, p89

​

A

a^3, p89

a^n, p89

Abbasid period, p72

abstruse, p85

abyss, p65

Acropolis building, p78
Aeschylus, God idea of, p81

aether, p69

aggregate, p77, and see Theory of Aggregates, p84,and see groups, p89, sets, p89, aggregate (new number), p75 

Ahmes, p58

Al-Khwarizmi, p72

Alexandrine mathematic, p63

algebra, p71, and see algebra-astronomy (of the Babylonian culture) , p63

alien, p53

Alsidzshi, p72 [citation not found]

Anaximander, p64

Antioch, p72

Apollonius, p69

arabesque, p72

Arabian Culture, p71, p72 and see Arabian schools (early), p71, and see Arabian-Islamic thinkers (mathematics), p63;

and see Arabian indeterminateness and Magian mathematics, p72

Arameans, p63

archaic style, p57

Archimedes, p59, quadrature of the parabola, p69, treatise on the grains of sand, p69, and exhaustion method, p69

Archytas, p66

Aristarchus, p68, and see Aristarchian system, p68

Attica, statuary, p71

Ausdehnungslehre (Grassman), p70

Autumnal cities, p79

 

B

Bach, p62

Baghdad 9th & 10th centuries intellects, p73

Baroque, decorative elements, p87, and see Renaissance into Baroque, p87 and scrollwork of Baroque, p87, mature Baroque, p87
becoming, 53

Beethoven, p81, and see his quartets, p81

being, p53

Bernini, p87

bounding function, p69

bow instruments, p62

Bruno, p56

Buddha, Nirvana of, p81
Byzantium Empire, p72

 

C

Caliphate (and Diocletian’s transformation), p72

canon of the statue, p58

Cardanus, p75 

cartouches, of Baroque p87

cathedrals (and infinity), p68

Cauchy, p73, and see Cauchy’s…limit idea, p86 

Chaldean-Persian school (and Alexandrine astronomy) p68

Chaldean circle division, p63 

chaos, p63

Charlemagne (and Roman Empire), p72

Christianity, p72 

chromatic, p85 
Classical Culture, p72  

co-ordinates, p69

Constantinian high relief, p72

continuum, p66, p77

convergence in infinite series, p85
Copernicus, p68

cosmos, p63

Ctesiphon, p63

cupola, p71

Cusanus, p69

 

D 

D’Alembert, p66

Dante, God idea of, p81 and see his Divina Comedia, p85

de Vinci (Leonardo), p69

Death, p54

Dedekind number bodes, p90 and see his “cut”, p77

definite integral, p75  

deism, p66

delimitation, p80
Desargues, p75 

Descartes (Cartesian coordinates), p61and analysis of the infinite, p66

differential equations, p89,

differential geometry, p75,

Differential principle, p86

Diocletian, p72

Diophantus, p63, and influence of Indian, early Arab, p71

Dipylon pottery, p73  

Direction, p54

Doric order, p58,

Doric temples, p58

draughtsmen, p67   

Dresden Zwinger, p87

Duns Scotus, p72

 

E

ecliptic co-ordinate system (of Babylonian astronomy), p63

Eddas, p88
Edessa, p63

Egyptian temple style, p58, cubic style, p69, mathematics, p63,  water control, p58, administration, p58 calendar, p58, building techniques, p58

Eratosthenes, p69

Euclidean geometry, p59, see Introduction page 42, and see congruence theorem of, p84,

Eudoxus, p66, p69

Euler, p78, and see his treated the differentials as zero, p86 

extension, p56

extension world, p80
 

F

Faust II, p70

Faustian, p68

Fermat, p69 and see his theorem, p76

figure (and northern contrapuntist), p82

fugue, p61

function, p72, p75, functions into infinite series, p75, Infinite series & Newton's binomial, p75, angular functions p74, congruence by angular functions,

                 p85, periodic functions p74, transformation of elliptic & integrals into multiply periodic functions (Abel, Gauss), p85

 

G

Gallileo, p81 

Gauss, p59, and see Gauss (& Euclidean geometry, axiom of parallels), p88

gems, art of the, p84

general integral, p75 

geometrica, p57 

Gluck, p78
Goethe, “mothers”, p70

Gothic cathedrals, p58 and see wall statuary of German cathedrals, p73

Gothic condition, p73

Goths, conquering, p88,

Gundisapora, p63

 

