Pietro Antonio Cataldi

Due lettioni, 1613

Pietro Cataldi (April 15, 1548 - February 11, 1626) was an Italian mathematician born and died in the city of Bologna known for his contributions to calculating square roots using arithmetic series.

Although he began his studies in his homeland, he did not study at his prestigious university. In 1569 he began to teach mathematics at the Florence Academy of Design, where he remained until 1570, when he moved to the University of Perugia. At the age of 48, Cataldi returned to Bologna, this time to the University, where he would remain immersed in teaching mathematics and astronomy at the University of Bologna until his death. During his last years he tried, without success, to establish a mathematics academy (a company to which he even dedicated part of his will). He also applied algebraic techniques to the military sphere.

In 1603 he found the sixth and seventh perfect numbers: 2¹⁶(2¹⁷ – 1) = 8,589,869,056 and 2¹⁸(2¹⁹ – 1)= 137,438,691,328.

He wrote important works on arithmetic, number theory (especially on perfect numbers), and algebra. Highlights:

• "Transformatione geometrica" (1611),
• "Trattato del manera brevissimo di trovare la radice quadra delli numeri et regole da approssimarsi di coninuo al vero nelle radici de' numeri non quadrati" (1613),
• "Arithmetic practice" (1617),
• "Operetta di ordinanze quadre" (1618). He also published a commented edition of
• "The Elements" from Euclides.