14(ab)i(ac)j(bc)k..., that the symbolic product (ab)i(ac)j(bc)k..., possesses the invariant property.

14possess the invariant property, and we may write (AB) i (AC)'(BC) k ...A P E B C...

14X (xa) ki (xb) k2 (xc) k3...axibx2cx3...xx = (AB) hi (AC) h2 (BC) h3...A11 4 13 A1,14131 A B I ?C"' B C "' X (XA) ki (XB) k2 (XC) k3...AXB122cCk...X If this be of order e and appertain to an nie L Eke-/1+2m =e, h i+h2+ï¿½ï¿½ï¿½+221+ji+j2+ï¿½ï¿½ï¿½+kl+li =n, hi+h3+..ï¿½+222+ji+j3+ï¿½ï¿½ï¿½+k2+12 = n, h2+h3+ï¿½ï¿½ï¿½+223+j2+%3+ï¿½.ï¿½+k3+13 =n; viz., the symbols a, b, c,...

14of the base are the projections of the sides AB, BC, CD,.

14Take any point P in the latter, and form triangles by joining P to each of the sides AB, BC, ...

00Any error of this kind will merely affect the form of the frame; if, however, another member be introduced between A and D, then if BC be shortened AD will be strained so as to extend it, and the four other members will be compressed; if G CB is lengthened AD will thereby be compressed, and the four other members extended; if the workman does not make CB and AD of exactly the right length they and all the members will be permanently strained.

00Arbogast's rule of the last and the last but one; in fact, taking the value of a to be unity, and, understanding this letter in each term, the rule gives b; c, b2; d, bc, b; e, bd, c, b c, b, &c., which, if b, c, d, e, &c., denote I, 2, 3, 4, &c., respectively, are the partitions of 1, 2, 3, 4, &c., respectively.

00But the discovery, by Bryennios in 1873, of the ancient Christian work called Ocbayrl TWV bc.)Beea airoarbXwv (published in 1883), has immensely extended the range of our knowledge, and has at the same time thrown a clear light on many notices in other sources which for want of proper interpretation had been previously neglected or incorrectly understood.

00Take AB equal to one-fourth of the given line; on AB describe a square ABCD; join AC; in AC produced find, by a known process, a point C 1 such that, when C 1 B 1 is drawn perpendicular to AB produced and C 1 D 1 perpendicular to BC produced, the rectangle BC,.

00bc, Blood-corpuscles.

00When the curve BC is reached, Fe 2 C1 6 - 12H 2 0 separates out, and the solution solidifies.

00If, ignoring temporarily and for simplicity the fact that part of the carbon may exist in the state of graphite, we consider the behaviour of iron in cooling from the molten state, AB and BC give the temperature at which, for any given percentage of carbon, solidification begins, and Aa, aB, and Bc that at which it ends.

00BC and OH give the prothe cast iron the properties needed, is brought about chiefly by ferrite into a mixture of adjusting the silicon-content, because the presence of this element favours the formation of graphite.

00Ridgeway, who maintains that the Iron age originated in central Europe, and that iron must consequently have been worked in those regions as far back as C. 2000 BC.

00No siege engines are depicted, even in the time of the Empire,, and the absence of original representations after the XXth Dynasty renders it difficult to judge the advances made in the art of war during the first half of the last millennium Bc. The inscription of Pankhi, however, proves that in the 8th century approaches and towers were raised against the walls of besieged cities Priesthood.The priesthood was in a great degree hereditary, though perhaps not essentially so.

004000-3300 BC.

00Uakim bC All MansCr], 386411 (9961020).

00Mostan~ir bC Tamim Maadd], 427487 (I 0351094).

00Adid bC Mahommed Abdallah], 555567 (I 160-f 171).

002), and fastening a string of length BC to C B Y C and F.

00By adjusting the right ascension of the plane ABC and rotating the axis with the angular velocity of the sun, it follows that BC will be the direction of the solar rays throughout the day.

00X is the mirror rotating about the point E, and placed so that (if EB is the horizontal direction in which the rays are to be reflected) (I) the normal CE to the mirror is jointed to BC at C and is equal in length to BE, (2) the rod DBC passes through a slot in a rod ED fixed to, and in the plane of, the mirror.

00Hence light incident along the direction BC will be reflected along CE.

00AB is the axis of rotation, BC an adjustable FIG.

00The rods BC and DB carry two small rods EF, GF jointed at F; at this joint there is a pin which slides in a slot on the rod BH, which is normal to the mirror X.

00It is easy to show that rays falling on the mirror in the direction BC will be reflected along BD.

00BC, CD..

00BA, BC is represented by 2BH, the tension in BA: tension in BC: weight at B

00as BA: BC: 2BH.

00Hence AD BC are Fm.

00For suppose that in consequence of the displacement a point of the lamina is brought from A to B, whilst the point of the lamina which was originally at B is brought to C. Since AB, BC, are two different positions of the same line in the B C lamina they are equal, and it is evident that the rotation could have been effected by a rotation about J,

00If, AB being held fixed, the 3 quadrilateral be slightly de formed, it is obvious that the instantaneous centre J will - be at the intersection of the - .~ straight lines AD, BC, since s the displacements of the points D, C are necessarily at right angles to AD, BC, respectively.

00parallel to CD, meeting BC, AD in C, D, respectively.

00Thus 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.

00And the force in HA can be resolved into two components acting in BC, CA, respectively.

00If F, Q, R, be any three forces acting along BC, CA, AB, respectively, the line of action of the resultant is determined by the consideration that the sum of the moments about any point on it must vanish.

00Thus ii AB, BC, CD represent the given loads, in the force-diagram, we construct the sides corresponding to OA, OB, OC, OD in the funicular; we then draw the closing line of the funicular polygon, and a parallel OE to it in the force diagram.

00To find the pressure exerted by a bar AB on the pin A we compound with the force in AB given by the diagram a force equal to P. Conversely, to find the pressure of the pin A on the bar AB we must compound with the force given by the diagram a force equal and opposite to P. This question arises in practice in the theory of three-jointed structures; for the purpose in hand such a structure is sufficiently represented by two bars AB, BC. The right-hand figure represents a portion of the force-diagram; in particular ZX represents the pressure of AB on B

00~ Three-dimensional Kinematics of a Rigid Body.The position of a rigid body is determined when we know the positions of three points A, B, C of it which are not colljnear, for the position of any other point P is then determined by the three distances PA, PB, PC. The nine co-ordinates (Cartesian or other) of A, B, C are subject to the three relations which express the invariability of the distances BC, CA, AB, and are therefote equivalent to six independent quantities.

