Euclid's CatasQI

Here we list all 48 2D constructions from the first six books of Euclid. To view them, you may (eventually) choose any of four formats:
  • [HTML]: This is a totally hypermedia version, using HTML FRAMES. It will appear in your Web browser as a sequence of English phrases (taken from Heath's 1908 translation of Euclid) on the left. Clicking one brings up the illustration which goes with it, on the right side of the browser.
  • [PDF]: Textbook style presentation, Euclid's text appears alongside our new illustrations, in Adobe Acrobat Reader. The time to download PDF is much longer than that of the HTML version.
  • [GIF]: The figures without the text, appears as a flip-book animation in your browser. A fast reminder of the construction.
  • [SWF]: Like the GIF format, but appears in the Macromedia Shockwave Plugin Player.

Book I: 14 Constructions, C#1 to C#14 (148 pages, 293 figures)
C#01 < p.01.01: To draw an equilateral triangle (vesica piscis)
2 pages, 6 figures [HTML] [PDF] [GIF] [SWF]
C#02 < p.01.02: To move a line
8 pages, 13 figures [HTML] [PDF] [GIF] [SWF]
C#03 < p.01.03: To move a line onto a line
8 pages, 14 figures [HTML] [PDF] [GIF] [SWF]
C#04 < p.01.09: To bisect an angle
6 pages, 12 figures [HTML] [PDF] [GIF] [SWF]
C#05 < p.01.10: To bisect a line
4 pp., 10 figs. [HTML] [PDF] [GIF] [SWF]
C#05B < p.01.10: To bisect a line (alternate construction)
4 pp, 5 figs [HTML] [PDF] [GIF] [SWF]
C#06 < p.01.11: To draw a perp at a point
6 pp, 10 figs [HTML] [PDF] [GIF] [SWF]
C#07 < p.01.12: To drop a perp from a point
6 pp, 11 figs [HTML] [PDF] [GIF] [SWF]
C#08 < p.01.22: To make a triangle of three lines
4 pp, 10 figs [HTML] [PDF] [GIF] [SWF]
C#08B < p.01.22: To make a triangle of three lines (alternate)
4 pp, 7 figs [HTML] [PDF] [GIF] [SWF]
C#09 < p.01.23: To move an angle onto a line at a point
8 pp, 11 figs [HTML] [PDF] [GIF] [SWF]
C#10 < p.01.31: To draw a parallel through a point
10 pp, 17 figs [HTML] [PDF] [GIF] [SWF]
C#11 < p.01.42: To draw a parallelogram equal to a triangle
18 pp, 31 figs [HTML] [PDF] [GIF] [SWF]
C#12 < p.01.44: Same, but with a given width
22 pp, 59 figs [HTML] [PDF] [GIF] [SWF]
C#12B < p.01.44: Same, but with a given width (alternate)
12 pp, 21 figs [HTML] [PDF] [GIF] [SWF]
C#13 < p.01.45: To draw a parallelogram equal to a figure
4 pp, 5 figs [HTML] [PDF] [GIF] [SWF]
C#14 < p.01.46: To draw a square on a given side
14 pp, 27 figs [HTML] [PDF] [GIF] [SWF]
C#14B < p.01.46: To draw a square on a given side (alternate)
8 pp, 14 figs [HTML] [PDF] [GIF] [SWF]
Book II: 2 Constructions, C#15 and C#16 (24 pages, 44 figures)
C#15 < p.02.11: To cut a line in golden section
14 pp, 26 figs [HTML] [PDF] [GIF] [SWF]
C#16 < p.02.14: To construct a square equal to a figure
10 pp, 18 figs [HTML] [PDF] [GIF] [SWF]
Book III: 6 Constructions, C#17 to C#22 (72 pages, 135 figures)
C#17 < p.03.01: To find the center of a circle
8 pp, 13 figs [HTML] [PDF] [GIF] [SWF]
C#18 < p.03.17: To draw a line touching a circle
12 pp, 23 figs [HTML] [PDF] [GIF] [SWF]
C#18B < p.03.17: To draw a line touching a circle (alternate)
12 pp, 23 figs [HTML] [PDF] [GIF] [SWF]
