1. After 2000 BCE the royal capital of Mari flourished. Mari stands not on the southern plain with its highly productive agriculture but much further upstream on the Euphrates.  Here agriculture and animal rearing were carried out close to each other in this region.
2. Herders need to exchange young animals,cheese, leather and meat in return for grain,metal tools, etc., and the manure of a penned flock is also of great use to a farmer. Yet, at the same time, there may be conflict between the regions.
3. In Mesopotamian nomadic communities of the western desert filtered into the prosperous agricultural heartland. Shepherds would bring their flocks into the sown area in the summer.
4. Such groups would come in as herders, harvest labourersor hired soldiers, occasionally become prosperous, and settle down. A few gained the power to establish their own rule. These included the Akkadians, Amorites,Assyrians and Aramaeans.
5. The kings of Mari, however, had to be vigilant; herders of various tribes were allowed to move in the kingdom, but they were watched.The camps of herders are mentioned frequently in letters between kings and officials. In one letter, an officer writes to the king that he has been seeing frequent fire signals at night – sent by one camp to another – and he suspects that a raid or an attack is being planned.
6. Located on the Euphrates in a prime position for trade – in wood,copper, tin, oil, wine, and various other goods that were carried in boats along the Euphrates – between the south and the mineral rich uplands of Turkey, Syria and Lebanon.
7. Boats carrying grinding stones, wood, and wine and oil jars, would stop at Mari on their way to the southern cities. Officers of this town would go aboard, inspect the cargo and levy a charge of about one-tenth the value of the goods before allowing the boat to continue downstream.
8. Thus, although the kingdom of Mari was not militarily strong, but it was exceptionally prosperous.

calar Triple Product

If a, b, c are three vectors, then (a * b) * c is called scalar triple product and is denoted by [a b c].

∴ [a b c] = (a * b) * c

Geometrical Interpretation of Scalar Triple Product

The scalar triple product (a * b) * c represents the volume of a parallelepiped whose coterminous edges are represented by a, b and c which form a right handed system of vectors.

Expression of the scalar triple product (a * b) * c in terms of components

a = a₁i + a₁j + a₁k, b = a₂i + a₂j + a₂k, c = a₃i + a₃j + a₃k is

Properties of Scalar Triple Products

1. The scalar triple product is independent of the positions of dot and cross i.e., (a * b) * c = a * (b * c).

2. The scalar triple product of three vectors is unaltered so long as the cyclic order of the vectors remains unchanged.

i.e., (a * b) * c = (b * c) * a= (c * a) * b
or
[a b c] = [b c a] = [c a b].

3. The scalar triple product changes in sign but not in magnitude, when the cyclic order is changed.

i.e., [a b c] = – [a c b] etc.

4. The scalar triple product vanishes, if any two of its vectors are equal.

i.e., [a a b] = 0, [a b a] = 0 and [b a a] = 0.

5. The scalar triple product vanishes, if any two of its vectors are parallel or collinear.

6. For any scalar x, [x a b c] = x [a b c]. Also, [x a yb zc] = xyz [a b c].

7. For any vectors a, b, c, d, [a + b c d] = [a c d] + [b c d]

8. [i j k] = 1

11. Three non-zero vectors a, b and c are coplanar, if and only if [a b c] = 0.

12. Four points A, B, C, D with position vectors a, b, c, d respectively are coplanar, if and only if [AB AC AD] = 0.

i.e., if and only if [b — a c— a d— a] = 0.

13. Volume of parallelepiped with three coterminous edges a, b,c is | [a b c] |.

14. Volume of prism on a triangular base with three coterminous edges a, b,c is 1 / 2 | [a b c] |.

15. Volume of a tetrahedron with three coterminous edges a, b,c is 1 / 6 | [a b c] |.

16. If a, b, c and d are position vectors of vertices of a tetrahedron, then

Volume = 1 / 6 [b — a c — a d — a].

Let S is the area of the bottom and h is the height of a parallelepiped, then the volume formula is,

V=S×h

Where,
S = Area of the bottom
h = Height

Example Find the volume of the parallelepiped, when 20cm2 is the area of the bottom and 10 cm is the height of the parallelepiped.

Solution:

Given,
Aare of the botton = S = 20cm2
Height = h = 10 cm

Volume formula is: V=S×h 

V=20×10

V=200cm3

Effects of Renaissance

(a) BEGINNING OF MODERN AGE

i) Humanism: Humanism was one of the movements that started in Italy in fourteenth century. Italian universities were centres of legal studies. Francesco Petrarch is known as ‘Father of Humanism’. He suggested a shift from the study of law to the ancient Roman culture and texts. The term ‘humanism’ was first used by Roman lawyer and essayist Cicero. Humanists thought that they were restoring ‘true civilisation’ after centuries of darkness, for they believed that a ‘Dark Age’ had set in after the collapse of the Roman Empire. The period from the fifth to fourteenth centuries was the Middle Ages, and the Modern Age started from fifteenth century.

• Humanistic art: In the fifteenth century, Florence was recognised for its  wo prominent Renaissance men. Dante Alighieri (1265-1321), an eminent poet and philosopher of Italy who wrote on religious themes (he is known for his classic ‘The DIvine Comedy‘), and Giotto (1267-1337), an artist who painted lifelike portraits, very different from the stiff figures done by earlier artists. From then it developed as the most exciting intellectual city in Italy and as a centre of artistic creativity.
• Humanistic literature, Humanities stream: By the early fifteenth century, the term ‘humanist’ was used for masters who taught grammar, rhetoric, poetry, history and moral philosophy. The Latin word humanitas, from which ‘humanities’ was derived, had been used many centuries ago to mean culture. These subjects were not drawn from or connected with religion, and emphasised skills developed by individuals through discussion and debate. Giovanni Boccaccio was the greatest writer and humanist who wrote Decameron. The universities of Padua and Bologna had been centers of legal studies.
• Humanists reached out to people in a variety of ways. Though the curricula in universities continued to be dominated by law, medicine and theology, humanist subjects slowly began to be introduced in schools, not just in Italy but in other European countries as well.

1. Contribution in the Field of  During the Medieval Ages, the work of imparting education to the people was done by the Church. Only the priests were able to read and write they too, provided education to the monks, etc. through the medium of Latin.

2. Contribution in the Field of Drama: In the Medieval age very few people could read. There was very little to read as books were almost scarce. Therefore drama became the most powerful medium of education.Plays in the local dialects were written to entertain as well as to educate the people who did not know Latin.

• Non-Economic Transactions are the transactions that cannot be measured in terms of money, i.e. do not involve receipt or payment.
• It is a non-economic activity because no sale/exchange of goods or services or money is involved. Just the order is placed.

Next to the emperor and the Senate, the other key institution of imperial rule was the army. Romans had a paid professional army where soldiers had to put in a minimum of 25 years of service. The army was the largest single organised body in the empire with 600,000 soldiers in the fourth century. The soldiers would constantly agitate for better wages and service conditions. These agitation often took the form of mutinies.

The emperor, the aristocracy and the army were the three main ‘players’in the political history of the empire. The success of individual emperors depended on their control of the army, and when the armies were divided, the result usually was civil war. Except for one notorious year (69 CE), when four emperors mounted the throne in quick succession, the first two centuries were free from civil war.