00(usually a~ small circle of the fixed sphere), and join JA, JB, JC, AB, BC

00The spherical A isosceles triangles AJB, BJC are con gruent, and we see that AB can be brought into the position BC by a rotation about the axis OJ through an FIG.

00This is the axis of the required screw; the amount of the translation is measured by the projection of AB or BC or CD on the axis; and the angle of rotation is given, by the inclination of the aforesaid bisectors.

00Hence, resolving along the tangents to the arcs BC, CA, respectively, we have ~ (3)

00the line of intersection (B); the arms (AB,BC) will then be proportional to the respective moments.

00The instantaneous centre of CD will be at the intersection of AD, BC, and if CD be drawn parallel to CD, the lines CC, DD may be taken to represent the virtual velocities of C, D turned each through B a right angle.

00The simplest case is that of a frame of three bars, when the three joints A, B, C fall into a straght line; a small displacement of the joint B at right angles to AC would involve changes in the lengths of AB, BC which are only of the second order of small quantities.

0052, if an infinitesimal deformation is possible without removing the bar CF, the instantaneous centre of CF (when AB is fixed) will be at the intersection of AF and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF.

00be situate at the vertices of a triangle ABC, the mass-centre of ~ and y is at a point A in BC, such that ~.

00If in (2) we put, L, M, N=O we get the case of free rotation; thus A~f=(BC)gr, B~=(CA)rp, (5)

00If we assume P Po cos am (~t+e), q =qo sin am (~it+o), r =To~ am (~t-i--~), (7) we find = ~ ~ = 9rp, i = ~0pg~ (8) Hence (5) will be satisfied, provided u~o BC o-qo CA kfi,r0AB

00The conditions (~) then lead to IA(AC) 2, ,2 (AC)(BC) 1 ~ tO qs B(BC)~ AB r0, C(BC) r~

00from the centre towards G; the angular velocity of the sheave is AC + BC

00Consider the link BC,, and let it be required to find the velocity of the point B having given the velocity of the point C. The principle upon which Engels 05:59, 27 Mar 2006 (PST)D

00From this pole set out Oc to represent the velocity of the point C. The direction of this must be at right angles to the line CD, because this is the only direction possible to the point C. If the link BC moves without turning, Oc will also represent the velocity of the point B; but, if the link is turning, B can only move about the ax~., C, and its direction of motion is therefore at right angles to the line CB.

00123 and 124) is the following: If points X and x are taken dividing the link BC and the tangential velocity cb, sothat cx: xb=CX:XB, then Ox represents the velocity of the point X in magnitude and direction.

00Let A be any origin, and let Ac represent the acceleration of the b point C, Ct the radial acceleration of B about C which must be in a direction parallel to BC, and tb the tan gential acceleration of B about C, C

00This follows by considering equation (4) for the two pairs of colours ac and bc. Until recently no glasses were known with a proportional degree of absorption; but R.

00In order to raise money he plundered a wealthy temple of Bel in Elam, but was killed by the inhabitants, 187 BC. (Diod.

00If four fluids, a, b, c, d, meet in a point 0, and if a tetrahedron AB CD is formed so that its edge AB represents the tension of the surface of contact of the liquids a and b, BC that of b and c, and so on; then if we place this tetrahedron so that the face ABC is normal to the tangent at 0 to the line of concourse of the fluids abc, and turn it so that the edge AB is normal to the tangent plane at 0 to the surface of contact of the fluids a and b, then the other three faces of the tetrahedron will be normal to the tangents at 0 to the other three lines of concourse of the liquids, an the other five edges of the tetrahedron will be normal to the tangent planes at 0 to the other five surfaces of contact.

00There is extant under his name a treatise on the gods and the heroic age, entitled Bc(3XtoOiJKn, a valuable authority on ancient mythology.

00The puddle at a was originally held up by the flat head of this pedestal; not so the puddle at b, which under the superincumbent weight settled down and produced the fault bc, accompanied with a shearing or tangential strain or, less probably, with actual fracture in the direction bd.

0014, water intrudes beneath that part of the masonry more readily than it can obtain egress along bc, or in any other direction towards the outer face, we shall have the uplifting and overturning pressure due to the full depth of water in the reservoir over the width ab added to the horizontal pressure, in which case all our previous calculations would be futile.

00If now a line be drawn from A to the bisector H of the side BC, it will meet the vertical through G in I and IJ =c(cos a+a sin a)/ur.

00Considering the equations ax +by +cz =d, a'x +b'y +c' z =d', a"x+b"y+cnz=d" and proceeding to solve them by the so-called method of cross multiplication, we multiply the equations by factors selected in such a manner that upon adding the results the whole coefficient of y becomes = o, and the whole coefficient of z becomes = o; the factors in question are b'c" - b"c', b"c - be", bc' - b'c (values which, as at once seen, have the desired property); we thus obtain an equation which contains on the left-hand side only a multiple of x, and on the right-hand side a constant term; the coefficient of x has the value a(b'c" - b"c') +a'(b"c - bc") +a'(bc' - b'c), and this function, represented in the form a, b,c, a' b'c', a" b" c" is said to be a determinant; or, the number of elements being 32, it is called a determinant of the third order.

00Moreover, the functions b'c" - b"c', b"c - bc", bc' - b'c used in the process are themselves the determinants of the second order l b",c"I?

00Thus, for three columns, it appears by either rule that 123, 231, 312 are positive; 213, 321, 132 are negative; and the developed expression of the foregoing determinant of the third order is =ab'c" - ab "c'+a'b "c - a'bc" - a"bc' - a"b'c. 3.

00of any couple, AB, for any given limits of temperature is the algebraic sum of the E.M.F.s between the same limits of temperature of the couples BC and CA formed with any other metal C. It is for this reason unnecessary to tabulate the E.M.F.s of all possible combinations of metals, since the E.M.F.

00Evaporation then continues at the constant temperature T, abstracting heat from the substance outside the refrigerator as shown by the line BC. The vapour is then compressed along the line CD to the temperature T2, when, by the action of the cooling water in the condenser, heat is abstracted at constant temperature and the vapour condensed along the line DA.

00Ashford BC is a relatively affluent district with a strong economy.

