# Mathematical Treasure: Manuel Ayala's Elementos de matematicas (Peru)

Author(s):
Frank J. Swetz (The Pennsylvania State University)

Peru achieved independence from Spanish rule in 1821. Elementos de matematicas (Elements of Mathematics), published in 1832, appears to have been written for use in this early period of independence. Its author, Manuel Ayala, identified himself as a presbyter, lay worker of the Catholic Church, Doctor of Mathematics, surveyor, and Professor of Latin—certainly a busy fellow. He wrote this book for the use of the officials of the “battalion” in Cuzco, perhaps the military force occupying this city at this time.

On page 12 of the Elements is a discussion of the operation of addition. A Table of Summation [Facts] is given.

Page 16 introduced multiplication as “repeated addition.” A Table of Multiplication Facts [Pythagorean Table] is given.

On page 113 is a discussion of obtaining the square roots of given numbers employing a variation of “Horner’s Method.” Examples of $\sqrt{54756} = 234$ and $\sqrt{7} = 2.63\,(2.6458)$ are given.

On pages 128 and 129 of the text is a discussion of the “Rule of Three” and the “Inverse Rule of Three.” Simple applications of proportions are used in obtaining the solutions for mercantile problems.

Page 140 explains the “Rule of Company” – that is, the division of a sum among several partners subject to possible mitigating conditions.

This material is obtained through the courtesy of the University of California Libraries. A complete digital copy can be read on the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Manuel Ayala's Elementos de matematicas (Peru)," Convergence (February 2017)