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
Extractions: 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.
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
Extractions: 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 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 Ahmes (c. 1650 B.C.E.) *MT Baudhayana (c. 700) 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) 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
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
Extractions: 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
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
Extractions: 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
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
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
Extractions: 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
History Of Mathematics: Greece 350?) Thymaridas (c. 350) dinostratus (c. 350) Speusippus (d http://aleph0.clarku.edu/~djoyce/mathhist/greece.html
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
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
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
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
Extractions: 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
Extractions: Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy ... The teaching of mathematics in Ancient Greece. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name below to go to that biography. Anaxagoras
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 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
Extractions: 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
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
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
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