00Bactrian coins of King Euthydemus (220 BC) are known in a copper-nickel alloy.

00amulets in the form of flies were being made in Egypt as early as 3500 BC or thereabouts.

00bronze age burial barrows dating back to 2,000 BC.

00Neolithic long barrows have been found to date from the early part of the period ranging from 4000 to 2500 BC.

00Phase 2: Mass extinction of marine benthos, including deep-water sponges in BC and many shallow-water taxa including brachiopods in Tibet.

00Lysistrata was produced in 411 BC - when Athens ' situation looked utterly bleak.

00Inscriptions there from the third century BC were written in good Persian chancellery Aramaic.

00The earth's circumference was actually measured around 240 BC by Eratosthenes with a high degree of accuracy.

00concentric earth ditches from the Neolithic period around 3,600 - 3,300 years BC.

00conquered by the romans in the 4th Century BC, it long retained its Greek culture.

00decorated pottery, chiefly from the fifth century BC.

00eighth century BC not the tenth.

00enlisted into the army at Prince Rupert, BC.

00The letter epsilon is squared off before 200 BC and after 200 AD, and is rounded during the 400 years in between.

00One of the earliest uses of biological weapons occurred in the 6th century BC when the Assyrians poisoned enemy wells with rye ergot.

00Picture shows ewer from the British Museum The British Museum has a handful of ancient materials from Afghanistan starting from 190 180 BC.

00exaltation degrees, is even older (786 BC ).

00Gordon's first project as a director utilized footage from One Million BC.

00glyptic art of the Mittanian Kingdom in the fifteenth century BC.

00A relatively homogeneous culture united the Bronze Age elite through much of China around the 14th century BC.

00inlaid panel dated 2000 BC.

00He believed that the Greek translation of the Old Testament (the Septuagint, dating from the third century BC) was divinely inspired.

00He showed that large amounts of the element iridium present in geological layers dating from about 65 million BC had a cosmic origin.

00literate elite in Babylon imagined a new community and gave it a history via ancient and invented traditions c 550 BC.

00Archimedes (287-212 BC Greece) is reputed to have used powerful lodestones to pull the nails out of enemy ships thus sinking them.

00Macedonia became the lynchpin in Greek affairs during the 4th century BC.

00BC: [It's] The beam of energy that I detected coming out of the ground, with a proton magnetometer.

00millenniumriman handles the 1st millenium BC with equal aplomb.

00millenniumthat deposits of silver were worked in Iran from the fourth millenium BC.

00millenniume earliest structures revealed during the survey were trackways from the 4th millenium BC, visible only very rarely at extreme low water.

00Moabite territory in the first millenium BC.

00These pebble mosaics could be found all around the Greek world from the 6th to 4th century BC.

00On North Muir are two outstanding examples of prehistoric burial mounds, which date to a period around 2,500 to 2,000 BC.

00The first century BC, Egyptian obelisk was brought to Rome from Heliopolis by emperor Caligula to adorn his circus.

00orthopedics 1991;14:1303-1305. [PubMed Abstract] Sonies BC, Dalakas MC.

00pebble mosaics could be found all around the Greek world from the 6th to 4th century BC.

00The portion BC is the light emitted after illumination and is called phosphorescence.

00timber pilings excavated from a deep layer of silt on the sea bed have been dated at 250 BC.

00Many fragments of Greek decorated pottery, chiefly from the fifth century BC.

00prehistoric burial mounds, which date to a period around 2,500 to 2,000 BC.

00pressure gaugeust have a certification card, a submersible pressure gage and a BC jacket.

00The hoard is possibly the imperial regalia of the royal house in East Anglia in the first century BC: the ancestors of Boudica.

00religion founded in India in the 6th century BC.

00Live media reportage hit the headlines and Hemp BC immediately re-opened for business.

00Dionysius of Halicarnassus First Century BC: Greek rhetorician.

00Garstang had found a continuous sequence of Egyptian scarabs at the site showing active use until about 1400 BC.

00Even at the budget end of the market, the Northern Diver Sea Eagle BC has n't scrimped on features.

00The great sphinx dated to within a few years of 2500 BC.

00Greek bronze statuary: from the beginnings through the fifth century BC.

00submersible pressure gage and a BC jacket.

00Ca Na Costa This is a stone circle which is believed to be a megalithic tomb dating back to 1600 BC.

00He believed that the Greek translation of the Old Testament (the Septuagint, dating from the third century BC) was divinely inspired.

00The fashion for architectural vignettes, often employing perspective trickery reached its zenith, however, in the 1st century BC.

00unbroken literary tradition dating back to the third century BC.

00upwelling area near the West coast of Vancouver Is and BC's north coast.

00By 800 BC society had begun to recover and even grow wealthy.

00PN = BC 2; similarly if g and G be the corresponding intersections of the normal, PG: Pg:: BC 2: AC 2.

00Money order cards are very convenient and cheap (up to 10 lire for bc. short private message can be written on them.

00For example, rae Arenarion in one climatic or geographical region might be in~~ med an a-Arenarion and one in a different region a a-Arena- ~j1j ri, and so on (Moss, bc. cit.).

001, Bc) usually typical in form.

00The line BC, representing the equilibrium between monoclinic and liquid sulphur, is thermodynamically calculable; the point B is found to correspond to 131Ã‚° and 400 atmospheres.

00the septal bars in bulk, bc, coelom.

00we may write (AB)i(AC)j(BC)k...

00(ab)i(ac)j(bc)k..., that the symbolic product (ab)i(ac)j(bc)k..., possesses the invariant property.

00Notice, therefore, that the symbolic product (ab)i(ac)j(bc)k...

00In order that (ab)i(ac)j(bc)k...

00possess the invariant property, and we may write (AB) i (AC)'(BC) k ...A P E B C...

00= t) 1 v ...axbxcx..., and assert that the symbolic product (ab)i(ac)'(bc)k...aibxc2...

00From the three equations ax = alxl+ a2x2, b.= blxl+b2x2, cx = clxi+c2x2, we find by eliminating x, and x 2 the relation a x (bc)+b x (ca) +c x (ab) =0.

00We may in any relation substitute for any pair of quantities any other cogredient pair so that writing -}-d 2, -d l for x 1 and x 2, and noting that gx then becomes (gd), the above-written identity bceomes (ad)(bc)+(bd)(ca)+(cd)(ab) = 0.

