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Sources of illustrations
Pictures on pages vi and x
All these pictures are freely available on the internet. Jan de Witt Painting by Jan de Baen (1633–1702)
Source: Rijksmuseum Amsterdam http://commons.wikimedia.org/wiki/File:Grand_Pensionary_Johan_de_Witt.jpg
René Descartes
Painting by Frans Hals (ca 1583−1666) Source: Louvre, Museum, Paris http://en.wikipedia.org/wiki/File:Frans_Hals_-_Portret_van_René_Descartes.jpg
Pierre de Fermat
http://commons.wikimedia.org/wiki/File:Pierre_de_Fermat.jpg
Frans van Schooten, jr.
http://commons.wikimedia.org/wiki/File:Frans_van_schooten_jr.jpg
François Viète
http://commons.wikimedia.org/wiki/File:Francois_Viete.jpg
Other pictures in Chapters 1−5
Most figures were drawn by Tobias Baanders (CWI, Amsterdam), with the following exceptions • Figure 5.8 was inspired by Heath [30] • Figure 5.9 was derived from Descartes [16] • Figure 5.13 (drawn by Jan Aarts) was derived from J.D. LAWRENCE, A catalog
of Special Curves, New York, Dover publications, 1972
Index
abscissa-axis 10, 17, 18, 27, 38, 49, 54, 259, 267, 270, 282, 286, 302
algebraic curve 301, 304 analysis 3−6, 257 analytic geometry 2−4, 7, 9, 14, 16, 25,
26 apex 26 Apollonius 2, 3, 5, 13, 14, 17, 18, 25,
38, 261, 270, 271, 277, 293, 295 Apollonius Batavus 3 Apollonius Gallus 3, 5 Apollonius Redivivus 3 Archimedes 2, 22, 261 Aristaeus the Elder 3 Aristotle 6, 258 Arithmetica Infinitorum by Wallis 25 Artis analyticae praxis by Harriot 25 axis/axes 14−18, 21, 28, 34, 37, 44, 46,
48, 122, 138, 158, 160, 178, 180, 236, 261, 262, 271, 276, 277, 281–285, 292–295, 302, 305, 308
Barrow, Isaac (1630–1677) 25 Bombelli, Rafael (1526–1572) 6 center(s) 9, 13, 17, 18, 20, 28, 49–51,
53, 54, 56–58, 126, 130, 132, 138, 144, 148, 152, 154, 158, 160, 170, 176, 178, 212, 218, 222, 226, 230, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 252, 268, 283, 284, 289, 290, 292, 294, 295, 297, 302, 308
circle(s) 7, 9, 13–15, 17, 18, 21–24, 38, 39. 41, 44, 50, 55–57, 60, 132, 134, 168, 172, 186, 210, 238, 240, 242, 244, 246, 250, 254, 257, 262, 264, 265, 277, 282, 286, 295–297. 300–303
coefficient(s) 6, 7, 13, 14, 17, 26, 28, 31, 265, 267, 269, 281, 282, 304
Collectio (Συναγωγη) 2–5, 298, 300 Collège de France 25
compositio, composition 1, 3, 17, 18, 28, 160, 272, 299
conic(s) 2, 5, 7, 12–14, 17, 21, 25–28, 43, 118, 202, 232, 252, 257, 293, 296, 297, 300, 304, 308
conical wedge 26 Conica 13, 261, 270, 271, 277, 293,
295, 296 conjugate 234, 252, 291 conjugate axis/axes 17, 46, 47, 51, 56,
57, 277, 280, 282, 284, 294 conjugate axis, associated 20, 45, 49 conjugate diameter 49, 52, 53, 56, 192,
263, 268, 272, 275, 276 conjugate direction 10, 17, 260, 289 constructive resolution (of equations) 9,
14, 23, 25, 26 conversim 32 coordinate axis/axes 38 coordinate system 7, 15, 26, 28 corollary (corollarium) 29, 31, 37, 41,
