Index

Allen, Elias, 235

Amsler, Jacob, 158

analogue computer. See computer, analogue

angle, 87; bisection of, 100; trisection of, 72, 102, 105–8, 110; units of measurement, 92–95

arch, 131

Archimedes of Syracuse, 146; trammel of, 290

area, 53, 112, 118, 138–70, 194; of circle. See circle, area of; of parallelogram. See parallelogram, area of; of triangle. See triangle, area of; surface, 128

axioms, 70

Bacon, Roger, 183

bearing, 188; thrust, 128

Beghin, Auguste, 237

Bernoulli, lemniscate, 58

binary, 182–84

Bird, John, 94

Bissaker, Robert, 236

Board of Longitude, 94

Boulton, Matthew, 22

Brahe, Tycho, 90

bridge, Royal Albert, 132

Brunel, Isambard Kingdom, 39, 132

calendar, 182

cam, 15, 197–99

cantilever, 256

Cassini, Jacques, 67

catenary, 127, 130

centreless grinding, 204

Chaucer, Geoffrey, 89

Chebyshev, Pafnuty, 28, 41, 62

circle, 70, 144, 188, 190, 279; arc of, 5, 60; area of, 144, 239; auxiliary, 290; circumscribed, 205; inscribed, 205; inverse of, 35; least squares reference, 205; minimum zone, 205; of proportion, 234, 251–54; squaring of, 72

CNC milling, 12, 197, 203

coin, 188

complete parallel motion. See linkage, parallel

computer: algebra system, xvii; analogue, xv, 170, 227; parallel, 118

cone, 126, 278

constructible. See construction, geometric

construction: geometric, 69–73

Conway, John, 275

coupling, Oldham, 201

Crowther, Phineas, 24

cube, 113, 126

Cundy, H. Martyn, xvi

curvature: centre of, 13; radius of, 132, 195

curve: algebraic, 59; convex, 190; trancendental, 127

cylindricity, 205

Delamain, Richard, 234–36, 251–54

disc. See circle

dissection, 112–26; Dudeney, 8;

Duijvestijn, 115; hinged, 7, 9;

Willcocks, 115

drill, square, 199–201

Dudeney, Henry Ernest, 8–9

Duijvestijn, A. J. W., 115

dwell, 197

ellipse, 13, 55, 195, 287–92;

ellipsograph, 290

ellipsoid, 292

engine: beam, 17–21, 25, 198; rotary, 201; steam locomotive, 47

envelope, 133, 214

epitrochoid, 202

Euclid, 65, 69, 230;Elements,1, 5–6, 70, 85, 144, 172

Euclidean Construction. See Construction, Geometric

Euler, Leonhard, 123, 190

evolute, 13, 132

experiment, 1

Fermat, Pierre de, 97

Flamsteed, John, 92

forces, 130

Forster, William, 251

Galilei, Galileo, 84, 90

Gascoigne, William, 91

Gauss, Carl Friedrich, 112

gear, 178–80, 202; elliptical, 55; hunting, 178

geometry: axioms of, 70; dynamic software, xvii

gradient, 174

Graham, George, 93

Grammelogia, 234, 251–54

Great Eastern, 39

greedy approach, 116

Greenwich. See Royal Observatory, Greenwich

Gunter, Edmund, 84, 234

Hardy, G. H., 80, 172

harmonograph, 184

Hart, H., 36, 38

Henrici, O., 151, 162

Hobbes, Thomas, 6

Hooke, Robert, 90

hunting cog. See gear, hunting

impossibility, proof of, 71

Kelland, 6–7, 9

Kempe, A. B., 17, 59

Kepler, Johannes, 231

kerf, 8

leap year. See calendar

length, 66–69, 84, 141; measurment, 211; yard, 66

line: broad, 10–15; straight, 15, 17–45, 65, 70; straight, approximate, 21; straight, equation of, 214; thin, 173

linkage, 171; Chebyshev, 28–32, 57; Chebyshev, paradoxical, 62–64; grasshopper, 41, 290; guide, 22, 39–41; Hart, 36–38; Hart A-frame, 38–39; inversor, 36, 54, 61; non-planar, 33; parallel, 21, 26; Pascal, 108; Peaucellier, 34, 36, 60; Roberts, 32–33; Roberts’s, 59; Scott Russell, 39, 53, 290; Watt, 22–28, 33, 41, 46, 49, 56–60

