1. Earliest Known Uses Of Some Of The Words Of Mathematics (Q) but it became known as a quadratrix when dinostratus used it for the quadrature of a circle (DSB, article "dinostratus"; Webster's New International Dictionary, 1909 http://members.aol.com/jeff570/q.html

Earliest Known Uses of Some of the Words of Mathematics (Q) Last revision: May 20, 2004 Q. E. D. Euclid (about 300 B. C.) concluded his proofs with hoper edei deiksai, which Medieval geometers translated as quod erat demonstrandum ("that which was to be proven"). According to Veronika Oberparleiter, the earliest known use in print of the phrase quod erat demonstrandum in a Euclid translation appears in the translation by Bartholemew Zamberti published in Venice in 1505. In Dialogues Concerning Two New Sciences (1638) in Latin Galileo used quod erat intentum, quod erat demonstrandum, quod erat probandum, quod erat ostendendum, quod erat faciendum, quod erat determinandum, and quod erat propositum. In 1665 Benedictus de Spinoza (1632-1677) wrote a treatise on ethics, Ethica More Geometrico Demonstrata, in which he proved various moral propositions in a geometric manner. He wrote the abbreviation Q. E. D., as a seal upon his proof of each ethical proposition. Isaac Barrow used quod erat demonstrandum, quod erat faciendum (Q. E. F.), quod fieri nequit (Q. F. N.), and quod est absurdum (Q. E. A.). Isaac Newton used the abbreviation Q. E. D.

2. Quadratrice De Dinostrate courbe suivante. courbe précédente. courbes 2D. courbes 3D. surfaces. fractals. polyèdres. QUADRATRICE DE DINOSTRATE. dinostratus' (or Hippias') quadratrix, Quadratrix des dinostratus (oder des Hippias) http://www.mathcurve.com/courbes2d/dinostrate/dinostrate.shtml

courbe suivante courbes 2D courbes 3D surfaces ... fractals QUADRATRICE DE DINOSTRATE Dinostratus' (or Hippias') quadratrix, Quadratrix des Dinostratus (oder des Hippias) Autre nom : sectrice d'Hippias. La quadratrice de Dinostrate O ) et une composante de son vecteur vitesse constante (ici, la composante sur Oy O d'une Comme son nom l'indique, cette courbe est une quadratrice ; en effet : n -sectrice ; en effet courbe suivante courbes 2D courbes 3D surfaces ... fractals , Jacques MANDONNET

3. History Of Mathematics: Chronology Of Mathematicians 350?) Thymaridas (c. 350) dinostratus (fl. c. 350) *SB http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan Table of Contents 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below List of Mathematicians 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *MT 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB

4. Greek Index Chrysippus. Cleomedes. Conon. Democritus. dinostratus. Diocles. Dionysodorus. Diophantus. Domninus Apollonius. Archimedes. Bryson. Carpus. dinostratus. Hippias. Hippocrates. Nicomedes. Oenopides http://stm21645-01.k12.fsu.edu/Greek_Index.htm

Index of Greek mathematicians Below are various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name to go to that biography. Some History Topics about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy Full List of Greek Mathematicians in our archive Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Greek Mathematicans/Philosophers Anaxagoras Antiphon Archytas Aristotle ... Zeno of Elea Greek Mathematicians/Astronomers Apollonius Archimedes Aristarchus Aristotle ... Theon of Smyrna Greek Mathematicians/Astronomers/Philosophers Aristotle Cleomedes Democritus Eudoxus ... Thales Greek Circle squarers Anaxagoras Antiphon Apollonius Archimedes ... Bryson Carpus Dinostratus Hippias Hippocrates Nicomedes ... Sporus Later Circle squarers al'Haitam Johann Bernoulli Cusa Franco of Liège James Gregory Lambert Leonardo Lindemann ... Search Suggestions JOC/EFR April 1999 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Indexes/Greek_index.html

5. Dinostratus dinostratus. Born about 390 BC in Greece Died about 320 BC. dinostratusis mentioned by Proclus who says (see for example 1 or 3) http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Dinostratus.html