42, 122, 124, 160, 162, 164, 176, 180, 182, 262, 271, 277, 280
cubus 6 curve(s) 2, 7, 9, 10, 13–18, 21, 24–28,
31, 32, 34–36, 38–42, 44, 45, 49, 50, 51, 53, 54, 56, 60, 62, 74, 76, 82, 86, 88, 92, 84, 98, 100, 104, 114, 116, 122, 126, 130, 132, 134, 138, 144, 148, 154, 160, 162, 170, 172, 178, 180, 186, 238, 240, 244, 246, 250, 257–259, 264, 265, 267, 268, 276. 277, 282–284, 286, 290, 291, 298, 300– 308
Debeaune, Florimond (1601–1652) 25 definition 2–4, 9, 12, 29, 38, 40, 42, 47,
49, 50, 52, 53, 56, 62, 257, 276, 281, 282, 285, 289, 294, 299, 305
degenerations 28, 270 demonstratio 28, 33–35, 40, 41, 45,
257–259, 261, 266, 282, 283, 285, 291, 292
316 Index
demonstration 10, 62, 104, 108, 110, 160, 188, 254, 257
Descartes, René (1596–1650) 2, 6–14, 16, 24, 25, 257, 281, 282, 300–308
descriptio 28, 33, 35, 40, 41, 257–259, 261, 265, 288, 290–292
description 2, 6, 16, 34−36, 39, 49, 53, 100, 136, 148, 168, 236, 265, 282
determinatio 28, 33, 35, 40, 257, 260, 265, 282, 283
determination 6, 7, 36, 62, 84, 88, 90, 96, 106, 108, 112, 128, 136, 142, 148, 152, 168, 236, 257, 301
Diogenes Laertius (3rd century) 3 Diophantus (200?–284?) 6 division(s) 5, 7, 66, 68, 92, 98, 106,
110, 140, 144, 148, 150, 152, 156, 158, 172, 176, 178, 222, 224, 230, 246, 250, 267, 270
Elements 2, 3, 29, 258, 262, 279, 299 ellipse 15–17, 20, 21, 26, 38, 39, 41, 42,
44, 50, 55–58, 60, 118, 132, 134, 168, 170, 176, 178, 180, 182, 186, 210, 238, 240, 242, 244, 246, 248, 250, 252, 254, 257, 261–265, 270, 271, 277, 280, 282, 283, 286, 291–295, 297, 301
Elsevier 24 equality sign 6 equation(s) 2, 6, 7, 9, 10, 12–18, 21–28,
31–51, 53–56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 78, 80, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 112, 114, 116, 118, 120, 124, 126, 128, 132, 134, 136, 140, 142, 144, 148, 152, 154, 158, 162, 166, 168, 170, 174, 176, 182, 186, 188, 190, 192, 194, 196, 198, 202, 204, 206, 210, 216, 218, 226, 230, 232, 234, 236, 238, 240, 242, 250, 254, 257–260, 262, 264, 266–271, 275, 276, 280, 282, 284, 286, 288–291, 300–306, 308
algebraic 6, 21, 25, 26, 301, 304
linear 16, 28, 31
Eratosthenes (276–194 BC) 24 Euclid (325?–265? BC) 2, 3, 29, 262,
272, 273, 279, 293, 295, 299 Eudoxus (408–355 BC) 3 exegetic analysis 4, 6 Exempla 28 Fermat, Clément-Samuel de 24 Fermat, Pierre de (1601–1665) 2, 3, 7,
10, 14–19, 21–25, 28, 273, 304 first quadrant 15, 27, 31 focal properties 25 focus/foci 37, 40, 42, 122, 160, 176,
261, 270–271, 277 Geometria à Renato Descartes 25 Géométrie by Descartes 2, 8–10, 12, 13,
16, 24, 25, 257, 281, 300, 302, 308 Ghetaldi, Marino (1566–1626) 3 Golius, Jacobus (1596?–1667) 9 half-line 15, 258, 259 Harriot, Thomas (1560–1621) 25 Heath, Thomas L. (1861–1940) 3, 295,
297, 298 Heiberg, Johan Ludvig (1854 –1928) 3 Hero, Heron (10–70) 3, 299 Hierius (early 5th century) 2 Hire, Philippe de la (1640–1718) 25, 26 homogenea 6, 18 Hultsch, F. 4, 298 hyperbola(s) 16, 17, 22, 23, 26, 28, 29,
