Franklin, B., On m. as a logical exercise 1303
Franklin, B., On the excellence of m. 324
Franklin, B., On the value of the study of m. 323
Franklin, F., On Sylvester’s weakness 1033
Frederick the Great, On geometry 1860
Freedom in m. 205—208 805
French m. 1210
Fresnel 662
Frischlinus 1801
Froebel, M. a mediator between man and nature 262
Function theory 709 1732 1754 1755
Functional exponent 1210
Functionality, Correlated to life 272
Functionality, The central idea of modern m. 254
Functions 1932 1933
Functions, Concept not used by Sylvester 1034
Fundamental concepts Chapter XX
Fuss, On Euler’s Tentamen novae theorae muskae 966
Galileo, On authority in science 1628
Galton 838
Gauss, And Newton compared 827
Gauss, Hia Disquisitiones Arithmeticae 1639 1640
Gauss, His estimate of Newton 1029
Gauss, His favorite pursuits 970
Gauss, His motto 649
Gauss, His power 964
Gauss, His style and method 983
Gauss, Lectures to three students 974
Gauss, M. and experiment 1531
Gauss, M. the queen of the sciences 1642
Gauss, Mere math’ns 820
Gauss, On imaginaries 1730
Gauss, On infinite magnitude 1960
Gauss, On non-euclidean geometry 2023—2028
Gauss, On number theory 1644
Gauss, On the advantage of new calculi 1215
Gauss, On the nature of space 2034
Gauss, On the notation sin V 1886
Gauss, The first of theoretical astronomers 971
Gauss, The greatest of arithmeticians 971
Gauss, The math, giant 972
Generalization in m. 245 246 252 253 327 728
Genius 819
Geometrical investigations 642 643
Geometrical training, Value of 1841 1842 1844—1846
Geometry Chapter XVIII
Geometry, A mechanical science 1865
Geometry, A natural science 1866
Geometry, Advantage of modem over ancient 711 712
Geometry, An excellent logic 428
Geometry, and algebra 525—527
Geometry, And analysis 1931
Geometry, And arithmetic 1604
Geometry, And experience 1814
Geometry, And music 965
Geometry, And observation 1830
Geometry, And patriotism^ 332
Geometry, Bacon s definition of 106
Geometry, Controversy in 1859
Geometry, Halsted’s definition of 1815
Geometry, Is figured algebra 1706
Geometry, Lack of concreteness 710
Geometry, Name inapt 1801
Geometry, Not an experimental science 1867
Geometry, Plato’s view of 429
Geometry, Should come before algebra 1767 1871 1872
Geometry, Sylvester’s definition of 110
Geometry, The fountain of all thought 451
Geometry, Value to mankind 332 449
Germain, Algebra is written geometry 1706
Gilman, Enlist a great math’n 808
Glaisher, On the expansion of the field of m. 634
Glaisher, On the importance of a well-chosen notation 634
Glaisher, On the importance of broad training 623
Glaisher, On the invention of logarithms 1616
Glaisher, On the need of text-books on higher m. 635
Glaisher, On the perfection of math, productions 649
Glaisher, On the theory of numbers 1640
Goethe, Estimate of m. 311
Goethe, His aptitude for m. 976
Goethe, M. an organ of the higher sense 273
Goethe, M. like dialectics 1307
Goethe, M. opens the fountain of all thought 461
Goethe, Math’ns bear semblance of divinity 804
Goethe, Math’ns like Frenchmen 813
Goethe, Math’ns must perceive beauty of truth 803
Goethe, On the exactness of m. 228
Goethe, On the infinite 1957
Golden age of m. 701 702
Golden age of m. Of art and m. coincident 1134
Gordan, When a math, subject is complete 636
Gow, Origin of Euclid 1832
Gower 1808
Grammar and m. compared 441
Grandeur of m. 325
Graphic method 1881
Graphomath 2101
Grassmann, Definition of equality 106
Grassmann, Definition of m. 106
Grassmann, Definition of magnitude 106
Grassmann, On rigor in m. 638
Grassmann, On the value of m. 1612