H

hard set, p58

harmony, p63 and see Pythagorean, origins in music, p63

Hayden,   p78

Helmholtz, p64

higher history, p55 

History, p55

homogenous, p77, p89

Hypsicles, p63

 

I

illimitable, p75 

impalpable,  p79

Indian soul (and zero), p66

Indian trigonometry, p84

inexorable, p80
Infinitesimal Calculus, p59

inscribed rectangles, p69

irrational numbers,  p65

 

J

Jansenists, p66

Justinian I, p81

 

K

Kant, sum of human knowledge, p59

Kepler, p71

key, p85 
Klein, p90

 

L

Lagrange, p78

Laplace,   p78

Leibnitz see Introduction p42; and the divine principle, p70, and Calculus, p70, and analysis situ, p70

Leochares, p90

Leucippus, p77

Life, p54

linear continuum, p77 

loci, p69

logarithm, p75, p88

Lysippus, p90

 

M

Magian, p71, and see Arabian culture, p72      

magnitudes, p66

Mandaeanism, p72

Manichaeism, p72

Manifold of points p74, “manifolds” of n p82, and see multi-dimensional space,p88

mathematical images, p89

mathematical number, p57

mechanical demarcation, p57 

Michelangelo (and Early Baroque), p87 

Moorish mosques, p80

mosaic, p71

Mozart, p78
 

N

Nature, p55

Neo-Platonism, p72

Newton, religious nature p71, Infinite series & Newton's binomial, p75 

nexus, p84
non-Archimedean number (number), p65

Non-Euclidean geometry, p67 

nonent, p64

Numbers, p67, imaginary p75, p77 complex numbers, p75, p77; real numbers, p77, irrationals, p77, Napierian base e p74, hypercomplex, p89

number surfaces, p77 

 

O

orchestra, modern p62, see four human voices, p62

Oresme, p67   

 

P

paradigm, p90

parallel axiom, p83

Parthenon sculptures, p81, and see Parthenon, p72

Pascal see Introduction page 42

Pergumum, alter of p85 

Persian Seleucia on Tigris, p68

Persian-Babylonian schools, p63 

perspective, p61 

phrasing, p85 
pi (number), p65

pietist, p66

Plato see Introduction page 9

Plotinus, p56; see God idea of, p81, see Plotinus and early Magian Culture, p72

Polis, p83

polyhedron, regular, page 81

polyphony, p63

Present, p54

proper, p53

pyramid temples, dimensions, p58

Pythagoreans, secret doctrines of, p66, Pythagoras (theorem), p61, Pythagoreans reforms, p83
 

Q

quadratures, p69, and see quadrature of the parabola , p69

quaternions of the calculus of vectors, p89

 

R

Rembrandt, infinity of, p81

Renaissance mathematics (and Classical tendency) p71

Revennate mosaics, p72

Riemann, p61, and see Riemann’s integral, p69, and Riemann (symbolism of the 2 planes) p71 

Rococo of Dresden. Paris, Vienna, p87

Romanesque construction & ornament, p58

Romano-Florentine colonnading & storying, p87

 

S

sarcophagi relief, p58 

Sassanid Empire, p72

second and third powers, p66

Serenus, p63

Sesostris, p81

Seleucus, p68

Soul, p54

space representation, p58 and see space commanding organ, p62

stereometry, p64, and see stereometric, p77

style of knowing, p60

subtilizing, p89

Syriac, p63

 

T

technics, world embracing spatial energy of modern,  p81 
Tema con Variazioni (18th century orchestral form), p84
theology of Counter Reformation, p66

thoroughbass, p61

Timaeus, p66

tone colour and tone effects , p62

totality, p89

transformations of groups, p84
transvalued, p71

 

U

unidimensional, p77

 

V

Vieta ,p71 and algebraic notation, p71

Vignola, early Baroque, p87

Vikings, conquering, p88

vivify, p61

Voltaire, p66

 

W

waking-consciousness, p54

Weierstrass, p62

World, p54

 

X

x + yi, p77

 

Y

Z

Zenodorus, p63