38–41, 44, 48–54, 60, 80, 118, 124, 126, 128, 130, 134, 136, 138, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 176. 186, 210, 212, 214, 216, 218, 220, 222, 226, 230, 232, 234, 236, 238, 257, 258, 261–271, 275, 277, 280, 282, 283, 286, 288–291, 295, 301, 302
immutable initial point 28, 31, 62, 70, 72, 74, 80, 84, 88, 90, 96, 100, 108, 112, 114, 124, 126, 128, 132, 136, 142, 152, 168
indefinite(ly) 28, 31, 62, 70, 72, 74, 80, 84, 86, 88, 90, 92, 96, 98, 100, 106, 108, 112, 122, 124, 126, 128, 136, 142, 144, 152, 154, 168, 170, 186, 196, 257, 258
Index 317
indeterminate 15, 28, 60, 62, 114, 116, 120, 132, 156, 170, 174, 240, 257
infinite(ly) 15, 28, 64, 118, 258, 307 infinitesimal methods 25 Isagoge 5, 14, 16, 21, 24 latitudo 6 latus 6 latus rectum 13, 18, 28, 36, 37, 46, 48,
49, 52, 53, 56–58, 72, 74, 76, 82, 86, 88, 92, 98, 102, 104, 106, 108, 110, 112, 116, 118, 126, 132, 144, 154, 156, 170, 214, 218, 222, 224, 226, 228, 230, 232, 234, 236, 240, 242, 244, 246, 248, 250, 252, 254, 258–264, 268, 270, 271, 275–277, 282, 284–286, 289, 292, 305
latus transversum 122, 132, 144, 154, 156, 170, 212, 214, 218, 222, 224, 226, 228, 230, 232, 234, 236, 240, 242, 244, 246, 248, 250, 252, 254
Leibniz, Gottfried Wilhelm (1646–1716) 26, 301
Leiden 9, 24 Liber Primus 2, 7, 24–26. 28, 29, 31,
32, 38, 49, 54, 56, 124, 126, 257, 258, 262, 263, 270–272, 277, 289, 292, 294, 302
Liber Secundus 1, 2, 25, 26, 28, 31, 263 (line) segment(s) 2, 4, 5, 7–9, 12, 15,
19, 21, 24–26, 28, 31, 37, 40–43, 54, 60, 64, 66, 70, 78, 90, 92, 96, 98. 102, 104, 106, 108, 112, 114, 116, 118, 120, 122, 124, 142, 144, 152, 154, 156, 160, 164, 170, 174, 176, 178, 180, 182, 186, 192, 196, 198, 202, 204, 206, 208, 210, 212, 216, 226, 236, 238, 240, 242, 244, 257–259, 267, 270, 274, 277, 279–282, 286, 287, 298–300, 308
Lieux Géométriques 25, 26 Loci plani 3, 14, 300 locus/loci 5, 7, 12–16, 18, 21, 24–26,
29, 31–33, 37–40, 42, 54, 56, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 98, 100, 104, 106, 108, 110, 112, 114, 116, 118,
120, 124, 126, 128, 130, 132, 134, 136, 138, 142, 144, 148, 152, 154, 156, 158, 168, 170, 174, 176, 182, 186, 188, 190, 204, 210, 216, 230, 232, 234, 236, 238, 240, 242, 250, 254, 257, 262, 270, 277, 281, 291, 293, 300, 302, 305
logistica numerosa 6 logistica speciosa 6 longitudo 6 Maire, Jan 24 major axis 17, 178, 281 Menaechmus 7 Mersenne, Père Marin Étienne (1568–
1648) 24 mesolabium 24 method 2, 3, 7, 9, 10, 12, 16, 17, 21–28,
31, 33, 39, 43, 84, 182, 257, 258, 266, 270, 298, 302, 306–308
~ of Descartes 2, 10, 12, 24 minor axis 178, 281 multiplication 7, 78, 80, 82, 92, 98, 104,
128, 140, 144, 148, 150, 152, 156, 172, 267, 299
negative abscissa 25 Notae Breves 24 ordinate-axis 10, 17, 34, 303 Oresme, Nicole (ca 1320–1382) 2 origin 10, 15, 17, 18, 38, 267, 282, 303,
