The History of Mathematics: A Brief Course

122 5. COUNTING 20, and there is a cowrie-shell figure standing for zero. The second vigesimal digit in a Maya number should nor ...

WHAT WAS COUNTED? 123 reason for noticing it. Like all stars, Sirius gains about four minutes per day on the Sun, rising a lit ...

124 5. COUNTING The Gregorian calendar. A modification of the Julian calendar was introduced in 1582 on the recommendation of Po ...

WHAT WAS COUNTED? 125 count). This Haab calendar is another point of resemblance between the Maya and Egyptian civilizations. ...

126 5. COUNTING required for the Moon to go halfway from full to new or vice versa. There is another, more plausible, astronomic ...

QUESTIONS AND PROBLEMS 127 the fifte to Venus, the sixte to Mercurius, the seventhe to the mone. And then ageyn the 8 houre is t ...

128 5. COUNTING revolution in 26,000 years) in the direction opposite to the Sun's motion along the ecliptic, a tropical year is ...

Chapter 6. Calculation In the present chapter we are going to look at processes that the modern calcula- tor has rendered obsole ...

130 6. CALCULATION for the result of dividing something in two parts. This linguistic peculiarity sug- gests that doubling is ps ...

EGYPT 131 then move up and mark the next row whose right-hand column contains an entry not larger than this remainder (in this ...

132 6. CALCULATION 1/8 + 1/16 + 1/32 + 1/64 = 63/64, the scribes apparently saw that unity could be restored (approximately), as ...

EGYPT 133 5 3 15^55 30 318 795 7 4 28^57 38 114 9 6 18 59 36 236 531 (^11) 6 66 61 40 244 488 610 13 8 52 104 63 42 126 15 10 ...

134 6. CALCULATION (subtract) parts, what are called hau (or aha) computations by the author, one can confidently attack any ari ...

2 CHINA 135 FIGURE 2. The Shang numerals. call § of a hekat of grain. Since this amount of grain goes into one jug, it follows t ...

136 6. CALCULATION we can illustrate the multiplication 324 · 29 as follows: 324 324 324 24 24 —>6 —>8 7 —>8 7 —>9 1 ...

CHINA 137 With this procedure for reducing fractions to lowest terms, a complete and simple theory of computation with fractio ...

138 6. CALCULATION 2.2. The Jiu Zhang Suanshu. This work is the most fundamental of the early Chinese mathematical classics. For ...

INDIA 139 Chapter 6 ("Fair Transportation") is concerned with the very important prob- lem of fair allocation of the burdens o ...

140 6. CALCULATION example, to do a long division with remainder, say, ^p, he would look for the next number after 22 that divid ...

MESOPOTAMIA 141 first approximation, turns up the number y| as the next approximation. Thus the fraction ^| represents an appr ...