Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Annotated square root computation in Liber Abaci and De Practica Geometrie by Fibonacci

Trond Steihaug

Abstract

We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. We annotate a translation of Liber Abaci based on transcripts from 1857 and 2020 and a translation from 2002 and a transcription of De Practica Geometrie from 1862 and a translation from 2008. We show that Fibonacci is demonstrating the same method for all examples in the MSS and that this method deviates from the traditional description of the digit--by--digit method. The description of the method used by Fibonacci is all verbal and summarized in tables for each square root example. The manuscripts and transcription of the Latin texts are incomplete for some of the examples and the transcription and translation contains minor discrepancies and some of the tables are incomplete and the missing digits are inserted.

Annotated square root computation in Liber Abaci and De Practica Geometrie by Fibonacci

Abstract

We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. We annotate a translation of Liber Abaci based on transcripts from 1857 and 2020 and a translation from 2002 and a transcription of De Practica Geometrie from 1862 and a translation from 2008. We show that Fibonacci is demonstrating the same method for all examples in the MSS and that this method deviates from the traditional description of the digit--by--digit method. The description of the method used by Fibonacci is all verbal and summarized in tables for each square root example. The manuscripts and transcription of the Latin texts are incomplete for some of the examples and the transcription and translation contains minor discrepancies and some of the tables are incomplete and the missing digits are inserted.
Paper Structure (24 sections, 27 equations, 22 figures)

This paper contains 24 sections, 27 equations, 22 figures.

Table of Contents

  1. Introduction
  2. The integer part and notation
  3. Integer part of the square root
  4. The annotation
  5. Square root computation in Liber Abaci
  6. Liber Abaci $\sqrt{743}$
  7. Liber Abaci $\sqrt{8754}$
  8. Liber Abaci $\sqrt{12345}$
  9. Liber Abaci $\sqrt{927435}$
  10. Liber Abaci $\sqrt{7234}$
  11. Square root computation in De Practica Geometrie
  12. De Practica Geometrie $\sqrt{153}$
  13. De Practica Geometrie $\sqrt{864}$
  14. De Practica Geometrie $\sqrt{960}$
  15. De Practica Geometrie $\sqrt{1234}$
  16. ...and 9 more sections

Figures (22)

  • Figure 1: Notation used in Hughes2008 to illustrate the square root of 864.
  • Figure 2: The actual computation of $\sqrt{864}$.
  • Figure 3: Notation used in the paper and illustration from Folie 12r of MS Urb. lat. 292 in Città del Vaticano, Biblioteca Apostolica Vaticana.
  • Figure 5: The first digit and the remainder in their correct column and row positions in Fibonacci's example for $\sqrt{743}$ in Liber Abaci
  • Figure 6: The final figure in Fibonacci's example for $\sqrt{743}$ in Liber Abaci.
  • ...and 17 more figures