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 Date: 1753-01-01, Vol. 22 Book Id: WPLBN0004337842 ► Abstract Description Details...Description: The Construction of a Quadratrix to the Circle, Being the Curve Described by Its Equable Evolution. Philosophical Transactions (1683-1775). 1753-01-01. 22:445–446...
 Date: 1753-01-01, Vol. 25 Book Id: WPLBN0004352205 ► Abstract Description Details...Description: The Construction and Properties of a New Quadratrix to the Hyperbola, By Mr. Perks. Communicated by Mr Abr. de Moivre, F. R. S Perks, M.; de Moivre, A Philosophical Transactions (1683-1775). 1753-01-01. 25:2253–2262...
 Book Id: WHEBN0003630344 Subjects: Greek language, Greece, Euclid Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...and geometer, and the brother of Menaechmus . He is known for using the quadratrix to solve the problem of squaring the circle . Life and work... ...g of the circle. Due to his work the trisectrix later became known as the quadratrix of Dinostratus as well. Although Dinostratus solved the problem...
 Date: 1916, Vol. 15, No. 3 Book Id: WPLBN0001040882 Subjects: Math ► Abstract Full Text Search Details...rallel to OA through K' meets the radius OK at a point K" belonging to the quadratrix. If P is the intersection ofOA with the quadratrix, it follows i... ...s upon the ratio in which the radius OA is di- vided by the point P of the quadratrix. If this ratio could be constructed by elementary geometry, the ... ...try, the quad- rature of the circle would be effected. The equation of the quadratrix in polar co-ordinates is 2<^ a n sin (^ where a= OA. Putting 4> ... ... (^ where a= OA. Putting 4> = o, r= Vo, we have w = 2a It appears that the quadratrix was first invented for the trisection of an angle and that its r... ...nes laid down by the ancients, for our curve is only a modification of the quadratrix considered by them.*^ ^Klein, F.: Fatuous Problems of Elementary...
 Book Id: WPLBN0000560924 ► Abstract Full Text Search Details...essary to describe a new curve for every dif­ ferent angle. By means of the Quadratrix an angle may be trisected; but the Quadratrix cannot be descr... ...eviously trisected in forming the curve. Tbe thing must be done before tbe Quadratrix C8n furnisb 8ny aid in doing it. By the Trocboid or Cycloid, ... ... oG.) . ]. Tbis curve may be conceived to be generated, some­ wbat like the quadratrix and spiral, in the following manDer. If 00 the centre D the r...
 Book Id: WHEBN0002909893 Subjects: Geometry, Public domain, Angle trisection Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... Archimedean Spiral Quadratrix of Hippias Sectrix of Maclaurin ... ...tion Neusis construction Quadratrix Doubling the cube ...
 Date: 1918, Vol. 28 Book Id: WPLBN0001000755 Collections: Law, American Libraries Collection ► Abstract Full Text Search Details... equal to the ordinates of the given figure, and the second figure is the quadratrix of the given figure. Thus from this very sinlple idea, we llave... ...quadrature of the circle, or that no algebraical line can be given as its quadratrix. What 1 call algebraical lines are those that Descartes calls g... ...all algebraical lines are those that Descartes calls ge0- metrical, and by quadratrixes I mean all curves that, being descnDecL will give the quadrat... ...s of the ordinates was the same thing as to find an ordinate (that of the quadratrix) ,II of which the difference is proportional to the given ordin... ...a product.1 ·'(From this probably arose the first Fnn of the idea of the Quadratrix, in the ~enll! used by Lribcliz.) H(Substitute Ba,.,ow and Mer... ...h as yet applied to series, and sums of powers. The consideration of the Quadratrix leads him to make a further study of Barrow; and he is led to x...
 Book Id: WPLBN0000038516 Subjects: Math ► Abstract Full Text Search Details...5-50) die sachlich und historisch so iiberaus wichtige Abhandlung liber die Quadratrix, die "von DINOSTBATUS, NIKOJrlEDES und einigen Jiingeren zur ... ... 51-80) des vierten Buches bilden weitere Untersuchungen, die meist mit der Quadratrix zu­ sammenhangen: Beziehungen der Quadratrix zur Spirale, Spir...
