CONTENTS OF VOL. I 
I. INTRODUCTORY pages 1-25 
The Greeks and mathematics 1-B 
Conditions favouring development of philosophy among the 
Greeks .......... 8-10 
Meaning and classification of mathematics . . . 10-18 
fa) Arithmetic and logistic ...... 13-16 
(/3) Geometry and geodaesia . . . . . . 16 
(y) Physical subjects, mechanics, optics, &c. . . . 17-18 
Mathematics in Greek education ..... 18-25 
II. GREEK NUMERICAL NOTATION AND ARITHMETICAL 
OPERATIONS 26-64 
The decimal system ........ 26-27 
Egyptian numerical notation ...... 27-28 
Babylonian systems 
(a) Decimal. (/3) Sexagesimal 28-29 
Greek numerical notation 29-45 
(a) The ‘Herodianic’ signs 30-31 
(/3) The ordinary alphabetic numerals . . . 31-35 
(y) Mode of writing numbers in the ordinary alphabetic 
notation . . . . . • • • 36-37 
(S) Comparison of the two systems of numerical notation 37-39 
(f) Notation for large numbers ..... 39-41 
(i) Apollonius’s‘tetrads’ ..... 40 
(ii) Archimedes’s system (by octads) . . . 40-41 
Fractions 
(n) The Egyptian system ...... 41-42 
(/3) The ordinary Greek form, variously written . . 42-44 
(y) Sexagesimal fractions 41-45 
Practical calculation 
(a) The abacus 46-52 
(/3) Addition and subtraction ...... 52 
(y) Multiplication 
(i) The Egyptian method ..... 52-58 
(ii) The Greek method . . • • • 53-54 
(iii) Apollonius’s continued multiplications. . 54-57 
(iv) Examples of ordinary multiplications . . 57-58 
(S) Division 58-60 
(e) Extraction of the square root 60-63 
(£) Extraction of the cube root 63-64