Magic squares
Seven planetary squares. Every row, column and diagonal makes the same total.
Saturn
15target for each line
| Columns, left to right | |||
|---|---|---|---|
| 1 | 2 | 3 | |
| Row 1 | 4 | 9 | 2 |
| Row 2 | 3 | 5 | 7 |
| Row 3 | 8 | 1 | 6 |
Shading follows the selected line.
Row 1
4 + 9 + 2 = 15
Matches 15.Every line agrees
Each number from 1 to 9 appears once. All 8 rows, columns and full diagonals total 15.
All cells total 45.
All lines
The printed page
Transcribed from the 1550 edition’s numeral table, keeping its orientation and repeated numbers. The Hebrew-letter table and seals beside it are separate material.
Why these totals?
A normal square of order n uses 1 through n² once each. Their total is n²(n² + 1) ÷ 2. Divide that equally among n rows to get n(n² + 1) ÷ 2.
Here: 3 × (9 + 1) ÷ 2 = 15. The tool also checks every column, both full diagonals, and that each number appears once.
Agrippa associates these seven orders with planets in Book II, chapter 22. The arithmetic can be checked without him.
Something to try
Open Venus in the 1651 printing. Some lines still give the expected total. Follow row 6 and column 2, then compare the earlier edition. How much of a pattern would you check before trusting it?
Our own study prompt.