... the most economical way to do some task and so on. Perhaps the two most sought after concepts in the history of the subject were the integral and the derivative, as they were a necessity in finding out information needed about the physical world. For example, computation of the derivative could provide the ... the Islamic mathematician Ibn al-Haytham (Alhazen) was the first to derive the formula for the sum of the fourth powers, and using mathematical induction, he developed a method that is readily generalizable to finding the formula for the sum of any integral powers, which was fundame...

• Word Count: 6149
• Approx Pages: 25
• Grade Level: Undergraduate

... Pinckney, who was part of the same party as Adams came in third.  By the laws of the United States, those that won the top two electoral vote totals would be President and Vice President. This result and another confusing election in 1800 led to the 12th amendment in 1804.  The most important part of the 12th amendment is that instead of casting two votes for President, each ... to adding this amendment. The 22nd amendment limits the president to only two 4-year terms in office.  Before the 22nd amendment, Presidents traditionally served two terms, following the example of George Wash...

• Word Count: 2226
• Approx Pages: 9
• Grade Level: Undergraduate

... Seattle, Washington by two young men, Paul Allen and William Henry Gates, III who had a dream of "a computer on every desk and in every home." This revolutionary idea was put into reality by creating a new industry and transforming how we work, live, learn, and play. Microsoft Corporation is the biggest Software Company in America and the 5th largest company in the United States, with ... benefits, and opportunities for customers and partners, openness in discussing our future directions, getting feedback, and working with others to ensure that their products and our platforms work well ...

• Word Count: 1828
• Approx Pages: 7
• Grade Level: Undergraduate

... throughout Christendom renounced property and established quasi-monastic groups which formed the basis of the order of Augustinian Canons. By the middle of the 12th century almost all of these bodies had adopted the Rule of St Augustine. Their rule was officially endorsed by the fourth Lateran Council in 1215. The Augustinian Hermits, or Austin Friars, are an entirely different group ... than once. One reformed congregation of Augustinians in Germany numbered among its members Martin Luther, who later castigated the order. The dissolution of the monasteries in England by Henry VIII inc...

• Word Count: 2701
• Approx Pages: 11
• Grade Level: Undergraduate

... the one before and after. It was during this time that the three voice tradition was replaced by the four part texture we see today (composers would use five, six, or even more voices). At the turn of the fifteenth century composers moved away from counterpoint that involved the piece being built off the ... thirds and sixths. This had its challenges as well as it meant that a fourth, a fifth and a third would be out of tune (Arkenberg 1). Composers experimented with intonation with systems like the mean-tone temperament where fifths were tuned small so thirds could sound well, which dif...

• Word Count: 2548
• Approx Pages: 10
• Grade Level: Undergraduate

... Sri Lanka to be cultivated. - The Padaviya Inscription (12th Century A.D.) This is the story of the Sinhala people working in peace and war under an unbroken monarchy during two millenniums and a half. The story begins with the Neolithic culture represented by the megalithic monuments found in the island, and runs through the fusion of this culture with an immigrant ... , absorbed a number states in the Gangetic valley, built up a powerful military force and organized an efficient administrative system by the close of the fourth century B.C. Alexander left for western Asia, the Indian pr...

• Word Count: 2922
• Approx Pages: 12
• Grade Level: Undergraduate