Europe: A History (260 page)

The Christianization of Europe

The Byzantine Empire

Europe’s Cultural Circles: an Interpretation
(after M. Shennan)

The Frankish Empire,
AD
800–77

Khazaria at its Greatest Extent,
c
.
AD
900

The Christian
Reconquista
in Iberia, 850–1493

Numerals and Mathematical Notation
(1)
Numerals:
(
a
) Phoenician (1st millennium
BC
), based on Egyptian hieroglyphic numerals, and similar to the Minoan system, (
b
) Greek (from 350
BC
), a literal system, and a close counterpart to Hebrew numerals, (c) Roman, (
d
) North Indian (Sanskrit, 1st millennium
AD
), (
e
) Eastern Arabic (10th cent.), (ƒ) Iberian Arabic (11th cent.). (
g
) Renaissance calligraphic, (
h
) Modern standard printed numerals. (
i
) Contemporary seven-bar digital. (After F. Cajori, A. Frutiger.)

1      2      3      4      5      6      7      8      9      10      20      100

a
.

b
.

c
.

d
.

e
.

f
.

g
.

h
.