Greek view of science 1429
Growth of m. 209 211 703
Gtroup, Notion of 1751
Hailer, On the infinite 1968
Hailey, On Cartesian geometry 716
Hall and Stevens, On the parallel axiom 2008
Hall, G. S., M. the ideal and norm of all careful thinking 304
Halsted, And Slyvester 1031 1032
Halsted, Definition of geometry 1816
Halsted, On Bolyai 924—926
Halsted, On m. as logic 1306
Halsted, On Sylvester 1030 1039
Hamilton, Sir William, His ignorance of m. 978
Hamilton, W. R., Discovery in light 1558
Hamilton, W. R., Estimate of Comte’s ability 943
Hamilton, W. R., Importance of his quaternions 333
Hamilton, W. R., On algebra as the science of time 1716 1716
Hamilton, W. R., On quaternions 1718
Hamilton, W. R., On trisection of an angle 2112
Hamilton, W. R., To the memory of Fourier 969
Hankel, Ancient and modem m. compared 718 720
Hankel, Characteristics of modern m. 728
Hankel, Definition of m. 114
Hankel, Euclid the only perfect model 1822
Hankel, Modem geometry a royal road 1878
Hankel, On aim in m. 608
Hankel, On Descartes 949
Hankel, On Euler’s work 966
Hankel, On freedom in m. 206
Hankel, On geometry 714
Hankel, On irrationals and imaginaries 1729
Hankel, On isolated theorems 621
Hankel, On philosophy and m. 1404
Hankel, On tact in m. 622
Hankel, On the origin of algebra 1736
Hankel, On the origin of m. 1412
Hankel, On the permanency of math, knowledge 216
Hankel, Variability the central idea in modern m. 720
Harmony 326 1208
Harris, M. gives command over nature 434
Hathaway, On Sylvester 1036
Heat, M. and the theory of 1552 1553
Heath, Character of Archimedes work 913
Heaviside, The place of Euclid 1828
Hebrew and Latin races, Aptitude for m. 838
Hegel 1417
Heiss, Famous anagrams 2066
Heiss, Reversible verses 2066
| Helmholtz A non-euclidean world 2029
Helmholtz On geometry 1836
Helmholtz On the importance of the calculus 1939
Helmholtz, Clifford on 979
Helmholtz, M. and applications 1446
Helmholtz, M. requires _ perseverance and great caution 240
Helmholtz, M. should take more important place in education 441
Helmholtz, M. the purest form of logical activity 231
Helmholtz, M. the purest logic 1302
Herbart, Definition of m. 117
Herbart, If philosophers understood m. 1416
Herbart, M. and invention 406
Herbart, M. and philosophy 1408
Herbart, M. and psychology 1683 1684
Herbart, M. indispensable to science 1602
Herbart, M. the chief subject for common schools 432
Herbart, M. the greatest blessing 1401
Herbart, M. the predominant science 209
Herbart, M. the priestess of definiteness and clearness 217
Herbart, On aptitude for m. 609
Herbart, On imagination in m 267
Herbart, On the importance of checks' 230
Herbart, On the method of m. 212 1676
Herbart, On the teaching of m. 616
Herbart, On trigonometry 1884
Hermite, On Cayley 936
Herschel, M. and astronomy 1664
Herschel, On probabilities 1692
Hiero 903 904
Higher m., Mellor’s definition of 108
Hilbert, On arithmetical symbols 1627
Hilbert, On nan-euclidean geometry 2019
Hilbert, On rigor in m. 637
Hilbert, On the abstract character of m. 638
Hilbert, On the importance of problems 624 628
Hilbert, On the nature of m. 266
Hilbert, On the solvability of problems 627
Hilbert, Problems should be difficult 629
Hill, Aaron, On Newton 1009
Hill, Thomas, A geometer must be tried by his peers 843
Hill, Thomas, Estimate erf Newton’s work 333
Hill, Thomas, M. and miracles 2167 2168
Hill, Thomas, M. expresses thoughts of God 275
Hill, Thomas, Math, language untranslatable 1210
Hill, Thomas, Math’ns difficult to judge 841
Hill, Thomas, Math’ns indifferent to ordinary interests of life 842