00(III.) Again in (I.) transposing a x (bc) to the other side and squaring, we obtain 2(ac) (bc)axbx = (bc) 2 a'+(ac) 2 bx- (ab) 2 c1.

00(IV.) and herein writing d 2, -d 1 for x l, x2, 2 (ac) (bc) (ad) (bd) = (bc) 2 (ad) 2 +(ac) 2 (bd) 2 - (ab) 2 (cd) 2.

002 (ac)(bc)anx xibn-i -1 x = (bc)2anbn-2Cn-2 + (ac)2an x x x The weight of a term aoÃ‚°a l l ...an n is defined as being k,+2k2+...

00(ab)(ac)bxcx = - (ab)(bc)axcx = 2(ab)c x {(ac)bx-(bc)axi = 1(ab)2ci; so that the covariant of the quadratic on the left is half the product of the quadratic itself and its only invariant.

00For two factors the standard form is (ab) 2; for three factors (ab) 2 (ac); for four factors (ab) 4 and (ab) 2 (cd) 2; for five factors (ab) 4 (ac) and (ab) 2 (ac)(de) 2; for six factors (ab) 6, (ab) 2 (bc) 2 (ca) 2, and (ab) 2 (cd) 2 (ef) 2 .

00Put M 1 For M, N I For N, And Multiply Through By (Ab); Then { (F, C6) } = (Ab) A X 2A Y B X 1 M N I 2 (Xy), ?) 2, = (A B)Ax 1B X 2B Y L I Multiply By Cp 1 And For Y L, Y2 Write C 2, C1; Then The Right Hand Side Becomes (Ab)(Bc)Am Lbn 2Cp 1 M I C P (F?) 2 M { N2 X, Of Which The First Term, Writing C P =, ,T, Is Mn 2 A B (Ab)(Bc)Axcx 1 M 2 N 2 P 2 2222 2 2 _2 A X B X C (Bc) A C Bx M N 2 2 2 M2Ã‚°N 2 N 2 M 2 2 A X (Bc) B C P C P (Ab) A B B(Ac) Ax Cp 2 = 2 (04) 2 1 (F,0) 2.4 (F,Y') 2 Ã¯¿½?; And, If (F,4)) 1 = Km " 2, (F??) 1 1 M N S X X X Af A _Af A Ax, Ax Ax Ax1 Observing That And This, On Writing C 2, C 1 For Y 11 Y 21 Becomes (Kc) K X 'T 3C X 1= (F,0 1 ', G 1; Ã¯¿½'Ã¯¿½1(F,O) 1 M 1=1 M 2 0`,4)) 2 0, T (Fm 2.4 (0,0 2 .F ' And Thence It Appears That The First Transvectant Of (F, (P) 1 Over 4) Is Always Expressible By Means Of Forms Of Lower Degree In The Coefficients Wherever Each Of The Forms F, 0, 4, Is Of Higher Degree Than The First In X 1, X2.

00From (ac) 2 (bd) 2 (ad)(bc) we obtain (bd) 2 (bc) cyd x +(ac) 2 (ad) c xdx - (bd) 2 (ad)axb x - (ac)2(bc)axbx =4(bd) 2 (bc)c 2.

00X (xa) ki (xb) k2 (xc) k3...axibx2cx3...xx = (AB) hi (AC) h2 (BC) h3...A11 4 13 A1,14131 A B I ?C"' B C "' X (XA) ki (XB) k2 (XC) k3...AXB122cCk...X If this be of order e and appertain to an nie L Eke-/1+2m =e, h i+h2+Ã¯¿½Ã¯¿½Ã¯¿½+221+ji+j2+Ã¯¿½Ã¯¿½Ã¯¿½+kl+li =n, hi+h3+..Ã¯¿½+222+ji+j3+Ã¯¿½Ã¯¿½Ã¯¿½+k2+12 = n, h2+h3+Ã¯¿½Ã¯¿½Ã¯¿½+223+j2+%3+Ã¯¿½.Ã¯¿½+k3+13 =n; viz., the symbols a, b, c,...

00To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.

00(ii.) By means of the commutative law we can collect like terms of a monomial, numbers being regarded as like terms. Thus the above expression is equal to 6a 5 bc 2, which is, of course, equal to other expressions, such as 6ba 5 c 2.

00The numerical factor 6 is called the coefficient of a 5 bc 2 (Ã¯¿½ 20); and, generally, the coefficient of any factor or of the product of any factors is the product of the remaining factors.

00of 6a 5 bc 2 and 12a 4 b 2 cd we mean the H.C.F.

00of a 5 bc 2 and a 4 b 2 cd.

00is a 4 bc and the L.C.M.

00Thus a(b+c) and (b+c)a give the same result, though it may be written in various ways, such as abdac, ca+ab, &c. In the same way the associative law is that A(BC) and (AB)C give the same formal result.

00Let P, Q denote the normal thrust across the sides bc, ca, and R the normal thrust across the base ab.

00The mutual intersections of the lines drawn from the points of division of the arc parallel to AB, and the lines drawn parallel to BC through the points of division of AB, are points on the quadratrix (fig.

00It consists of two branches AC and BC, which meet in a lowest point C. It will be seen that as we increase the percentage of B from nothing up to that of the mixture C, the freezing-point becomes lower and lower, but that if we further increase the percentage of B in the mixture, the freezing-point rises.

00represented by a point P, so chosen that the perpendicular Pa on to the side BC gives the percentage of A in the alloy, and the perpendiculars Pb and Pc give the percentages of B and C respectively.

00(3) Expansion or compression at constant temperature, represented by curves called Isothermals, such as BC, AD, the form of which depends on the nature of the working sub stance.

00A cycle such as ABCD enclosed by parts of two isothermals, BC, AD, and two adiabatics, AB, CD, is the simplest form of cycle for theoretical purposes, since all the heat absorbed, H', is taken in during the process represented by one isothermal at the temperature o', and all the heat rejected, H", is given out during the process represented by the other at the temperature 0".

00It will be observed that the areas representing H and W both depend on the form of the path BC, but that the difference of the areas representing the change of intrinsic energy dE is independent of BC, which is a boundary common to both H and W.

002, let BC be a small portion of any isothermal corresponding to the temperature 0', and AD a neighbouring isothermal 0".

00Let BE be an isometric through B meeting AD in E, and EC an isopiestic through E meeting BC in C. Let BA, CD be adiabatics through B and C meeting the isothermal 0" in A and D.

