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First Year Math Tutorial

Alexis Doval, 27 févr. 2015

Illustrations to accompany the study of Euclid's [i]Elements[/i]

Table des matières

Euclid's Elements - First Semester
1. Elements I.01
2. Elements I.02
3. Elements I.03
4. Elements I.04
5. Elements I.09
6. Elements I.10
7. Elements I.11
8. Elements I.16
9. Elements I.21
10. Elements I.22
11. Elements I.32
12. Elements I.34
13. Elements I.35
14. Elements I.36
15. Elements I.37
16. Elements I.41
17. Elements I.42
18. Elements I.43
19. Elements I.44
20. Elements I.45
21. Elements I.47
22. Elements II.01
23. Elements II.02
24. Elements II.03
25. Elements II.04
26. Elements II.05
27. Elements II.06
28. Elements II.07
29. Elements II.08
30. Elements II.09
31. Elements II.10
32. Elements II.11
33. Elements II.12
34. Elements II.14
35. Elements III.14
36. Elements III.16
37. Elements III.17
38. Elements III.20
39. Elements III.21
40. Elements III.22
41. Elements III.25
42. Elements III.26
43. Elements III.28
44. Elements III.32
45. Elements III.33
46. Elements III.36
47. Elements IV.1
48. Elements IV.2
49. Elements IV.3
50. Elements IV.4
51. Elements IV.5
52. Elements IV.10
53. Elements IV.11
54. Elements IV.12
55. Elements IV.15
56. Elements IV.16
57. Elements VI.1
58. Elements VI.2
59. Elements VI.3
60. Elements VI.4
61. Euclid VI.9
Euclid's Elements - Second Semester
1. Euclid's Extreme and Mean Proportion Constructions
2. Elements 10.6 corollary
3. Euclid Book XI Prop 4
4. Euclid Book XI Prop 5
5. Euclid Book XI Prop 6 & 8
6. Euclid Book XI Prop 9
7. Euclid Book XI Prop 10
8. Euclid Book XI Prop 11
9. Euclid Book XI Prop 15
10. Euclid Book XI Prop 17
11. Euclid Book XI Prop 19
12. Euclid Book XI Prop 20
13. Euclid XI Prop 23
14. Euclid XI Props 29 & 30
15. Euclid Book XII Prop 17
16. Figure for Euclid XIII.3
17. Figure for Euclid XIII.15
18. Cube-Octahedron
19. Octahedron-Cube Inscribed (2)
20. Euclid XIII.18
Ptolemy Almagest
1. Arc and Chord Lengths in a Circle
2. Figure for Almagest I.13.7 - version 2
3. Figure for Almagest I.13.7
4. Ptolemy Almagest - Fig. I.15
5. Ptolemy Almagest - Fig. I.16
General
1. Logarithmic Spiral

Euclid's Elements - First Semester

Illustrations for Books I-IV

Elements I.01

Euclid's Elements - Second Semester

Figures for Euclid's Elements

1. Euclid's Extreme and Mean Proportion Constructions
2. Elements 10.6 corollary
3. Euclid Book XI Prop 4
4. Euclid Book XI Prop 5
5. Euclid Book XI Prop 6 & 8
6. Euclid Book XI Prop 9
7. Euclid Book XI Prop 10
8. Euclid Book XI Prop 11
9. Euclid Book XI Prop 15
10. Euclid Book XI Prop 17
11. Euclid Book XI Prop 19
12. Euclid Book XI Prop 20
13. Euclid XI Prop 23
14. Euclid XI Props 29 & 30
15. Euclid Book XII Prop 17
16. Figure for Euclid XIII.3
17. Figure for Euclid XIII.15
18. Cube-Octahedron
19. Octahedron-Cube Inscribed (2)
20. Euclid XIII.18

Euclid's Extreme and Mean Proportion Constructions

Euclid VI.13 shows how to get a mean proportional to two other lines using a semicircle ADB.[br]Euclid II.11 shows how to cut a single line into extreme and mean proportion using squares AG and AH.[br][br]Sliding point D on the circle produces any number of three lines in extreme and mean proportion, but only when C coincides with M is the diameter cut in extreme and mean proportion.[br][br]Is there a way, using only the circle construction of VI.13, to find where pont M is such that the diameter AB is cut in extreme and mean proportion?

Ptolemy Almagest

Figures for Ptolemy Almagest propositions

1. Arc and Chord Lengths in a Circle
2. Figure for Almagest I.13.7 - version 2
3. Figure for Almagest I.13.7
4. Ptolemy Almagest - Fig. I.15
5. Ptolemy Almagest - Fig. I.16

3.1.

Arc and Chord Lengths in a Circle

General

1. Logarithmic Spiral

4.1.

Logarithmic Spiral

A variation on the classic construction, with adjustable angle and number or radial rays.[br][br]Play and make some pretty things![br][br]But you can also look for exponential patterns.

Logarithmic Spiral

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