Dinostratus Born: about 390 BC in Greece Died: about 320 BC Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Dinostratus is mentioned by Proclus who says (see for example [1] or [3]):- Amyclas of Heraclea, one of the associates of Plato , and Menaechmus , a pupil of Eudoxus who had studied with Plato , and his brother Dinostratus made the whole of geometry still more perfect. It is usually claimed that Dinostratus used the quadratrix, discovered by Hippias , to solve the problem of squaring the circle Pappus tells us (see for example [1] or [3]):- For the squaring of the circle there was used by Dinostratus, Nicomedes and certain other later persons a certain curve which took its name from this property, for it is called by them square-forming in other words the quadratrix It appears from this quote that Hippias discovered the curve but that it was Dinostratus who was the first to use it to find a square equal in area to a given circle. Proclus , who claims to be quoting from Eudemus , writes (see [1]):- Nicomedes trisected any rectilinear angle by means of the conchoidal curves, of which he had handed down the origin, order, and properties, being himself the discoverer of their special characteristic. Others have done the same thing by means of the quadratrices of

6. Dinostratus Biography of dinostratus (390BC320BC) dinostratus. Born about 390 BC in Greece It is usually claimed that dinostratus used the quadratrix, discovered by Hippias, to solve the problem of squaring the http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dinostratus.html

Dinostratus Born: about 390 BC in Greece Died: about 320 BC Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Dinostratus is mentioned by Proclus who says (see for example [1] or [3]):- Amyclas of Heraclea, one of the associates of Plato , and Menaechmus , a pupil of Eudoxus who had studied with Plato , and his brother Dinostratus made the whole of geometry still more perfect. It is usually claimed that Dinostratus used the quadratrix, discovered by Hippias , to solve the problem of squaring the circle Pappus tells us (see for example [1] or [3]):- For the squaring of the circle there was used by Dinostratus, Nicomedes and certain other later persons a certain curve which took its name from this property, for it is called by them square-forming in other words the quadratrix It appears from this quote that Hippias discovered the curve but that it was Dinostratus who was the first to use it to find a square equal in area to a given circle. Proclus , who claims to be quoting from Eudemus , writes (see [1]):- Nicomedes trisected any rectilinear angle by means of the conchoidal curves, of which he had handed down the origin, order, and properties, being himself the discoverer of their special characteristic. Others have done the same thing by means of the quadratrices of

7. References For Dinostratus References for dinostratus. Biography The URL of this page is http//wwwhistory.mcs.st-andrews.ac.uk/References/dinostratus.html. http://www-gap.dcs.st-and.ac.uk/~history/References/Dinostratus.html

References for Dinostratus Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: G J Allman, Greek geometry from Thales to Euclid (Dublin, 1889). T L Heath, A History of Greek Mathematics I (Oxford, 1921). B L van der Waerden, Science awakening (Groningen, 1954). Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR April 1999 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Dinostratus.html

8. Dinostratus dinostratus. Born about 390 BC in Greece Died about 320 BC. Showbirthplace location dinostratus is mentioned by Proclus who says. http://sfabel.tripod.com/mathematik/database/Dinostratus.html

var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Dinostratus Born: about 390 BC in Greece Died: about 320 BC Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Dinostratus is mentioned by Proclus who says Amyclas of Heraclea, one of the associates of Plato , and Menaechmus , a pupil of Eudoxus who had studied with Plato , and his brother Dinostratus made the whole of geometry still more perfect. Dinostratus used the quadratrix, discovered by Hippias , to solve the problem of squaring the circle. Pappus tells us For the squaring of the circle there was used by Dinostratus, Nicomedes and certain other later persons a certain curve which took its name from this property, for it is called by them square-forming in other words the quadratrix. It appears that Hippias discovered the curve but it was Dinostratus who was the first to use it to find a square equal in area to a given circle. Dinostratus probably did much more work on geometry but nothing is known of it. References (2 books/articles) References elsewhere in this archive: Show me the quadratrix Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996

9. History Of Mathematics: Greece 350?) Thymaridas (c. 350) dinostratus (c. 350) Speusippus (d http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

10. DINOSTRATUS - Thesaurus Terms By HyperDictionary.com Dictionary, Medical Dictionary. Search Dictionary dinostratus. COPYRIGHT© 20002003 WEBNOX CORP. HOME ABOUT HYPERDICTIONARY. http://www.hyperdictionary.com/thesaurus/Dinostratus

11. References For Dinostratus References for the biography of dinostratus References for dinostratus. Biography in Dictionary of Scientific Biography http//wwwhistory.mcs.st-andrews.ac.uk/ References/dinostratus.html http://www-history.mcs.st-and.ac.uk/~history/References/Dinostratus.html

References for Dinostratus Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: G J Allman, Greek geometry from Thales to Euclid (Dublin, 1889). T L Heath, A History of Greek Mathematics I (Oxford, 1921). B L van der Waerden, Science awakening (Groningen, 1954). Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR April 1999 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Dinostratus.html