C#19 < p.03.25: To draw a complete circle given a segment
8 pp, 14 figs [HTML] [PDF] [GIF] [SWF]
C#20 < p.03.30: To bisect a circumference
4 pp, 7 figs [HTML] [PDF] [GIF] [SWF]
C#21 < p.03.33: To draw a segment with a given angle, on a given line
12 pp, 24 figs [HTML] [PDF] [GIF] [SWF]
C#22 < p.03.34: To draw a segment with a given angle, in a given circle
16 pp, 31 figs [HTML] [PDF] [GIF] [SWF]
Book IV: 16 Constructions, C#23 to C#38 (208 pages, 379 figures)
C#23 < p.04.01: To fit a line in a circle
2 pp, 3 figs [HTML] [PDF] [GIF] [SWF]
C#24 < p.04.02: To inscribe a triangle in a circle
16 pp, 30 figs [HTML] [PDF] [GIF] [SWF]
C#25 < p.04.03: To circumscribe a triangle around a circle
20 pp, 38 figs [HTML] [PDF] [GIF] [SWF]
C#26 < p.04.04: To inscribe a circle in a triangle
12 pp, 23 figs [HTML] [PDF] [GIF] [SWF]
C#27 < p.04.05: To circumscribe a circle around a triangle
6 pp, 11 figs [HTML] [PDF] [GIF] [SWF]
C#28 < p.04.06: To inscribe a square in a circle
6 pp, 11 figs [HTML] [PDF] [GIF] [SWF]
C#29 < p.04.07: To circumscribe a square around a circle
14 pp, 26 figs [HTML] [PDF] [GIF] [SWF]
C#30 < p.04.08: To inscribe a circle in a square
6 pp, 9 figs [HTML] [PDF] [GIF] [SWF]
C#31 < p.04.09: To circumscribe a circle around a square
4 pp, 5 figs [HTML] [PDF] [GIF] [SWF]
C#32 < p.04.10: To construct a golden triangle
14 pp, 25 figs [HTML] [PDF] [GIF] [SWF]
C#33 < p.04.11: To inscribe a pentagon in a circle
34 pp, 66 figs [HTML] [PDF] [GIF] [SWF]
C#34 < p.04.12: To circumscribe a pentagon around a circle
10 pp, 18 figs [HTML] [PDF] [GIF] [SWF]
C#35 < p.04.13: To inscribe a circle in a pentagon
8 pp, 14 figs [HTML] [PDF] [GIF] [SWF]
C#36 < p.04.14: To circumscribe a circle around a pentagon
8 pp, 13 figs [HTML] [PDF] [GIF] [SWF]
C#37 < p.04.15: To inscribe a hexagon in a circle
10 pp, 16 figs [HTML] [PDF] [GIF] [SWF]
C#38 < p.04.16: To inscribe a 15-gon in a circle
38 pp, 71 figs [HTML] [PDF] [GIF] [SWF]
Book VI: 10 Constructions, C#39 to C#48 (102 pages, 188 figures)
C#39 < p.06.09: To cut a prescribed piece from a line
8 pp, 15 figs [HTML] [PDF] [GIF] [SWF]
C#40 < p.06.10: To cut a line similar to another cut line
8 pp, 14 figs [HTML] [PDF] [GIF] [SWF]
C#41 < p.06.11: To find a third proprotional
6 pp, 10 figs [HTML] [PDF] [GIF] [SWF]
C#42 < p.06.12: To find a fourth proportional
6 pp, 12 figs [HTML] [PDF] [GIF] [SWF]
C#43 < p.06.13: To find a mean proportional
8 pp, 15 figs [HTML] [PDF] [GIF] [SWF]
C#44 < p.06.18: To describe a figure similar to a given figure
12 pp, 22 figs [HTML] [PDF] [GIF] [SWF]
C#45 < p.06.25: To describe a figure similar to one and equal to another
42 pp, 80 figs [HTML] [PDF] [GIF] [SWF]
C#46 < p.06.28: To apply a parallelogram to a line, given area and defect
6 pp, 8 figs [HTML] [PDF] [GIF] [SWF]
C#47 < p.06.29: To apply a parallelogram to a line, given area and excess
4 pp, 8 figs [HTML] [PDF] [GIF] [SWF]
C#48 < p.06.30: To divide in extreme and mean ratio (DEMR)
2 pp, 4 figs [HTML] [PDF] [GIF] [SWF]
C#X17 < New Construction for the 17-gon
x pp, x figs [HTML] [PDF] [GIF] [SWF]

Revised 29 June 2000 by Ralph Abraham
abraham@vismath.org