00Then by relations (2) the heat, H, absorbed in the isothermal change BC, is to the work, W, done in the cycle ABCD in the ratio of o to (o' - o").

00saturated vapour), in which it occupies a volume v", the line BC represents the change of volume (v" - v').

00It is not necessary in this example that AB, CD should be adiabatics, because the change of volume BC is finite.

00EF is the change of volume corresponding to a change of pressure BE when no heat is allowed to escape and the path is the adiabatic BF, EC is the change of volume for the same change of pressure BE when the path is the isothermal BC. These changes of volume are directly as the compressibilities, or inversely as the elasticities.

00Byington, The Puritan in England and America (Bc,ston, 1896) and The Puritan as Colonist and Reformer (Boston, :899)..

0019) represent a gun at height BD above water-level DC, elevated to such an angle that a shot would strike the water at C. Draw EB parallel to DC. It is clear that under these conditions, if a tangent sight AF be raised to a height F representing the elevation due to the range BC, the object C will be on the line of sight.

00of the base are the projections of the sides AB, BC, CD,.

00Take any point P in the latter, and form triangles by joining P to each of the sides AB, BC, ...

00Also, let angle ABC =7r - 0, angle BCD =ir - 4, angle between BC and AD = G.

00(iii) If = o, so that AD is parallel to BC, it becomes area = 2ah+ 2 (cot cot ct,)h2.

00BC, BD, AD, in P, Q, R, S (fig.

00By drawing Ac and Ad parallel to BC and BD, so as to meet the plane through CD in c and d, and producing QP and RS to meet Ac and Ad in q and r, we see that the area of Pqrs is (x/h - x 2 /h 2) X area of cCDd; this also is a quadratic function of x.

00But the interval b bc" gives nearly twice as many beats and is not nearly so dissonant.

00Any error of this kind will merely affect the form of the frame; if, however, another member be introduced between A and D, then if BC be shortened AD will be strained so as to extend it, and the four other members will be compressed; if G CB is lengthened AD will thereby be compressed, and the four other members extended; if the workman does not make CB and AD of exactly the right length they and all the members will be permanently strained.

00Arbogast's rule of the last and the last but one; in fact, taking the value of a to be unity, and, understanding this letter in each term, the rule gives b; c, b2; d, bc, b; e, bd, c, b c, b, &c., which, if b, c, d, e, &c., denote I, 2, 3, 4, &c., respectively, are the partitions of 1, 2, 3, 4, &c., respectively.

00But the discovery, by Bryennios in 1873, of the ancient Christian work called Ocbayrl TWV bc.)Beea airoarbXwv (published in 1883), has immensely extended the range of our knowledge, and has at the same time thrown a clear light on many notices in other sources which for want of proper interpretation had been previously neglected or incorrectly understood.

00Take AB equal to one-fourth of the given line; on AB describe a square ABCD; join AC; in AC produced find, by a known process, a point C 1 such that, when C 1 B 1 is drawn perpendicular to AB produced and C 1 D 1 perpendicular to BC produced, the rectangle BC,.

00bc, Blood-corpuscles.

00When the curve BC is reached, Fe 2 C1 6 - 12H 2 0 separates out, and the solution solidifies.

00If, ignoring temporarily and for simplicity the fact that part of the carbon may exist in the state of graphite, we consider the behaviour of iron in cooling from the molten state, AB and BC give the temperature at which, for any given percentage of carbon, solidification begins, and Aa, aB, and Bc that at which it ends.

00BC and OH give the prothe cast iron the properties needed, is brought about chiefly by ferrite into a mixture of adjusting the silicon-content, because the presence of this element favours the formation of graphite.

00Ridgeway, who maintains that the Iron age originated in central Europe, and that iron must consequently have been worked in those regions as far back as C. 2000 BC.

00No siege engines are depicted, even in the time of the Empire,, and the absence of original representations after the XXth Dynasty renders it difficult to judge the advances made in the art of war during the first half of the last millennium Bc. The inscription of Pankhi, however, proves that in the 8th century approaches and towers were raised against the walls of besieged cities Priesthood.The priesthood was in a great degree hereditary, though perhaps not essentially so.

004000-3300 BC.

00Uakim bC All MansCr], 386411 (9961020).

00Mostan~ir bC Tamim Maadd], 427487 (I 0351094).

00Adid bC Mahommed Abdallah], 555567 (I 160-f 171).

002), and fastening a string of length BC to C B Y C and F.

00By adjusting the right ascension of the plane ABC and rotating the axis with the angular velocity of the sun, it follows that BC will be the direction of the solar rays throughout the day.

00X is the mirror rotating about the point E, and placed so that (if EB is the horizontal direction in which the rays are to be reflected) (I) the normal CE to the mirror is jointed to BC at C and is equal in length to BE, (2) the rod DBC passes through a slot in a rod ED fixed to, and in the plane of, the mirror.

00Hence light incident along the direction BC will be reflected along CE.

00AB is the axis of rotation, BC an adjustable FIG.

00The rods BC and DB carry two small rods EF, GF jointed at F; at this joint there is a pin which slides in a slot on the rod BH, which is normal to the mirror X.

00It is easy to show that rays falling on the mirror in the direction BC will be reflected along BD.

00BC, CD..

00BA, BC is represented by 2BH, the tension in BA: tension in BC: weight at B

00as BA: BC: 2BH.

00Hence AD BC are Fm.

00For suppose that in consequence of the displacement a point of the lamina is brought from A to B, whilst the point of the lamina which was originally at B is brought to C. Since AB, BC, are two different positions of the same line in the B C lamina they are equal, and it is evident that the rotation could have been effected by a rotation about J,

00If, AB being held fixed, the 3 quadrilateral be slightly de formed, it is obvious that the instantaneous centre J will - be at the intersection of the - .~ straight lines AD, BC, since s the displacements of the points D, C are necessarily at right angles to AD, BC, respectively.

00parallel to CD, meeting BC, AD in C, D, respectively.

00Thus 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.

00And the force in HA can be resolved into two components acting in BC, CA, respectively.

00If F, Q, R, be any three forces acting along BC, CA, AB, respectively, the line of action of the resultant is determined by the consideration that the sum of the moments about any point on it must vanish.

00Thus ii AB, BC, CD represent the given loads, in the force-diagram, we construct the sides corresponding to OA, OB, OC, OD in the funicular; we then draw the closing line of the funicular polygon, and a parallel OE to it in the force diagram.