12. Www.hyperdictionary.com/dictionary/dinostratus More results from www.hyperdictionary.com References for dinostratusReferences for dinostratus. JOC/EFR December 1996 The URL of this page is http//wwwhistory.mcs.st-andrews.ac.uk/history/References/dinostratus.html. http://www.hyperdictionary.com/dictionary/dinostratus

13. D Index Translate this page Leonard (593*), Dickstein, Samuel (76) Dieudonné, Jean (138*) Digges, Thomas (353)Dinghas, Alexander (86*) Dini, Ulisse (66*) dinostratus (148) Diocles (116 http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/D.htm

Names beginning with D The number of words in the biography is given in brackets. A * indicates that there is a portrait. d'Alembert , Jean (2501*) D'Arcy Thompson W (479*) d'Oresme , Nicole (191*) D'Ovidio , Enrico (414) Dandelin , Germinal (392) Danti , Egnatio (257) Dantzig, David van (55) Dantzig, George Darboux , Jean (814*) Darwin , George (167) Dase , Zacharias (125) Davenport , Harold (700*) Davidov , August (64*) Davies , Evan (299*) de Beaune , Florimond (316) de Bessy , Bernard (86) de Billy , Jacques (150) de Bourgainville , Louis (74) de Boislaurent , Budan (171) de Broglie , Louis duc (488*) de Carcavi , Pierre (439) de Coriolis , Gustave (121*) de Coulomb , Charles (95*) de Fermat , Pierre (2491*) de Fontenelle , Bernard (255*) de Groot , Johannes (444*) , Ernest (239) , Guillaume (204*) de La Condamine , Charles (480*) de La Faille , Charles (233) de La Hire , Philippe (297) de La Roche , Estienne (275) de Lagny , Thomas (186*) de Moivre , Abraham (379*) , Joseph (216) de Montmort , Pierre (300) De Morgan , Augustus (856*) de Prony , Gaspard (1015*) de Ortega , Juan (157) de Rham , Georges (741*) de Roberval , Gilles (349) de Saint-Venant de Sitter , Willem (483*) de Sluze de Tilly , Joseph (179) de Tinseau , D'Amondans (144) de Witt , Jan (412) de Wronski , Josef (324*) Dechales , Claude (175) Dedekind , Julius (2081*) Dee , John (358*) Dehn , Max (679*) del Ferro , Scipione (93) Delamain , Richard (393) Delambre , Jean (213*) Delaunay , Charles (172*) Deligne , Pierre (362*) Delone , Boris (485*) Delsarte , Jean (416*) Democritus of Abdera (188*) Denjoy , Arnaud (86*) Deparcieux , Antoine (71)

14. QUADRATRIX i. \t\fi !\ \. * . i /. 7 7. !/ /. FIG. 2. of this class are those ofdinostratus and EW Tschirnhausen, which are both related to the circle. http://99.1911encyclopedia.org/Q/QU/QUADRATRIX.htm

QUADRATRIX QUADRATRIX (from Lat. quadrator, squarer), in mathe matics, a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves FIG. i. ;/ i / FIG. 2. of this class are those of Dinostratus and E. W. Tschirnhausen, which are both related to the circle. The cartesian equation to the curve is y = x cot . which shows that the curve is symmetrical about the axis of y, and that it consists of a central portion flanked by infinite branches (fig. 2). The asymptotes are *= *=2na, n being an integer. The intercept on the axis of y is 2a/x; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected. The curve also permits the solution of the problems of duplicating a cube (q.v.) and trisecting an angle. The quadratrix of Tschirnhausen is constructed by dividing the arc and radius of a quadrant in the same number of equal parts as before. The mutual intersections of the lines drawn from the points of division of the arc parallel to AB, and the lines drawn parallel to BC through the points of division of AB, are points on the quadratrix (fig. 3). The cartesian equation is y a cos Trx/2a. The curve is periodic, and cuts the axis of x at the points #= =*=(2n-i)a, n being an integer; the maximum values of y are =*=a. Its properties are similar to those of the quadratrix of Dinostratus. QUACK QUADRATURE

15. Greek Mathematics Index Chrysippus. Cleomedes. Conon. Democritus. dinostratus. Diocles. Dionysodorus. Diophantus. Domninus Apollonius. Archimedes. Bryson. Carpus. dinostratus. Hippias. Hippocrates. Nicomedes. Oenopides http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Greeks.html

