# BC Sentence Examples

- The Third Servile War occurred in the Roman Republic from 73
**BC**to 71**BC**. - (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. - In 58
**BC**, Clodius Pulcher ran on a "free grain for the poor" platform as he tried to become tribune. - For 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.). - 2, let
**BC**be a small portion of any isothermal corresponding to the temperature 0', and AD a neighbouring isothermal 0". - Let 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. - It 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. - Saturated vapour), in which it occupies a volume v", the line
**BC**represents the change of volume (v" - v'). - The 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. - If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.
- If these are first drawn it is easy, for any position of the loads, to draw the lines B'C, B'D, B'E, and to find the sum of the intercepts which is the total bending moment under a load.
- Money order cards are very convenient and cheap (up to 10 lire for
**bc**. short private message can be written on them. - We may write (AB)i(AC)j(
**BC**)k... - (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. - For 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 . - To 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. - (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. - Of 6a 5
**bc**2 and 12a 4 b 2 cd we mean the H.C.F. - Is a 4
**bc**and the L.C.M. - Thus 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. - Let P, Q denote the normal thrust across the sides
**bc**, ca, and R the normal thrust across the base ab. - But the faces
**bc**, ca, over which P and Q act, are also equal, so that the pressure on each face is equal. - Radii 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. - Represented 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. - A 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". - It 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. - Then 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"). - It is not necessary in this example that AB, CD should be adiabatics, because the change of volume
**BC**is finite. - EF 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. - 19) 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. - 7 let base
**BC**=2a, and let h be the distance, measured at right angles to**BC**, from the middle point of**BC**to AD. - Also, let angle ABC =7r - 0, angle
**BCD**=ir - 4, angle between**BC**and AD = G. - (iii) If = o, so that AD is parallel to
**BC**, it becomes area = 2ah+ 2 (cot cot ct,)h2. - By 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. - Thus the interval b'c" with frequencies 495 and 528, giving 33 beats in a second, is very dissonant.
- But the interval b
**bc**" gives nearly twice as many beats and is not nearly so dissonant. - Again b'c" and CG have each 33 beats per second, yet the latter interval is practically smooth and consonant.
- Around 430
**BC**, Athens, embroiled in the Second Peloponnesian War, endured three years of epidemics that wiped out a third of its inhabitants. - If you look back across the span of time, you see wood plows being used in 4000
**BC**, then irrigation five hundred years later. - An iron plow comes three thousand years later in 500
**BC**, along with intensive row cultivation. - The 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. - The septal bars in bulk,
**bc**, coelom. - (ab)i(ac)j(
**bc**)k..., that the symbolic product (ab)i(ac)j(**bc**)k..., possesses the invariant property. - Notice, therefore, that the symbolic product (ab)i(ac)j(
**bc**)k... - Possess the invariant property, and we may write (AB) i (AC)'(
**BC**) k ...A P E B C... - We 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. - 2 (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+... - (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. - X (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,... - The 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. - Of a 5
**bc**2 and a 4 b 2 cd. - Of the base are the projections of the sides AB,
**BC**, CD,. - = t) 1 v ...axbxcx..., and assert that the symbolic product (ab)i(ac)'(
**bc**)k...aibxc2... - From 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. - -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. - From (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. - From 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. - 1,
**Bc**) usually typical in form. - In order that (ab)i(ac)j(
**bc**)k...