00To find the pressure exerted by a bar AB on the pin A we compound with the force in AB given by the diagram a force equal to P. Conversely, to find the pressure of the pin A on the bar AB we must compound with the force given by the diagram a force equal and opposite to P. This question arises in practice in the theory of three-jointed structures; for the purpose in hand such a structure is sufficiently represented by two bars AB, BC. The right-hand figure represents a portion of the force-diagram; in particular ZX represents the pressure of AB on B

00~ Three-dimensional Kinematics of a Rigid Body.The position of a rigid body is determined when we know the positions of three points A, B, C of it which are not colljnear, for the position of any other point P is then determined by the three distances PA, PB, PC. The nine co-ordinates (Cartesian or other) of A, B, C are subject to the three relations which express the invariability of the distances BC, CA, AB, and are therefote equivalent to six independent quantities.

00(usually a~ small circle of the fixed sphere), and join JA, JB, JC, AB, BC

00The spherical A isosceles triangles AJB, BJC are con gruent, and we see that AB can be brought into the position BC by a rotation about the axis OJ through an FIG.

00This is the axis of the required screw; the amount of the translation is measured by the projection of AB or BC or CD on the axis; and the angle of rotation is given, by the inclination of the aforesaid bisectors.

00Hence, resolving along the tangents to the arcs BC, CA, respectively, we have ~ (3)

00the line of intersection (B); the arms (AB,BC) will then be proportional to the respective moments.

00The instantaneous centre of CD will be at the intersection of AD, BC, and if CD be drawn parallel to CD, the lines CC, DD may be taken to represent the virtual velocities of C, D turned each through B a right angle.

00The simplest case is that of a frame of three bars, when the three joints A, B, C fall into a straght line; a small displacement of the joint B at right angles to AC would involve changes in the lengths of AB, BC which are only of the second order of small quantities.

0052, if an infinitesimal deformation is possible without removing the bar CF, the instantaneous centre of CF (when AB is fixed) will be at the intersection of AF and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF.

00be situate at the vertices of a triangle ABC, the mass-centre of ~ and y is at a point A in BC, such that ~.

00If in (2) we put, L, M, N=O we get the case of free rotation; thus A~f=(BC)gr, B~=(CA)rp, (5)

00If we assume P Po cos am (~t+e), q =qo sin am (~it+o), r =To~ am (~t-i--~), (7) we find = ~ ~ = 9rp, i = ~0pg~ (8) Hence (5) will be satisfied, provided u~o BC o-qo CA kfi,r0AB

00The conditions (~) then lead to IA(AC) 2, ,2 (AC)(BC) 1 ~ tO qs B(BC)~ AB r0, C(BC) r~

00from the centre towards G; the angular velocity of the sheave is AC + BC

00Consider the link BC,, and let it be required to find the velocity of the point B having given the velocity of the point C. The principle upon which Engels 05:59, 27 Mar 2006 (PST)D

00From this pole set out Oc to represent the velocity of the point C. The direction of this must be at right angles to the line CD, because this is the only direction possible to the point C. If the link BC moves without turning, Oc will also represent the velocity of the point B; but, if the link is turning, B can only move about the ax~., C, and its direction of motion is therefore at right angles to the line CB.

00123 and 124) is the following: If points X and x are taken dividing the link BC and the tangential velocity cb, sothat cx: xb=CX:XB, then Ox represents the velocity of the point X in magnitude and direction.

00Let A be any origin, and let Ac represent the acceleration of the b point C, Ct the radial acceleration of B about C which must be in a direction parallel to BC, and tb the tan gential acceleration of B about C, C

00This follows by considering equation (4) for the two pairs of colours ac and bc. Until recently no glasses were known with a proportional degree of absorption; but R.

00In order to raise money he plundered a wealthy temple of Bel in Elam, but was killed by the inhabitants, 187 BC. (Diod.

00If four fluids, a, b, c, d, meet in a point 0, and if a tetrahedron AB CD is formed so that its edge AB represents the tension of the surface of contact of the liquids a and b, BC that of b and c, and so on; then if we place this tetrahedron so that the face ABC is normal to the tangent at 0 to the line of concourse of the fluids abc, and turn it so that the edge AB is normal to the tangent plane at 0 to the surface of contact of the fluids a and b, then the other three faces of the tetrahedron will be normal to the tangents at 0 to the other three lines of concourse of the liquids, an the other five edges of the tetrahedron will be normal to the tangent planes at 0 to the other five surfaces of contact.

00There is extant under his name a treatise on the gods and the heroic age, entitled Bc(3XtoOiJKn, a valuable authority on ancient mythology.

00The puddle at a was originally held up by the flat head of this pedestal; not so the puddle at b, which under the superincumbent weight settled down and produced the fault bc, accompanied with a shearing or tangential strain or, less probably, with actual fracture in the direction bd.

00If now we assume the water to have a depth d above the base, the total water pressure represented by the triangle kbh will have its centre at d/3 from the base, and by the parallelogram of forces, assuming the density of the masonry to be 2.5, we find that the centre of pressure upon the base bc is shifted from the centre of the base to a point i nearer to the outer toe c, and adopting our assumption of uniformly varying intensity of stress, the rectangular diagram of pressures will thus be distorted from the figure bfgc to the figure of equal area bjlc, having its centre o vertically under the point at which the resultant of all the forces cuts the base bc. For any lower level the same treatment may, step by step, be adopted, until the maximum intensity of pressure cl exceeds the assumed permissible maximum, or the centre of pressure reaches an assigned distance from the outer toe c, when the base must be widened until the maximum intensity of pressure or the centre of pressure, as the case may be, is brought within the prescribed limit.

0014, water intrudes beneath that part of the masonry more readily than it can obtain egress along bc, or in any other direction towards the outer face, we shall have the uplifting and overturning pressure due to the full depth of water in the reservoir over the width ab added to the horizontal pressure, in which case all our previous calculations would be futile.

00If now a line be drawn from A to the bisector H of the side BC, it will meet the vertical through G in I and IJ =c(cos a+a sin a)/ur.

