- Page 1:
THEORETIC ARITHMETIC IN THREE BOOKS
- Page 4 and 5:
IV INTRODUCTION the mathematical di
- Page 6 and 7:
INTRODUCTION works, like the remain
- Page 8 and 9:
VIII INTRODUCTION fore, that the so
- Page 10 and 11:
INTRODUCTION the other of such as a
- Page 12 and 13:
XII INTRODUCTION must her inherent
- Page 14 and 15:
XIV INTRODUCTION principles existin
- Page 16 and 17:
XVI INTRODUCTION indissoluble perma
- Page 18 and 19:
XVIII INTRODUCTION mathematics to p
- Page 20 and 21:
XX INTRODUCTION utility it administ
- Page 22 and 23:
XXII INTRODUCTION may not energize
- Page 24 and 25:
INTRODUCTION tradition, however, of
- Page 26 and 27:
XXVI INTRODUCTION Nicomachus, which
- Page 28 and 29:
INTRODUCTION perplexity, and that h
- Page 30 and 31:
INTRODUCTION ever, requisite that w
- Page 32 and 33:
XXXII INTRODUCTION that he is ignor
- Page 34 and 35:
XXXIV INTRODUCTION tirely the prais
- Page 37 and 38:
THEORETIC ARITHMETIC BOOK ONE CHAPT
- Page 39 and 40:
that all motion is after rest, and
- Page 41 and 42:
since it is not possible for divisi
- Page 43 and 44:
dle. And these indeed are the commo
- Page 45 and 46:
monad is either even or odd. It can
- Page 47 and 48:
is denominated the evenly-odd, and
- Page 49 and 50:
terms should accord with its proper
- Page 51 and 52:
ural order, 1.3.5.7.9.11.13.15.17.
- Page 53 and 54:
agreeably to the form of the evenly
- Page 55 and 56:
12, 20, and 28, the sum of the extr
- Page 57 and 58:
numbers proceeding from them are re
- Page 59 and 60:
THE generation however and origin o
- Page 61 and 62:
ever will give the mode of measurin
- Page 63:
THE SIEVE OF ERATOSTHENES. Here 7 m
- Page 66 and 67:
pass the sum of the whole number, i
- Page 68 and 69:
CHAPTER XV. On the generation of th
- Page 70 and 71:
CHAPTER XVI. On relative quantity,
- Page 72 and 73:
consequent order, these even number
- Page 74 and 75:
For the sesquialter has for its lea
- Page 76 and 77:
CHAPTER XIX. That the multiple is m
- Page 78 and 79:
which 4 is, is compared with the ro
- Page 80 and 81:
number besides containing the whole
- Page 82 and 83:
superquadripartient, may likewise b
- Page 84 and 85:
to them, duple sesquiquartan ratios
- Page 86 and 87:
the impression of itself, defines a
- Page 88 and 89:
If, however, the multiples which ar
- Page 90 and 91:
tan, the superquadripartient ratio
- Page 93 and 94:
BOOK TWO CHAPTER I. How all inequal
- Page 95 and 96:
BOOK Two 57 reduced to equality. Fo
- Page 97 and 98:
BOOK Two 59 alters as much distant
- Page 99 and 100:
BOOK Two 61 ratio is composed from
- Page 101 and 102:
BOOK Two CHAPTER IV. On the qztanti
- Page 103 and 104:
BOOK Two 65 distended by a triple d
- Page 105 and 106:
These triangular numbers are genera
- Page 107 and 108:
BOOK Two 69 But in these numbers al
- Page 109 and 110:
BOOK Two 71 triangle of a class imm
- Page 111 and 112:
BOOK Two 73 22 is formed from the s
- Page 113 and 114:
BOOK Two 75 third, a pentagonal; th
- Page 115 and 116:
Two does not only not arrive at uni
- Page 117 and 118:
BOOK Two 79 to have four angles and
- Page 119 and 120:
BOOK Two 81 parity. Hence, in conse
- Page 121 and 122: BOOK Two 83 the principles of thing
- Page 123 and 124: BOOK Two 85 from the monad, are sai
- Page 125 and 126: pared with the first number longer
- Page 127 and 128: BOOK Two 89 and twice 16, has for i
- Page 129 and 130: atios. Let them, therefore, be alte
- Page 131 and 132: BOOK Two 93 ity. For 1 is the whole
- Page 133 and 134: BOOK Two 95 ticipate of an immutabl
- Page 135 and 136: BOOK Two 97 are opposite to those a
- Page 137 and 138: BOOK Two is equal to the sum of the
- Page 139 and 140: BOOK Two 101 will be the same multi
- Page 141 and 142: BOOK Two 103 terms there is a great
- Page 143 and 144: BOOK Two 105 from 8, and one side f
- Page 145 and 146: BOOK Two 107 by the greater, by the