 Book Id: WHEBN0003189382 Subjects: Golden ratio, Polygon, Triangle center Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... Q Quadrant (plane geometry) Quadratrix of Hippias S Special... ... Q Quadrant (plane geometry) Quadratrix of Hippias S Special...
 Book Id: WPLBN0001162946 ► Abstract Full Text Search Details... Trisectrix, Involute and Spiral of Archimedes. Parallel Curves. Conchoid. Quadratrix. Cissoid. Tractrix. Witch of Agnesi. Cartesian Ovals. Cassian Ov... ...ns for the purpose of solving one or the other of these problems, were the Quadratrix and Conchoid, whose construction is given later in this chapter;... .... 157 and 158 for the principles of their construction. THE CONCHOID. THE QUADRATRIX. 67 Ov c+Om; On=c Om; we may therefore express the relation to o... ...ons this surface is called the Conchoidal Hyperboloid. (See Fig. 219). THE QUADRATRIX OF DINOSTRATUS. 197. In Fig. Ill let the radius T rotate uniform... ... radius T; the locus of the intersection of MN with the radius will be the Quadratrix. Points 68 THEORETICAL AND PRACTICAL GRAPHICS. exterior to the ... ... amount equal to the diameter of the circle; the number of branches of the Quadratrix may therefore be infinite. It may be proved analytically that th... ...from equal to 2 r H- IT. 198. To trisect an angle, as T a, by means of the Quadratrix, draw the ordinate ap, trisect p T by s and x and draw 8 c and %...
 Date: 1890, Vol. 1 Book Id: WPLBN0000994108 Subjects: Philosophy, Filosofie, Philosophie ► Abstract Full Text Search Details...:n menlioned by the later Greek mathematicians, and by the Romans calJed "quadratrix." Regarding the nature of th is CUTVe we have exact knowledge f... ...nowledge from Pappus. But it will be s ufficienl. here, to state that the quadratrix is not a circle nor a portion of a circle, so that its construc... ...rwards, about the year )50. the mathematician Dinostratus showed that the quadratrix could also be used to solve the problem of rectification, and f...
 Book Id: WHEBN0000075837 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...classes. A mathematical discovery ascribed to Hippias is sometimes called the quadratrix of Hippias. His great skill seems to have consisted in del...
 Book Id: WPLBN0001294966 Collections: American Libraries Collection ► Abstract Full Text Search Details...lloxodrome. 180. Die Sinuslinie als Affine der Trochoide. Bern. Tschirnhauskns Quadratrix, Zwei weitere Erzeugungen der Sinuslinie. 181. Die hyperboli... ...Die Kochleoide als Schwerpunktslinie des Kreises. 186. Inverse der Kochleoide: Quadratrix des Dinostratus. Bern. Tangenteneigenschaft der Kochleoide u... ... worden war. Für die andere ist a = \ h . Das ist die von Ozanam »Geometrische Quadratrix« genannte Kurve; sie ist affin zur Versiera^^). *^) Ozanam, ... ...ibl. math. 1897, 7—12, 33/4). Leibniz benutzte die Quadratur der Geometrischen Quadratrix zur Aufstellung seiner berühmten Keihe i jt == 1 — i + i — f... ...ch die mit der Glei- chung y == a sin (jtx 12 a) stellte Tsohirnhausen^^^) als Quadratrix des Kreises auf. Eine geometrische Erzeugung der Sinuslinien... ...lg. 123. der Gleichung q = a Ö/sin6 ist von historischem Interesse. Sie heißt »Quadratrix des Dinosteatus«, da sich dieser Geometer (4. Jahrh. v. Chr.... ...o- KowÄLEWSKi, S. 100. — Die Kochleoide wurde zuerst von J. Perks (anonym) als Quadratrix in Phil. Trans. 1700, Nr. 260 aufgestellt. Als Schwerpunktsl... ... auf eine zur Schrauben- achse sen'k.rechte Ebene, so ist die Frojelction eine Quadratrix des Dinostratus. Auch den einfachen Beweis dieses Satzes mög... ...dalen 213. Pseudozykloiden 213; gespitzte 215; ungespitzte 216. Ptolemäus 231. Quadratrix d. Dinostratus 258/59. — , , geometrische 251. — des Tschirn...