00Considering the equations ax +by +cz =d, a'x +b'y +c' z =d', a"x+b"y+cnz=d" and proceeding to solve them by the so-called method of cross multiplication, we multiply the equations by factors selected in such a manner that upon adding the results the whole coefficient of y becomes = o, and the whole coefficient of z becomes = o; the factors in question are b'c" - b"c', b"c - be", bc' - b'c (values which, as at once seen, have the desired property); we thus obtain an equation which contains on the left-hand side only a multiple of x, and on the right-hand side a constant term; the coefficient of x has the value a(b'c" - b"c') +a'(b"c - bc") +a'(bc' - b'c), and this function, represented in the form a, b,c, a' b'c', a" b" c" is said to be a determinant; or, the number of elements being 32, it is called a determinant of the third order.

00Moreover, the functions b'c" - b"c', b"c - bc", bc' - b'c used in the process are themselves the determinants of the second order l b",c"I?

00Thus, for three columns, it appears by either rule that 123, 231, 312 are positive; 213, 321, 132 are negative; and the developed expression of the foregoing determinant of the third order is =ab'c" - ab "c'+a'b "c - a'bc" - a"bc' - a"b'c. 3.

00of any couple, AB, for any given limits of temperature is the algebraic sum of the E.M.F.s between the same limits of temperature of the couples BC and CA formed with any other metal C. It is for this reason unnecessary to tabulate the E.M.F.s of all possible combinations of metals, since the E.M.F.

00Evaporation then continues at the constant temperature T, abstracting heat from the substance outside the refrigerator as shown by the line BC. The vapour is then compressed along the line CD to the temperature T2, when, by the action of the cooling water in the condenser, heat is abstracted at constant temperature and the vapour condensed along the line DA.

00In addition, images engraved in walls of what appear to be people infected with polio are found in Egypt dating back to at least 1400 BC.

00But first we must go further back, from Shakespeare at the end of the sixteenth century to Plato around 370 BC.

00The hoard is possibly the imperial regalia of the royal house in East Anglia in the first century BC: the ancestors of Boudica.

00J Jains Followers of Jainism, which is a religion founded in India in the 6th century BC.

00Live media reportage hit the headlines and Hemp BC immediately re-opened for business.

00Dionysius of Halicarnassus First Century BC: Greek rhetorician.

00Around 30 BC she began to rouse only on the night of the full moon.

00Garstang had found a continuous sequence of Egyptian scarabs at the site showing active use until about 1400 BC.

00Even at the budget end of the market, the Northern Diver Sea Eagle BC has n't scrimped on features.

00In 1500 BC in Egypt, a shaved head was considered the ultimate in feminine beauty.

00The Great Sphinx dated to within a few years of 2500 BC.

00Greek bronze statuary: from the beginnings through the fifth century BC.

00By the end of the 3rd century BC mosaics with pebbles were being replaced by those with tesserae made from stone and glass.

00Ca Na Costa This is a stone circle which is believed to be a megalithic tomb dating back to 1600 BC.

00The fashion for architectural vignettes, often employing perspective trickery reached its zenith, however, in the 1st century BC.

00Tamil has an unbroken literary tradition dating back to the third century BC.

00Identifying 3-D plankton from net hauls in the upwelling area near the West coast of Vancouver Is and BC 's north coast.

00By 800 BC society had begun to recover and even grow wealthy.

00The Roman Empire existed from 27 BC to 476 AD.

00Dating back to the Bronze Age (3500-2000 BC), rug making is the most ancient traditions of the Persian culture.

00This technique of creating a targeted fire goes back to the 7th century BC.

00It's origins as a power source can be traced back thousands of years, to as early as 5000 BC.

00Hydropower: Hydropower was first used in 100 BC to turn a waterwheel that turned gears used for grinding grain into flour.

00Some of the earliest turbines date back to 200 BC in Persia (modern day Iran), even older than their famous Dutch counterparts.

00The first reference of the medicinal use of aloe vera was found on Sumarian clay tablets dating from between 2200-1700 BC.

00Another early reference to aloe and its healing properties is found in the Egyptian Papyrus Ebers, the oldest preserved Egyptian medical texts dating from approximately 1500 BC.

00Tibetan herbal medicine is an ancient practice that can trace its roots as far back as 300 BC.

00The first wall stencils, which were made out of leaves, can be seen on cave walls dating to the Paleolithic period (30,000 BC to 9,000 BC).

00In fact, if you take a look at the timeline of skiing, you will see that the earliest skis were discovered in Russia in 6300 BC.

00From 206 to 205 BC, the Han Dynasty ruled in China.

00BC High is a Catholic college-preparatory school for boys.

00Raw BC - Based in British Columbia, Canada, this forum contains lots of local support, as well as forums for recipes and discussion for members worldwide.

00There is early evidence that the caretakers of the Chinese Army's horses used acupuncture as early as 2,000 BC, during the Zang and Chow Dynasties.

00There are also texts about acupuncture for animals that are as old as 221 BC.

00The process originated in Korea around 37 BC, when the excess heat from stoves was used to heat a home's floors.

00Turquoise is the most prominently used gemstone in Native American jewelry, and its use dates to before 200 BC.

00Records of backgammon-like boards and pieces date back as far as 3000 BC, if you can believe that.

00Set in 300 BC in ancient Greece, you were abandoned at birth for an unknown reason.

00M.D., et al. Pediatric Gastrointestinal Disease: Pathophysiology, Diagnosis, Management, 3rd ed. Boston: BC Decker, 2000.

00By 672 BC, the I Ching was growing in popularity and, during the Warring States period of 475-221 BC, was assembled into book form.

00The recovered Ma Wang Dui manuscript, buried in 168 BC, pretty much mirrors the content of the texts that we use today with a few changes in the ordering of the hexagrams.

00Considered by many to be the founder of Taoism, Lao Tzu lived from 604-531 BC.

00Reversible Halter BC Cami: This beautiful cami/tankini is outfitted with a gold ring detail at its center, and this cut-out does much in the way to impart a subtle femininity to the look.

00This was created around 500 BC and is often credited as the official Royal game of India because the story goes that members of royalty often played it on outdoor boards.

00Historians do not know when French kissing specifically started but some of the earlier manuscripts detailing kissing were found in India around 1500 BC.

00She moved to Tampa, the world headquarters for Ironman, Iron Girl and IronKids, from Whistler, BC, a ski resort a future site of the 2010 Winter Olympic Games.

00In ancient Babylon, there was a set list of laws called the "Code of Hammurabi", that dates back to 1700 BC.

00The Epic is an ancient Mesopotamian poem written around 2000 BC.

00Take this BC Footwear's Naughty But Nice shoe in burgundy.