Hill, Thomas, On Bernoulli’s spiral 922
Hill, Thomas, On geometry and literature 1847
Hill, Thomas, On m. as a language 1209
Hill, Thomas, On mathesis ana poetry 1126
Hill, Thomas, On poesy and m. 1126
Hill, Thomas, On quaternions 1719
Hill, Thomas, On the imaginary 1734
Hill, Thomas, On the spirit of mathesis 274
Hill, Thomas, Value of m. 332
Hindoos, Grandest achievement of 1615
History and m. 1599
History of m. 615 616 625 635
Hobson, A great math’n a great artist 1109
Hobson, Definition of m. 118
Hobson, Functionality the central idea of m. 264
Hobson, On m. and science 1608
Hobson, On the growth of m. 703
Hobson, On the nature of m. 262
Hobson, On theoretical investigations 663
Hoffman, Science and poetry not antagonistic 1122
Holzmuller, On the teaching of m. 618
Homer’s method 1744
Hooker 1432
Hopkinson, M. a mill 239
Howison, Definition of arithmetic 1612
Howison, Definition of m. 134 136
Hudson, On the teaching of m. 612
Hughes, On science for its own sake 1646
Humboldt, M. and astronomy 1667
Hume, Objection to abstract reasoning 1941
Hume, On certainty in m. 1863
Hume, On geometry 1862
Hume, On the advantage of math, science 1438
Humor in m. 539
Hutton, On Bernoulli 919
Hutton, On Euler’s knowledge 968
Hutton, On the method of fluxions 1911
Huxley, Negative qualities of m. 260
Hyper-space 2030 2031 2033 2036—2038
Hyperbolic functions 1929 1930
Ignes fatui in m. 2103
Ignorabimus, None in m. 627
Ignorance of m. 310 331 807 1537 1577
Imaginaries 722 1729—1735
Imagination in m. 246 251 253 256—258 433 1883
Importance of concept of 727
Importance of concept of Forsyth on 1747
Importance of concept of Keyser on 1748
Importance of concept of Lie on 1752
Importance of concept of Sylvester on 1742
Improvement of elementary m. 617
Incommensurable numbers, contingent truths like 1966
Indian m. 1736 1737
Induction in m. 220—223 244
Induction in m. and analogy 724
Infinite collection, Definition of 1959 1960
Infinite divisibility 1945
Infinitesimal Analysis 1914
Infinitesimals 1905—1907 1940 1946 1954
Infinitum, Ad 1949
Infinity and infinite magnitude 723 928 1947 1948 1950 1958
Integers, Kronecker on 1634 1635
Integral numbers, Minkowsky on 1636
Integrals, Invention of 1922
Integration 1919—1921 1923 1925
International Commission on m. 601 602 938
Intuition and deduction 1413
Invariance, Correlated to life 272
Invariance, Keyser on 1749
Invariance, MacMahon on 1746
Invariants, Changeless in the midst of change 276
Invention in m. 251 260
Inverse process 1207
investigations (see Research)
Irrationals 1729
Isolated theorems in m. 620 621
Jacobi, Aphorism 1636
Jacobi, Die “Ewige Zahl 1643
Jacobi, His talent for philology 980
Jefferson, Om m. and law 1697
Johnson, Aptitude for numbers 1617
Johnson, His recourse to m. 981
Johnson, On round numbers 2137
Journals and transactions 635
Jowett, M. as an instrument in education 413
Judgment, M. requires 823
Jupiter’s eclipses 1544
Justitia, The goddess 824
Juvenal, Nemo mathematicus etc. 831
Kant, Doctrine of space 2003
Kant, Doctrine of time 2001
Kant, Esthetic elements in m. 1862 1863
Kant, His view of m. 1436 1437
Kant, M. follows the safe way of science 201
Kant, M. the embarrassment of metaphysics 1402
Kant, On m. and science 1608
Kant, On m. in primary education 431
Kant, On the a priori nature of m. 130
Kant, On the difference between m. and philosophy 1436
Kant, On the origin of scientific m. 201
Karpinsky, M. and efficiency 1673
Kasner, On modem geometry 710
Kasner, “Divinez avant de demontrer” 630
Kelland, On Euclid’s elements 1817
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