History Topics: Index of Ancient Greek mathematics Articles about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy ... The teaching of mathematics in Ancient Greece. Various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name below to go to that biography. Full List of Greek Mathematicians in our archive Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Greek Mathematicans/Philosophers Anaxagoras Antiphon Archytas Aristotle ... Zeno of Elea Greek Mathematicians/Astronomers Apollonius Archimedes Aristarchus Aristotle ... Theon of Smyrna Greek Mathematicians/Astronomers/Philosophers Aristotle Cleomedes Democritus Eudoxus ... Thales Greek Circle squarers Anaxagoras Antiphon Apollonius Archimedes ... Bryson Carpus Dinostratus Hippias Hippocrates Nicomedes ... Sporus Later Circle squarers Al-Haytham Johann Bernoulli Cusa James Gregory ... Search Form JOC/EFR January 2004 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Indexes/Greeks.html

16. Quadratrix Quadratrix (n.) A curve made use of in the quadrature of other curves;as the quadratrix of dinostratus or of Tschirnhausen. Click http://www.thebigletterlist.net/word/q-Quadratrix.html

Quadratrix (n.) A curve made use of in the quadrature of other curves; as the quadratrix of Dinostratus or of Tschirnhausen. Quadratrix Alltheweb (Cached) Results Web Results Quadratrix Quadratrix of Hippias. Cartesian equation: y = xcotx/2a Definitions of the Associated curves. Evolute. Involute 1. Involute 2. Inverse curve wrt origin. Inverse wrt another circle. Pedal curve wrt origin. Pedal wrt another point ... The quadratrix was discovered by Hippias of Elis in 430 BC ... Hippias' Quadratrix Hippias' Quadratrix . Around 420 B.C., ... Hippias of Elis discovered a quadratrix curve also known as a trisectrix. Hippias' quadratrix was the first curve in recorded ... Quadratrix of Hippias from MathWorld Quadratrix of Hippias from MathWorld The quadratrix was discovered by Hippias of Elias in 430 BC, and later studied by Dinostratus in 350 BC MacTutor Archive. It can be used for angle ... QUADRATRIX QUADRATRIX QUADRATRIX from Lat. quadrator, squarer, in mathe matics, a curve having ordinates which are ... The quadratrix of Dinostratus was well known to the ancient jreek geometers ...

17. QUADRATRIX QUADRATRIX (from Lat. quadrator, squarer), in mathe matics, a curve having ordinates which are a measure of the area (or quadrature) of another curve. The quadratrix of dinostratus was well known http://www.1911encyclopedia.org/Q/QU/QUADRATRIX.htm

QUADRATRIX QUADRATRIX (from Lat. quadrator, squarer), in mathe matics, a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves FIG. i. ;/ i / FIG. 2. of this class are those of Dinostratus and E. W. Tschirnhausen, which are both related to the circle. The cartesian equation to the curve is y = x cot . which shows that the curve is symmetrical about the axis of y, and that it consists of a central portion flanked by infinite branches (fig. 2). The asymptotes are *= *=2na, n being an integer. The intercept on the axis of y is 2a/x; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected. The curve also permits the solution of the problems of duplicating a cube (q.v.) and trisecting an angle. The quadratrix of Tschirnhausen is constructed by dividing the arc and radius of a quadrant in the same number of equal parts as before. The mutual intersections of the lines drawn from the points of division of the arc parallel to AB, and the lines drawn parallel to BC through the points of division of AB, are points on the quadratrix (fig. 3). The cartesian equation is y a cos Trx/2a. The curve is periodic, and cuts the axis of x at the points #= =*=(2n-i)a, n being an integer; the maximum values of y are =*=a. Its properties are similar to those of the quadratrix of Dinostratus. QUACK QUADRATURE

18. Quadratrix Of Hippias From MathWorld Quadratrix of Hippias from MathWorld The quadratrix was discovered by Hippias of Elias in 430 BC, and later studied by dinostratus in 350 BC (MacTutor Archive). It can be used for angle http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/QuadratrixofHippia

19. ICHB Math Department - Squaring The Circle Hippias and dinostratus are associated with the method of squaringthe circle using a quadratrix. The curve it thought to be the http://math.ichb.ro/modules.php?name=News&file=article&sid=19

20. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï Turkey Died 19 April 1974 in Berlin, Germany Dini, Ulisse Dini Born 14 Nov 1845in Pisa, Italy Died 28 Oct 1918 in Pisa, Italy dinostratus, dinostratus Born http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=D

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