Ars magna, or, The rules of algebra by Girolamo Cardano

By Girolamo Cardano

CARDANO, G.: ARS MAGNA OR the principles OF ALGEBRA. TRANSLATED through T. R. WITMER [1968, REPRINT]. manhattan, manhattan, 1993, xxiv 267 p. figuras.Encuadernacion unique. Nuevo.

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715 116. 212 Solve each problem. 117. The highest temperature ever recorded in Juneau, Alaska, was 90°F. The lowest temperature ever recorded there was - 22°F. What is the difference between these two temperatures? ) 118. On August 10, 1936, a temperature of 120°F was recorded in Ponds, Arkansas. On February 13, 1905, Ozark, Arkansas, recorded a temperature of - 29°F. What is the difference between these two temperatures? ) 119. 35 in his checking account. 00, which overdraws his account. 50. 27 from his part-time job at Arby’s.

3 25 6 3 6 3 6 (a) 3 # 3 = 3 squared, or 32 # (b) 6 6 # 6 = 6 cubed, or 63 FIGURE 17 NOW TRY EXERCISE 2 EXAMPLE 2 Evaluate. (a) 72 (b) 1- 722 2 (c) - 7 Evaluate. (a) 52 = 5 # 5 = 25 52 means 5 2 3 2 (b) a b = 3 3 (c) 2 6 = 2 (d) 1- 325 Evaluating Exponential Expressions 5 is used as a factor 2 times. # 5, NOT 5 # 2. # 2 3 # 2 8 = 3 27 #2#2#2#2# 2 3 is used as a factor 3 times. 2 = 64 = 1- 321- 321- 321- 321- 32 = - 243 The base is - 3. (e) 1- 226 = 1- 221- 221- 221- 221- 221- 22 = 64 (f ) The base is - 2.

A is positive for all positive numbers a. Concept Check In Exercises 11 and 12, evaluate each exponential expression. (b) - 82 82 11. (a) (c) 1- 822 (b) - 43 12. (a) 43 (d) - 1- 822 (c) 1- 423 (d) - 1- 423 Write each expression by using exponents. See Example 1. # 13. 10 16. 3 2 19. z # 10 # 10 # 10 14. 8 3 2 #8# 8 15. 17. 1- 921- 921- 92 #z#z#z#z#z# z 20. a 3 4 # 3 4 # 3 4 # 3 4 # 3 4 18. 1- 921- 921- 921- 92 #a#a#a# a Evaluate each expression. See Example 2. 21. 42 22. 2 4 23. 283 24. 913 1 3 25.

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