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Black & White - University of Toronto Libraries

Black & White - University of Toronto Libraries

Black & White - University of Toronto

  • Page 6 and 7: BY THE SAME AUTHORS NUMBERS, VARIAB
  • Page 8 and 9: Qft
  • Page 10 and 11: iv Preface appreciated by all who h
  • Page 12 and 13: " vi Preface the superstructur
  • Page 14 and 15: viii Preface or with any philosophi
  • Page 16 and 17: x Preface science of Quaternions. W
  • Page 18 and 19: xii Preface introduction of a new p
  • Page 20 and 21: xiv Preface tions under which two o
  • Page 23 and 24: CONTENTS. PART I. VARIABLES AND QUA
  • Page 25 and 26: Contents xix Algebra, be complanar.
  • Page 27 and 28: Contents xxi relations. One-valued
  • Page 29 and 30: FUNDAMENTAL CONCEPTIONS OF MODERN M
  • Page 31 and 32: Natural Numbers 3 marking the eradi
  • Page 33 and 34: Denominate Quantities 5 oranges is
  • Page 35 and 36: " " " Value-classes
  • Page 37 and 38: Variables are not Quantities 9 come
  • Page 39 and 40: Arrangement in a Variable 11 value-
  • Page 41 and 42: Arrangement in Point Aggregates 13
  • Page 43 and 44: Order 15 (the "inverse order&q
  • Page 45 and 46: Unifarious Arrangements 17 in Calcu
  • Page 47 and 48: Multifarious Arrangements 19 say th
  • Page 49 and 50: Multiplex Arrangements 21 entered t
  • Page 51 and 52: Constitution of Variables 23 unless
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    Sorts of Quantities 25 them to the

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    Kinds of Quantities 27 1685, and it

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    Varieties of Quantities 29 developi

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    Protomonic and Neomonic 31 ternions

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    Positive and Negative 33 Some moder

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    Ratios and Quotients 35 tertraction

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    " " " " "

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    . . . Unit of a Variety 39 of the m

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    Quantuplicity 41 of an abstract var

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    etc., Numerical Values 43 numerical

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    Natural and Relational Quantities 4

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    Vectors 47 abstract quantities whic

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    Currencies and Magnitudes 49 we wil

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    Null Vectors 51 concurrent. Moreove

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    Quaternions 53 a to b, classing the

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    e a relational quantity. Quaternion

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    Scalars 57 titles ("negative r

  • Page 87 and 88:

    Frege s View of Zeroes 59 tion of o

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    Quantities and Symbols 61 " 1

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    Definition of a Quaternion 63 matic

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    Degraded Quaternions 65 establishme

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    Tensors and Versors 67 quaternions

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    Quadrantal Quaternions 69 It can be

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    Conjugate Quantities 71 its own con

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    " The i, j and k Imaginaries 7

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    Formal and Entitative Algebras 75 r

  • Page 105 and 106:

    Constitution of a Sort 77 abstract

  • Page 107 and 108:

    Constitution of a Kind 79 the condi

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    Formation of Kinds 81 and only that

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    Confluence 83 gives in each case a

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    Selection of Zeroes 85 the Fahrenhe

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    Contrafluence 87 ably be ascribed a

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    The Positives and the Negatives 89

  • Page 119 and 120:

    The Abstract Positives and Negative

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    Single-variety Kinds 93 volumes. Th

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    Single-variety Kinds 95 the includi

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    Schubert on Negative Numbers 97 acc

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    Schubert on Negative Numbers 99 Hav

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    Symbols and Quantities 101 both cas

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    Principle of Permanence 103 ciple,

  • Page 133 and 134:

    Principle of Permanence 105 algebra

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    " Origin of Negative Quantitie

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    Origin of Negative Quantities 109 a

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    Primitive and Complex Kinds 111 the

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    Protomonic and Neomonic Kinds 113 m

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    Protomonic and Neomonic Kinds 115 w

  • Page 145 and 146:

    Protomonic and Neomonic Kinds 117 p

  • Page 147 and 148:

    " Protomonic and Neomonic Kind

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    Arithmetical Algebra 121 ing the sl

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    Single Algebra 123 quantity; and, i

  • Page 153 and 154:

    Double Algebra 125 or complex, notw

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    " " Triple Algebras 127 l

  • Page 157 and 158:

    " Pluquaternions 129 And so we

  • Page 159 and 160:

    " Real and Imaginary Vectors 1

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    Real and Imaginary Vectors 133 thre

  • Page 163 and 164:

    " Biquaternion-s 135 of unknow

  • Page 165 and 166:

    " Biquaternions 137 nation \/

  • Page 167 and 168:

    " " " Biquaternions

  • Page 169 and 170:

    The Work of Argand 141 was supposed

  • Page 171 and 172:

    " The Biquaternions of Cliffor

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    Views now Current about Variables 1

  • Page 175 and 176:

    Newtonian Definitions 147 and unkno

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    " Symbol Definitions 149 i, j,

  • Page 179 and 180:

    " Harnack on Variables 151 def

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    Russell on Variables 153 one were t

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    The Proper Definition 155 ders the

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    Nominalist View of Categories 157 t

  • Page 187 and 188:

    Nominalist View of Definition 159 t

  • Page 189 and 190:

    Progressions 161 and function are b

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    Series 163 type, the only differenc

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    Series 165 to a determined law. The

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    " Multiplex Series 167 to spea

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    Sequences 169 though we do not reca

  • Page 199 and 200:

    Consentaneous Functional Relations

  • Page 201 and 202:

    Functional Relations Factitious 173

  • Page 203 and 204:

    Independent Variables 175 relation

  • Page 205 and 206:

    Independent Variables 177 paragraph

  • Page 207 and 208:

    " Early Views of Functions 179

  • Page 209 and 210:

    " Dirichlet s Definition 181 m

  • Page 211 and 212:

    Dirichlet s Definition 183 interval

  • Page 213 and 214:

    " the function Current Views o

  • Page 215 and 216:

    " Current Views of Functions 1

  • Page 217 and 218:

    Current Views of Functions 189 acco

  • Page 219 and 220:

    Current Views of Functions 191 tion

  • Page 221 and 222:

    The Errors of Riemann 193 though th

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    " The Errors of Riemann 195 do

  • Page 225 and 226:

    The Errors of Riemann 197 assigning

  • Page 227:

    INDEX OF SURNAMES. Alembert, D 181

  • Page 230 and 231:

    INDEX OF TOPICS Functional relation

  • Page 233 and 234:

    FUTURE PARTS OF FUNDAMENTAL CONCEP

  • Page 235 and 236:

    Future Parts of This Work 207 aberr

  • Page 237 and 238:

    Future Parts of This Work 209 PART

  • Page 239 and 240:

    Future Parts of This Work 211 tion.

  • Page 241 and 242:

    Future Ports of This Work 213 at XL

  • Page 243 and 244:

    " Future Parts of This Work 21

  • Page 247:

    QA Richardson, Robert 9 Porterfield