 Book Id: WPLBN0000038519 Subjects: Math ► Abstract Full Text Search Details... Pbylik, 11, 21, 84. 40. n, 8S. Preiaaulgaben, 61. P.eudo-Verllera, 41. Quadratrix, fl. Quadratur, 11, 14. RaAn, fOe Recenlionen, 8, 4, ti, 6,...
 Book Id: WHEBN0003252820 Subjects: Lithuania, Russian Empire, Ukmergė Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details...Computing ;Mathematical contributions Description of Abdank-Abakanowicz quadratrix ;Other Photo of Château de Costaeres built by Abdank-Abakano...
 Book Id: WPLBN0002227812 Collections: Modern Regression, American Libraries Collection ► Abstract Full Text Search Details... metrical functions, and the next three to the ellipse ; the eighth to the quadratrix, and the ninth to the spheroid. The seventh is as follows) : (7)...
 Date: 1890, Vol. 26 Book Id: WPLBN0001000625 Subjects: Philosophy, Filosofie, Philosophie ► Abstract Full Text Search Details... to the ordinat~ of the given figure, and then this second figure is' the quadratrix of the given one; and thus from this extremely elegant consider...
 Book Id: WHEBN0034242810 Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... 0:54 41. "Quadratrix"   ...
 Book Id: WPLBN0001055713 Collections: Modern Regression, American Libraries Collection ► Abstract Full Text Search Details... metrical functions, and the next three to the ellipse ; the eighth to the quadratrix, and the ninth to the spheroid. The seventh is as follows) : (7)...
 Book Id: WPLBN0000556292 ► Abstract Full Text Search Details... of Plato, pupil of Eudoxus, and brother of Dinostratus (the inventor of the quadratrix), discovered and investigated the various curves made by trunc...
 Book Id: WHEBN0000097805 Subjects: Isaac Newton, London, England Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... = r3; #x3 + y3 = rxy, called la galande ; #y = (r − x) tan πx/2r, the quadratrix ; and #y = r tan πx/2r. It will be sufficient here to take ...
 Book Id: WPLBN0000816248 ► Abstract Full Text Search Details...e sophists. HIPPIAS FIO. 5 . of Elis first dis- covered the curve called the quadratrix. This curve (Fig. 5) is obtained by the intersection of the mo... ...7 ; Pappus, I, p. 253). From an analytical point of view the equation of the quadratrix is the natural result of the following equation in which r is ... ...ural result of the following equation in which r is the radius vector of the quadratrix, a the radius of the circle, and 6 the angle AOR. w u Or sin W... ...y the intersection of a cone and a plane suitably placed. Such curves as the quadratrix of Hippias, the conchoid of Nicomedes and the cissoid of Diode... ...he same position at the beginning and the end of the operation. In tracing a quadratrix, for example, the radius of the circle moves angularly whilst ...
 Date: 1850, Vol. 51-52 Book Id: WPLBN0001614028 Subjects: Insurance, Economy, Risk ► Abstract Full Text Search Details... metrical functions, and the next three to the ellipse ; the eighth to the quadratrix, and the ninth to the spheroid. The seventh is as follows) : (7)...
 Book Id: WHEBN0000091111 Subjects: Greek mathematics, Angle, Origami Collections: World Heritage Encyclopedia ► Abstract Full Text Search Details... geometry Intercept theorem List of geometry topics Morley's trisector theorem Quadratrix Trisectrix Additional referencesCourant, Richard, Herbert ...