Littlewood, J. E., xiii, 187

logarithm, 85, 134, 228–33, 260; invention of, 230–31

Mannheim, Amédée, 236

mass: centre of, 139, 170, 256–58, 263, 271, 277, 292

model, 49, 116, 138, 202, 266; exhibition, xvi

Mondrian, Piet, 17

motion, parallel. See linkage, parallel

Napier, John, 230

Newton, Sir Isaac, 231, 249, 251

Nicomachus of Gerasa, 113

number: artificial, 85; co-prime, 173; constructible, 78; irrational, 175–77, 185, 223; transcendental, 79

d’Oresme, Nicole, 259

origami, 110, 125

Oughtred, William, 227, 234–36, 240, 251–54

pantograph, 51

parabola, 13, 43–45, 127, 134

parallel postulate, 70

parallelogram parallelogram: area of, 142

Pascal, 107

Peaucellier, Charles Nicolas, 34, 60

pendulum, 66

pentagon, 98, 212

perimeter, 194

π, 72, 79–80, 92, 238–39

planimeter, 149–70; Goodmans, 163; hatchet, 138, 161–70

Poincaré, Henri, 255

polygon, 87, 95, 118

polyhedron, 273–74

Pope Clement IV, 183

proportional dividers, 105

Prytz planimeter. See planimeter, hatchet

Prytz, Holgar, 139, 161–65

pseudosphere, 128

pursuit curve. See tractrix

Pythagoras of Samos, 172

Pythagorean theorem. See Theorem, Pythagorean

radian, 92

Ramanujan, S., 80

rational number. See number, irrational

Reuleaux, Franz, 190

Roberts, Richard, 32

rotor, Reuleaux’s, 189–91, 193–94, 197; making, 202

roundness, 190–91

Royal Observatory, Greenwich, 93

Sangwin, Guy William Farrier, 246

Sarrus, Pierre Frédéric, 33

scale: circular, 240; double, 85; folded, 237; logarithmic, 85, 231; of decimals, 84; specially designed, 241; Vernier, 81–83, 116, 153, 162, 188, 267

Scott Russell, 39

sector, 84–87

series: arithmetic, 113, 247; geometric, 122; harmonic, 259–61

slide rule, 227–49; bespoke, 241; circular, 240–41; invention of, 233–37, 251; logarithmic, 229–33, 237–40;

non-logarithmic, 247

snowflake, Koch’s, 146

standard: British, 16, 206–10; International paper, 177; length, 66–69, 180–82

Stone, Edmund, 235

surface texture, 205

tetrahedron, 273

theorem: Barbier’s, 194; Circle, 1–2, 76; Constructible numbers, 78; Green’s, 169; isoperimetric, 150; Pythagorean, 6–7, 14, 29, 34, 43, 56, 77, 98, 119–20, 127, 143–44, 190, 286, 290, 293

Thompson, Francis, 20

thread, screw, 91; metric, 180; pitch of, 66

tractrix, 127, 141, 168

triangle, 213; area of, 144; equilateral, 108; isosceles, 123, 193, 199, 209; similar, 85

Troughton, Edward, 68

uphill roller, 278

vee-block, 11, 207, 210

Vernier, Pierre, 81

volume, 227

Watt, James, 20, 22–24, 52

Watts, Harry James, 199

White, James, 43

Willcocks, T. H., 115

yángm, 125

yard. See length, yard

year. See calendar

yoke, Scotch, 198