00Playboy, Rampage, Punkrose, Chinese Laundry, Carlos Santana, Sugar, Roca Wear, BC Footwear, and BCBGirls--just to name a few.

00Tribal art can be found as far back as 1500 BC, continuing into more modern times such as some tribes in Africa that were only recently discovered in the 1960s.

00The Greeks first invented a working alarm clock around 250 BC, when they created a water clock, also known as a "clepsydra."

00Ever since the Greek philosopher Plato (428-348 BC) relied on an ancient water alarm clock to signal important events (rumored), people have strived to take control of time.

00It is believed that the idea of progressive resistance dates back to Milo of Croton, a 6th century BC wrestler who lived in a Grecian city in what is now southern Italy.

00Silk was developed in China, perhaps as far back as 200 BC.

00If I Were a Boy was actually written by singer songwriter BC Jean.

00These celebrations actually date back to ancient Babylon around 2000 BC.

00The tradition of celebrating the new year in the spring continued until 153 BC when the Roman senate adopted January 1 as the first day of the new year.

00The use of a baby as a symbol of a new year originated around 600 BC in Greece when Greeks commemorated Dionysus, the god of wine, by displaying a baby as a reminder of rebirth and fertility.

00Although Superman is an American classic, much of the WB series Smallville is shot in British Columbia (BC) near or in Vancouver.

00The long shots of downtown Metropolis are actually downtown Vancouver, BC.

00The Luthor Corporation building exteriors were filmed at the Surrey Central City building in Surrey, BC.

00Downtown Smallville is really Cloverdale, BC, a small, quiet community whose picturesque buildings are representative of an idealized view of small town life.

00With this definition in mind, the history of robots dates back to 270 BC when Ctesibus, an Greek engineer of that time, invented water clocks and organs with movable figures.

00While robotics have been around since 270 BC, the term robot wasn't coined until 1921 when the Czech writer Karel Capek wrote a play called Rossum's Universal Robots, also known as R.U.R.

00Combat helmets have been in use since almost one thousand years BC and have continued throughout history as an important piece of personal protective gear.

00The Binary Cubic.-The complete system consists of f=aa,(f,f')'=(ab)2a b =0 2, (f 0)= (ab) 2 (ca)b c=Q3, x x x x x x and (0,0')2 (ab) 2 (cd) 2 (ad) (bc) = R.

01The Binary Cubic.-The complete system consists of f=aa,(f,f')'=(ab)2a b =0 2, (f 0)= (ab) 2 (ca)b c=Q3, x x x x x x and (0,0')2 (ab) 2 (cd) 2 (ad) (bc) = R.

01Money order cards are very convenient and cheap (up to 10 lire for bc. short private message can be written on them.

02we may write (AB)i(AC)j(BC)k...

02(IV.) and herein writing d 2, -d 1 for x l, x2, 2 (ac) (bc) (ad) (bd) = (bc) 2 (ad) 2 +(ac) 2 (bd) 2 - (ab) 2 (cd) 2.

02For two factors the standard form is (ab) 2; for three factors (ab) 2 (ac); for four factors (ab) 4 and (ab) 2 (cd) 2; for five factors (ab) 4 (ac) and (ab) 2 (ac)(de) 2; for six factors (ab) 6, (ab) 2 (bc) 2 (ca) 2, and (ab) 2 (cd) 2 (ef) 2 .

02To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.

02of 6a 5 bc 2 and 12a 4 b 2 cd we mean the H.C.F.

02is a 4 bc and the L.C.M.

02Thus a(b+c) and (b+c)a give the same result, though it may be written in various ways, such as abdac, ca+ab, &c. In the same way the associative law is that A(BC) and (AB)C give the same formal result.

02Let P, Q denote the normal thrust across the sides bc, ca, and R the normal thrust across the base ab.

02But the faces bc, ca, over which P and Q act, are also equal, so that the pressure on each face is equal.

02represented by a point P, so chosen that the perpendicular Pa on to the side BC gives the percentage of A in the alloy, and the perpendiculars Pb and Pc give the percentages of B and C respectively.

02It will be observed that the areas representing H and W both depend on the form of the path BC, but that the difference of the areas representing the change of intrinsic energy dE is independent of BC, which is a boundary common to both H and W.

02(iii) If = o, so that AD is parallel to BC, it becomes area = 2ah+ 2 (cot cot ct,)h2.

02By drawing Ac and Ad parallel to BC and BD, so as to meet the plane through CD in c and d, and producing QP and RS to meet Ac and Ad in q and r, we see that the area of Pqrs is (x/h - x 2 /h 2) X area of cCDd; this also is a quadratic function of x.

02But the faces bc, ca, over which P and Q act, are also equal, so that the pressure on each face is equal.

02The line BC, representing the equilibrium between monoclinic and liquid sulphur, is thermodynamically calculable; the point B is found to correspond to 131° and 400 atmospheres.

03Notice, therefore, that the symbolic product (ab)i(ac)j(bc)k...

032 (ac)(bc)anx xibn-i -1 x = (bc)2anbn-2Cn-2 + (ac)2an x x x The weight of a term ao°a l l ...an n is defined as being k,+2k2+...

03(ab)(ac)bxcx = - (ab)(bc)axcx = 2(ab)c x {(ac)bx-(bc)axi = 1(ab)2ci; so that the covariant of the quadratic on the left is half the product of the quadratic itself and its only invariant.

03The numerical factor 6 is called the coefficient of a 5 bc 2 (ï¿½ 20); and, generally, the coefficient of any factor or of the product of any factors is the product of the remaining factors.

03of a 5 bc 2 and a 4 b 2 cd.

03= t) 1 v ...axbxcx..., and assert that the symbolic product (ab)i(ac)'(bc)k...aibxc2...

04From the three equations ax = alxl+ a2x2, b.= blxl+b2x2, cx = clxi+c2x2, we find by eliminating x, and x 2 the relation a x (bc)+b x (ca) +c x (ab) =0.

04-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

04From (ac) 2 (bd) 2 (ad)(bc) we obtain (bd) 2 (bc) cyd x +(ac) 2 (ad) c xdx - (bd) 2 (ad)axb x - (ac)2(bc)axbx =4(bd) 2 (bc)c 2.

04-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

04From that vantage point, if you had tried to look fifty years ahead to what the world would be like in the year 2500 BC, you would have expected very little change.

051, Bc) usually typical in form.

08In order that (ab)i(ac)j(bc)k...

08

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