 Book Id: WPLBN0001246864 Collections: American Libraries Collection ► Abstract Full Text Search Details.... Bernoulli her (Act. Erud. 1G91). Q u a d r a t r i X. Allgemeine Definition. Quadratrix ist eine Ciirve, die, über derselben Axe mit einer gegebenen... ... durch ihre Ordinaten die Flächenräume dieser angiebt. Geschichte. Die älteste Quadratrix ist die des Dinostra- tus, eines Zeitgenossen des Plato. Der... ...ssen des Plato. Der allgemeine Begriff stammt von Newton (Opuscula I, p. 102). Quadratrix des Dinostratus: Sei ein rechtwinkliges Coordinatensystem ge... ... Bogen sich zum Yiertelkreis verhält wie r — y : r, so gehört dieser Punkt der Quadratrix an. Gleichung der Curve 2 > qp 7t Mn (p Diese Curve hat unen... ...ni'^ cp — 2 cp sin cp cos cp -L g?' ^ n siu'^ cp (sin cp — cp cos cp) 33* 516 Quadratrix. und die Coordinaten des Krümmungsmittelpunktes: r sin'^ cp ... ... cp -| 1 log sin cp dcp, n
 Date: 1869, Volume: 34 May-Oct 1886 Book Id: WPLBN0002213989 ► Abstract Full Text Search Details...ostratus, brother of Menajchmus, whose name occurs in connection w-ith the quadratrix. Dr. AUman states the case of Dinostratus versus Hippias : "The ... ... versus Hippias : "The result of the whole discussion seems to be that the quadratrix was invented, probably by Hippias of Elis, with the object of tr...
 Date: 1869, Volume: 64 May-Oct 1901 Book Id: WPLBN0002213992 Subjects: Science, Natuurwetenschappen ► Abstract Full Text Search Details...(e = 2) and intersecting circle, a rect- angular hyperbola and circle, the quadratrix, the companion to the cycloid, and the Archimedean spiral, but n...
 Book Id: WPLBN0001030661 Subjects: Mathematics, Math, Natural Sciences ► Abstract Full Text Search Details... inverse with regard to vertex of Witch ofAgnesi : xy"^ = ia^ (2a-cc). n X Quadratrix of Dinostratus : y xcot^r . J d ITX ,, ,, Tschirnhausen : y = a ... ...; Partial, 206; Successive, 200-1. Dimensions of Units : 250. Dinostratus, Quadratrix : 231. Diodes, Cissoid : 230. Diophantine Equations : 28-30. Dis... ...n, 9, 10. Pythagorean Equation: 30. Quadrangle : 109. See Quadri- lateral. Quadratrix : Dinostratus, 231 ; Tschirnhausen, 231. Quadrilateral : C. P. 2...
 Date: 1810, Vol. 8 Book Id: WPLBN0001828282 ► Abstract Full Text Search Details... la(l they change into a (Iraight line. In the Pliil. Tranf. N' 260, a new quadratrix to the circle IS found by this means, being the curve defcribed ...
 Date: 1827, Volume: Year 1868-69 Book Id: WPLBN0001761189 Subjects: Society of Friends, Quakers, Theology ► Abstract Full Text Search Details...atus, which can readily bo described mechanically, and has been called the quadratrix of Dinostratus, because it has the property of thus solving the ...
 Book Id: WPLBN0001176719 Collections: Universal Library Collection ► Abstract Full Text Search Details...se and Sale ^ zSxtia Pyramid *^fgJ Q Quadrangle Quadrant s5^ Quadratic sSr Quadratrix Quantity Quotient i R / V Kadian Radius 45 ,Circnm ?5&iis& , Ine...
 Date: 1809, Vol. 5 Book Id: WPLBN0001126662 Subjects: Science -- Societies, Scientists, Technology ► Abstract Full Text Search Details...... 298 Dr. Ja, Keill, Dissect, of old J. Baylis 299 Biograph. Notice of Dr. Ja. Keill ibid Mr. Perks, Quadratrix to the Hyperb 302 Account of S. Dale... ...arkable and primary properties; as likewise those of the Conchoid, Cycloid, Logarithmic Line, Cissoid, Quadratrix, and Spiral Lines; and is very full ... ...- tain lines, whose squares or rectangles give the area of the figure desired. Of this sort is the old quadratrix of Dinostratus, by which the circle ... ... point ; which is its second property. III. The next property, and from which I call it the hyperbolic quadratrix, is this, in fig. Q, let fae be a pa... ... i, draw la parallel to the asymptote eh, intersecting the diagonal ih in M, FH in g, and touching the quadratrix in a. I say, that the hyperbolic are... ...bolic area ilm, is equal to a rectangle, whose sides are the ordinate ga and twice fh, the axis to the quadratrix, that is, the trilineal ilm = 2ph X ... ...^;, --T >sk IV. Supposing the same things as in the precedent proposition, I say, that the area of the quadratrix po^hf, is equal to half the square o... ... after the manner ofthe preceding proposition. VII. The radius of the curvature of any particle of the quadratrix is —— , and thus found geometrically... ... point ; which is its second property. III. The next property, and from which I call it the hyperbolic quadratrix, is this, in fig. Q, let fae be a pa...
