ENGLISH INDEX
583
Gizeh, and Medum 128: measure- 155, 167, 216: construction of
mentof height by Thales 129—30 ; regular pentagon 160-2: astro-
volume of pyramid 176, 180, 217, nomical system (non-geocentric)
ii. 21, &c., volume of frustum ii. 168-5 : definitions 166 : on order
334. of planets ii. 242.
Pythagoras 65—6,121,131,133, 138:
travels 4-5, story of bribed pupil Qay en hem, height (of pyramid)
24—5: motto 25,141: Heraclitus, 127.
Empedocles and Herodotus on, Quadratic equation: solved by Py-
65: Proclus on discoveries of, 84- thagorean application of areas
5, 90,119,141,154: made mathe- 150-2, 167, 394-6, 422-3: nu-
matics a part of liberal education merical solutions ii. 344, ii. 448,
141, called geometry ‘inquiry’ ii. 463-5.
166, used definitions 166 : arith- Qundratrix 2, 23,171,182, 218, 219,
metic (theory of numbers) 66-80, 225-30, ii. 379-82.
figured numbers 76-9: gnomons Quadrivium of Pythagoreans 11.
77, 79: ‘friendly’ numbers 75: Quinary system of numerals 26.
formula for right-angled tri- Quintilian ii. 207.
angles in rational numbers 79- Qusta b. Luqa, translator of Euclid
80: founded theory of proportion 362, ii. 453.
84-5, introduced ‘ perfect ’ pro
portion 86 : discovered depen- Rangabe, A. R. 49-50.
dence of musical intervals on Ratdolt, Erhard, first edition of •
numerical ratios 69, 75—6, 85, Euclid 364-5.
165 : astronomy 162-3, earth Reductio ad absurdum 372 : already
spherical ib., independent move- used by Pythagoreans 168.
ment of planets 67, 163: Theorem Reduction (of a problem) 372.
of Pythagoras 142, 144-9, how Reflection: equality of angles of
discovered ? 147-9, general proof, incidence and reflection 442, ii.
how developed ib., Pappus’s ex- 294, ii. 353-4.
tension ii. 369-71. Refraction 6—7,444: first attempt
Pythagoreans 2, 11, 220: quadri- at a law (Ptolemy) ii. 294.
vium 11: a Pythagorean first Regiomontanus 369, ii. 27, ii. 453-4.
taught for money 22: first to Regula Nicomachi 111.
advance mathematics 66: ‘all Rhabdas, Nicolas, 40, ii. 324 n., ii.
things are numbers’ 67-9 : ‘num- 550-3.
her ’ of an object 69, ‘ number in Rhind Papyrus : mensuration in,
the heaven’ 68: figured numbers 122-8: algebra in, ii. 440-1.
69 ; definition of unit 69: 1 is Right-angled triangle : inscribed
odd-even 71: classification of by Thales in circle 131; theorem
numbers 72-4: ‘ friendly ’ num- of Eucl. I. 47, attributed to
hers 75: 10 the ‘perfect’ number Pythagoras 142, 144-5, supposed
75: oblong numbers 82-3, 108, Indian origin of, 145-6.
114 : side-and diameter-numbers Right-angled triangles in rational
giving approximations to V 2, 91— numbers: Pythagoras’s formula
3: first cases of indeterminate 80, Plato’s 81, Euclid’s 81-2,
analysis 80, 91, 96-7 : sum of 405: triangle (3, 4, 5) known to
angles of triangle = 27?, 135, Egyptians 122: Indian examples
143: geometrical theorems attri- 146: Diophantus’s problems on,
buted to, 143-54: invented appli- ii. 507-14.
cation of areas and geometrical Robertson, Abram, ii. 27.
algebra 150-4: discovered the in- Rodet, L. 234.
commensurable 65, 90-1, 154, Rodolphus Pius ii. 26.
with reference to y2 155, 168: Roomen, A. van, ii. 182.
theory of proportion only ap- Rudio, F. 173, 184, 187-91, ii.
plicable to commensurables 153, 539.
