Historical Context & Book Introduction

• "The Ground of Arts" - arithmetic book written 1542 by Robert Record
• First book aimed at general public explaining arithmetic in English
• England behind mathematical curve due to breaking from Catholic Church
• Missed Renaissance developments happening in Italy/Europe
• Published just before English Renaissance
• Record added verse bits to make math fun and accessible

Indo-Arabic Numeral System Introduction

• Book introduced new Indo-Arabic numeral system to England
• Place value table showing digits 9,8,7,6,5,4,3,2,1
• Each digit can be placed in any position up to millions/tens of millions
• Major innovation: introduction of zero symbol (circle)

The "Cipher" - Early Name for Zero

• Zero called "Cipher" (spelled "cyph") in 1542
• Not called "zero" (French word appeared ~1650 in England)
• Cipher had mystical connotations - means nothing yet makes numbers big
• French word "chiffre" still means digit
• Shakespeare referenced the "O" shape but cipher was standard term
• No other word existed for zero in late 1500s

Times Tables Technique (6-9 Range)

• Record introduced diagonal line method for difficult multiplication (8×7)
• Process:
  • Draw diagonal lines connecting corners
  • Find number bonds to 10 for each digit
  • Multiply the bond numbers
  • Subtract along chosen diagonal
• Example 8×7: bonds are 2,3 → 2×3=6 → 7-2=5 → answer 56
• Example 8×9: bonds are 2,1 → 2×1=2 → 9-2=7 → answer 72

Mathematical Proof of Technique

• Algebraic explanation for why diagonal method works
• For numbers A×B: uses (10-A) and (10-B)
• Units: (10-A)×(10-B) = 100-10A-10B+AB
• Tens: B-(10-A)×10 = 10B+10A-100
• Combined result cancels to AB (original multiplication)
• Works for any numbers, not just 6-9 range
• Example 5×13: 5+5=10, 13-3=10 → -5×3=-15 → 80-15=65

Long Multiplication Example

• Word problem: 264 men with 29 lambs each
• Shows 264×29 calculation using period methods
• Record crossed out numbers as tracking method
• No carrying notation shown (kept in head)
• Result: 7,656 lambs total
• Missing cipher (zero) in tens place but not needed

Origin of Multiplication Symbol Theory

• No multiplication symbol existed when book written (1542)
• William Oughtred credited with × symbol invention ~1630
• No documented source for where Oughtred got the idea
• Theory: × symbol derived from Record's diagonal line technique
• Big X pattern obvious in times table method
• Miniature version became multiplication symbol
• Not yet official Wikipedia explanation

Shakespeare Connections

• Record's book published ~20 years before Shakespeare's birth
• Shakespeare first generation learning this arithmetic system
• Romeo & Juliet reference: "fight by the book of arithmetic"
• Henry V opening: actor as "crooked figure" (one) with others as "ciphers"
  • Makes million from seven actors (1 + 6 zeros)
• King Lear: references being nothing without figure in front (like 10 without 1)
• Shakespeare excited by cipher concept throughout plays
• Sophisticated mathematical references for the era