 Book Id: WPLBN0000813242 Collections: Math, History, Education, Social Sciences, Canadian Libraries Collection ► Abstract Full Text Search Details...his same curve was used later in the quadrature of the circle, it received the name of quadratrix? 1 ISAAC NEWTON, Universal Arithmetick. Translated b... ...f descrip- ion be applied, then the screw must be excluded. 8 For a description of the quadratrix, see Gow, p. 164. That the in- 56 A HISTORY OP MATH... ..., x y 2ia f = 2ax. Then a 4 = a 2 / = 2a s x, x*= 2a 3 . But Hippocrates ventor of the quadratrix was Hippias of Elis is denied by HANKEL, p. 151, and... ...Pythagoreans, 14, 27, 29, 30, 49-53, 66, 136, 250. Quadratic equations. See Equations. Quadratrix, 55. Quadrature of the circle. See Squar- ing of cir...
 Book Id: WPLBN0000813241 Collections: Math, History, Education, Social Sciences, American Libraries Collection ► Abstract Full Text Search Details...ve was used later in the quadrature of the circle, it received the name of quadratrix. 3 1 ISAAC NEWTON, Universal Arithmetick. Translated by the late... ...on be applied, then the screw must be excluded. 8 For a description of the quadratrix, see Gow, p. 164. That the in- 66 A HISTORY OF MATHEMATICS The ... ...y*=2ax. Then x 4 = a V = 2 a?x, x B = 2a s . But Hippocrates ventor of the quadratrix was Hippias of Elis is denied by HANKEL, p. 151, and ALLMAN, p. ... ..., 14, 27, 29, 30, 49-53, 66, 136, 250. Quadratic equations. See Equations. Quadratrix, 55. Quadrature of the circle. See Squar- ing of circle. Quadrat...
 Book Id: WPLBN0000808652 Subjects: Math Collections: Math, History, Education, Social Sciences, Universal Library Collection ► Abstract Full Text Search Details...urve was used later in the quadrature of the circle, it received the name of quadratrix* 1 ISAAC NEWTON, Universal Arithmetick. Translated by the late... ...tion be applied, then the screw must be excluded. 8 For a description of the quadratrix, see Gow, p. 164. That the in- 6 A HISTORY OF MATHEMATICS The... ...y 2 =2ax. Then a; 4 = a~f = 2a z x, y?= 2a 3 . But Hippocrates ventor of the quadratrix was Hippias of Ells is denied by HANKEL, p. 151, and ALLMAN, p... ...ans, 14, 27, 29, 30, 49-53, 66, 136,250. Quadratic equations. See Equations, Quadratrix, 55. Quadrature of the circle. See Squar ing of circle. Quadra...
 Book Id: WPLBN0001255603 Subjects: Mathematical recreations, Math, Mathematics ► Abstract Full Text Search Details...at Plato was not born till 429 B. C. and Euclid much later. Hippias of Elis invented the quadratrix for the tri- section of an angle, and it was later... ...me, 191; of the camels, 193- Puzzles, geometric, 109. Pythagorean proposition, 121, 164. Quadratrix, 123. Quadrature of the circle, 122-129. Quaternio...
 Book Id: WPLBN0000878501 Subjects: Conic sections, Geometry, Analytic, Curves Collections: Geometry, Math, History, American Libraries Collection ► Abstract Full Text Search Details... loci. Thus Pappusf ascribes to Dinos- tratus and Nicomedes the use of the quadratrix for squaring the circle ; and Proclus (on Euclid I. 9) relates t... ...f discovered the genesis and investigated the properties), others used the quadratrix of Hippias or Nicomedes for the same purpose, whilst others by m... ...s to be noticed that the construction of such a curve as, for example, the quadratrix implies the conception of the idea of a Locus, of which before t... ...d that, as geometers before and after him were led to the discovery of the quadratrix, the conchoid and other plane loci in their attempts to square t... ...to attempt the construction * We have seen, from his acquaintance with the quadratrix, that Dinostratus, the brother of Menaechmua not to mention Hipp...
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