306 Ozonam, Jacques (1640–1717) 26 Pappus of Alexandria (ca 290 – ca 350)
2–5, 9, 10, 13, 14, 21, 257, 293, 298–300, 303, 304, 306–308
parabola(s) 7, 13, 15–18, 22, 23, 26, 27, 32–37, 43, 45–48, 60, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 136, 186, 190, 192, 194, 196, 204, 206, 257–262, 264, 265, 270, 271, 275, 282–285, 301, 303–306, 308
Parabola of Descartes 13, 308 parallel translation(s) 26, 54, 282 Parent, Antoine (1666–1716) 25 Pascal, Blaise 24
318 Index
Pascal, Étienne 24 plane curves 2, 10, 13, 21, 24, 25, 300,
304 planimetric 25 planum 6 Plato 3 poristic analysis 4, 6 power taking 7 Prade 3 Problema(ta) 2, 21, 28, 29 product(s) 6–9, 12, 21, 60, 78, 84, 170,
182, 184, 254, 262, 286, 288, 290, 291, 299, 300
propositio 21, 29 Pythagoras, school of 3 quadratic equation(s) 9, 12, 16, 25, 27,
28, 43 quadrato-quadratum 6 quadratum 6, 16 quotient 8, 9, 98, 118, 144 Rabuel, C. (1669–1728) 16, 31, 306 radix 6 Recorde, R. (ca 1510–1558) 6 Regula Universalis 27, 28, 258, 270 Regula Universalis, second 27, 262 Regula Universalis, third 27, 28 rhetic analysis 4, 6 ridge 26 Roberval, G.P. de (1602–1675) 24 root 7–9, 12, 13, 22, 26 rotation 16, 18, 27, 282, 284 Snellius, W. (1580–1626) 3 solidum 6 straight line 4, 7, 15, 16, 26–28, 31, 32,
41–44, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 104, 112, 114, 118, 122, 124, 136, 138, 142, 144, 152, 162, 164, 166, 168, 170, 180, 182, 186, 192, 194, 196, 198, 200, 202, 204, 206, 210, 214, 216, 218, 220, 222, 226, 230, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 254, 257, 258, 262, 282, 300, 301, 304, 308
surface 25
symmetry axis/axes 14, 17, 20, 28, 37, 261, 277, 278, 283, 284–286
symptomata of Apollonius 25 synthesis (συνθεσις) 3–5, 17, 28 terminus alterius 15 terminus localis 16 Theaitetus 3 Theorema(ta) 2, 28, 29 Thomas, I. 4, 298 Tractatus de sectionibus conicis of
Wallis 25 transverse axis 41, 42, 46, 47, 49–51,
53, 54, 56, 160, 162, 176, 180, 182, 271, 275, 277, 280, 285, 286, 294
Treatise of Algebra, both Historical and Practical of Wallis 26
trident 13, 303, 305, 306 trisection of the angle 24 umbilical point 37, 122, 160 unit element 8 v-axis 269 Van Schooten, Jr., Frans (1615–1660)
1, 3, 9, 24, 25, 281 vertex/vertices 14, 17, 28, 34, 37, 45–
48, 53–55, 74, 76, 82, 86, 88, 92, 98, 102, 104, 110, 112, 114, 122, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 236, 258–262, 270, 283–286, 291, 305
Viète, François (1540–1603) 2–7, 9, 14, 16, 21, 23, 261
Wallis conocuneus 26 Wallis, John (1616–1703) 25–26 Wantzel, P.L. (1814–1848) 12 Witt, Jan de (1625–1672) 1, 10, 16, 17,
25–29, 31, 33, 34, 38–40, 42–45, 48–50, 55, 56, 60, 257–264, 266, 267, 269–274, 277–284, 286–291, 294, 302
Wolff, Christian von (1679–1754) 2 x-axis 16, 31, 32, 34, 40, 282 y-axis 15, 31, 282 zetetic analysis 4, 5