- Page 147 and 148: BOOK Two 109 tertian ratio, or that
- Page 149 and 150: BOOK Two 111 ratio, arises from a c
- Page 151 and 152: BOOK Two 113 to 10 is a quadruple r
- Page 153 and 154: BOOK Two 115 For here the greatest
- Page 155 and 156: BOOK Two 117 by length, breadth, an
- Page 157 and 158: BOOK Two The greatest harmonies. Pr
- Page 159 and 160: BOOK Two 121 which is 18416, we mus
- Page 161 and 162: BOOK Two former diameter, exceeds i
- Page 163 and 164: BOOK Two In the geometrical fractio
- Page 165 and 166: BOOK Two The parts of 51=17)
- Page 167 and 168: BOOK Two 129 In the second place, i
- Page 169 and 170: BOOK Two them; (see Chap. 15, Book
- Page 171: BOOK Two 133 of this series into th
- Page 175 and 176: BOOK Two 137 Hence it appears that
- Page 177 and 178: BOOK Two CHAPTER XL On another spec
- Page 179 and 180: BOOK Two 141 remainder is 383. But
- Page 181 and 182: BOOK Two 143 In the fourth place th
- Page 183 and 184: BOOK Two And these expressions when
- Page 185 and 186: BOOK Two 147 Divisors, with the add
- Page 187 and 188: BOOK Two 149 is generated by man, t
- Page 189 and 190: ROOK Two dissimilating, increasing
- Page 191 and 192: BOOK Two 153 Again, when he says, "
- Page 193 and 194: BOOK Two 155 have a contrary nature
- Page 195 and 196: BOOK Two If three gnomons of square
- Page 197 and 198: BOOK THREE CHAPTER I On the manner
- Page 199 and 200: mon the term first is adapted to al
- Page 201 and 202: sav7ov. Syrianus adds, "But Philola
- Page 203 and 204: from the art which he possesses, fa
- Page 205 and 206: val things without interval are the
- Page 207 and 208: intellect, male and female, God, an
- Page 209 and 210: y Styx, viz. they continue through
- Page 211 and 212: for they say that the monadic natur
- Page 213 and 214: parent. Of figures, likewise, those
- Page 215 and 216: the duad was called indefinite and
- Page 217 and 218: ina, Triton, and the perfect of the
- Page 219 and 220: ner (than the triad,) a manifold, o
- Page 221 and 222: Pythagoreans every number, because
- Page 223 and 224:
analogy or proportion comprehends t
- Page 225 and 226:
The fifth is of figures. The sixth
- Page 227 and 228:
consequence of moving circularly* a
- Page 229 and 230:
Iie further informs us, that they d
- Page 231 and 232:
tion of parts, and is more properly
- Page 233 and 234:
With respect to the appellation tru
- Page 235 and 236:
"The heptad is called Minerva, beca
- Page 237 and 238:
ooddess, and this, as Proclus infor
- Page 239 and 240:
as far as to the monad which is nat
- Page 241 and 242:
this I suppose he alludes to the eq
- Page 243 and 244:
xav~a apt0~ov 89' eau709.) Proclus
- Page 245 and 246:
lastly, according to Chalcidius on
- Page 247 and 248:
8~ 1 and +1= 9 the second ) 8X 7 an
- Page 249 and 250:
"Hence it is the first number of wh
- Page 251 and 252:
tion of 2 to itself, as by the mult
- Page 253 and 254:
any triangular gnomon, and unity is
- Page 255 and 256:
have a masculine property.* The mal
- Page 257 and 258:
6X 1 and +1= 7 the 2ndj 6X 7 and +1
- Page 259 and 260:
ers is also most musical. For 6 has
- Page 261 and 262:
that which is generated, in order t
- Page 263 and 264:
whole body, which extends to four t
- Page 265 and 266:
anged in seven orders, exhibit an a
- Page 267 and 268:
ody; but from the reason of the imm
- Page 269 and 270:
est boundary of the duration in the
- Page 271 and 272:
19; for the sum of these is 64. And
- Page 273 and 274:
9X 1 and +1= 10 the 2nd 9 x 10 and
- Page 275 and 276:
Egyptians that the death of Osiris
- Page 277 and 278:
ADDITIONAL NOTES P. 3. The motion o
- Page 279 and 280:
geometry and masic, which are prior
- Page 281 and 282:
Such therefore is the doctrine of t
- Page 283 and 284:
For the purpose of facilitating the
- Page 285 and 286:
from the triangle above it, and thr