Page:A History Of Mathematical Notations Vol I (1928).djvu/15

1. PARAGRAPHS

2. Double Significance of R and l ................................................................................................................................................................................................................................................................................................................................................................................................

   291

3. Facsimiles of Symbols in Manuscripts ................................................................................................................................................................................................................................................................................................................................................................................................

   293

4. Two General Plans for Marking Powers ................................................................................................................................................................................................................................................................................................................................................................................................

   294

5. Early Symbolisms: Abbreviative Plan, Index Plan ................................................................................................................................................................................................................................................................................................................................................................................................

   295

6. Notations Applied Only to an Unknown Quantity, the Base Being Omitted ................................................................................................................................................................................................................................................................................................................................................................................................

   296

7. Notations Applied to Any Quantity, the Base Being Designated ................................................................................................................................................................................................................................................................................................................................................................................................

   297

8. Descartes’ Notation of 1637 ................................................................................................................................................................................................................................................................................................................................................................................................

   298

9. Did Stampioen Arrive at Descartes’ Notation Independently? ................................................................................................................................................................................................................................................................................................................................................................................................

   299

10. Notations Used by Descartes before 1637 ................................................................................................................................................................................................................................................................................................................................................................................................

    300

11. Use of Hérigone's Notation after 1637 ................................................................................................................................................................................................................................................................................................................................................................................................

    301

12. Later Use of Hume’s Notation of 1636 ................................................................................................................................................................................................................................................................................................................................................................................................

    302

13. Other Exponential Notations Suggested after 1637 ................................................................................................................................................................................................................................................................................................................................................................................................

    303

14. Spread of Descartes' Notation ................................................................................................................................................................................................................................................................................................................................................................................................

    307

15. Negative, Fractional, and Literal Exponents ................................................................................................................................................................................................................................................................................................................................................................................................

    308

16. Imaginary Exponents ................................................................................................................................................................................................................................................................................................................................................................................................

    309

17. Notation for Principal Values ................................................................................................................................................................................................................................................................................................................................................................................................

    312

18. Complicated Exponents ................................................................................................................................................................................................................................................................................................................................................................................................

    313

19. D. F. Gregory’s $(+)^{r}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    314

20. Conclusions ................................................................................................................................................................................................................................................................................................................................................................................................

    315

21. Signs for Roots ................................................................................................................................................................................................................................................................................................................................................................................................

    316–38

22. Early Forms, General Statement ................................................................................................................................................................................................................................................................................................................................................................................................

    316, 317

23. The Sign ℞, First Appearance ................................................................................................................................................................................................................................................................................................................................................................................................

    318

24. Sixteenth-Century Use of ℞ ................................................................................................................................................................................................................................................................................................................................................................................................

    319

25. Seventeenth-Century Use of ℞ ................................................................................................................................................................................................................................................................................................................................................................................................

    321

26. The Sign l ................................................................................................................................................................................................................................................................................................................................................................................................

    322

27. Napier’s Line Symbolism ................................................................................................................................................................................................................................................................................................................................................................................................

    323

28. The Sign √ ................................................................................................................................................................................................................................................................................................................................................................................................

    324–38

29. Origin of √ ................................................................................................................................................................................................................................................................................................................................................................................................

    324

30. Spread of the √ ................................................................................................................................................................................................................................................................................................................................................................................................

    327

31. Rudolff’s Signs outside of Germany ................................................................................................................................................................................................................................................................................................................................................................................................

    328

32. Stevin’s Numeral Root-Indices ................................................................................................................................................................................................................................................................................................................................................................................................

    329

33. Rudolff and Stifel's Aggregation Signs ................................................................................................................................................................................................................................................................................................................................................................................................

    332

34. Descartes' Union of Radical Sign and Vinculum ................................................................................................................................................................................................................................................................................................................................................................................................

    333

35. Other Signs of Aggregation of Terms ................................................................................................................................................................................................................................................................................................................................................................................................

    334

36. Redundancy in the Use of Aggregation Signs ................................................................................................................................................................................................................................................................................................................................................................................................

    335

37. Peculiar Dutch Symbolism ................................................................................................................................................................................................................................................................................................................................................................................................

    336

38. Principal Root-Value ................................................................................................................................................................................................................................................................................................................................................................................................

    337

39. Recommendation of the U.S. National Committee ................................................................................................................................................................................................................................................................................................................................................................................................

    338

40. Signs for Unknown Numbers. ................................................................................................................................................................................................................................................................................................................................................................................................

    339–41

41. Early Forms ................................................................................................................................................................................................................................................................................................................................................................................................

    339