The MathematicianJ. Wilcox, 1751 - 399 sider |
Inni boken
Resultat 1-5 av 54
Side 41
... let this Value be fubftituted for n in the firft Equation , and it will become x + a = 2 myy P 2 y 2 2px ነገ P P = = 2 ; confequently a 2 xxx ; or G 2x ; The MATHEMATICIAN . 41 Diameter produced) between the Vertex and Inter- ...
... let this Value be fubftituted for n in the firft Equation , and it will become x + a = 2 myy P 2 y 2 2px ነገ P P = = 2 ; confequently a 2 xxx ; or G 2x ; The MATHEMATICIAN . 41 Diameter produced) between the Vertex and Inter- ...
Side 48
... Equation yax - xxax2 , a Semi- 9 a + x12 χάς circle be defcribed ; it is required to exhibit in fi- nite Terms , the exact Ratio between that Semi- circle , and the whole curvilineal Space included between the faid Curve and its Axis ...
... Equation yax - xxax2 , a Semi- 9 a + x12 χάς circle be defcribed ; it is required to exhibit in fi- nite Terms , the exact Ratio between that Semi- circle , and the whole curvilineal Space included between the faid Curve and its Axis ...
Side 72
... Equations taken from the latter gives , 4tz = 4bx ; therefore z = 46x bx ; which being fubftituted in Place of 4t ... Equation of the Curve . 2 2 2 DEFINITION . - A third Proportional to the tranfverfe and con- jugate Axis , is called ...
... Equations taken from the latter gives , 4tz = 4bx ; therefore z = 46x bx ; which being fubftituted in Place of 4t ... Equation of the Curve . 2 2 2 DEFINITION . - A third Proportional to the tranfverfe and con- jugate Axis , is called ...
Side 73
... Equation of the Curve for c2 , a new Equation of the Curve will be pro- duced in Terms of the Parameter , & c . viz . ty ' 2 2 = tpx - px ; or y1 = 2 x 2 xtx - x ; therefore t : pt - xxx : y ' . QE . D. COROLLARY . As the Rectangle of ...
... Equation of the Curve for c2 , a new Equation of the Curve will be pro- duced in Terms of the Parameter , & c . viz . ty ' 2 2 = tpx - px ; or y1 = 2 x 2 xtx - x ; therefore t : pt - xxx : y ' . QE . D. COROLLARY . As the Rectangle of ...
Side 76
... the conjugate Axe , and the Rectangle of the Abfciffa into the Parameter , to the Square of the conjugate Axe ; that is , FG : BG × LR : : ED2 — BG x LR : ED2 . DE- - 4 DEMONSTRATIO N. From the Equation of the Curve 76 The MATHEMATICIAN .
... the conjugate Axe , and the Rectangle of the Abfciffa into the Parameter , to the Square of the conjugate Axe ; that is , FG : BG × LR : : ED2 — BG x LR : ED2 . DE- - 4 DEMONSTRATIO N. From the Equation of the Curve 76 The MATHEMATICIAN .
Vanlige uttrykk og setninger
Abfciffa Abfcifs affigned Affymptotes alfo alſo Anfwered by John Arch Bafe Baſe becauſe bifecting Cafe Center Circle circumfcribing Cofine confequently Curve defcribed DEMONSTRATION determine Diameter Difference Diſtance draw Ellipfe equal Equation expreffed Expreffion faid fame fecond fhall fhew fimilar Triangles fince finite firft firſt flowing Quantities Fluent Fluxions fome fuch fuppofed Geometry given greateſt Hyperbola increaſe infcribed infinite infinite Series Interfection John Turner laft leffer lefs Magnitude Meaſure Method Method of Fluxions Motion muſt Number Ordinate paffing Parabola parallel Parallelogram Parameter perpendicular Pofition Point of Contact PROBLEM Progreffion Prop propofed Proportion Q. E. D. PROPOSITION Radius Reaſoning Rectangle refpectively reprefent right Angle right Line Semi-diameter Sides Sine Sir Ifaac Space Square Subtangent Tangent thefe theſe thofe thoſe thro tion tranfverfe Axe Trapezium ultimate Ratio Velocity Vertex whence whofe
Populære avsnitt
Side 157 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Side 193 - Velocity with which they increase and are generated; I sought a Method of determining Quantities from the Velocities of the Motions or Increments, with which they are generated; and calling these Velocities of the Motions or Increments Fluxions, and the generated Quantities Fluents, I fell by degrees upon the Method of Fluxions, which I have made use of here in the Quadrature of Curves, in the Years 1665 and 1666.
Side 6 - They found, that similar triangles are to each other in the duplicate ratio of their homologous sides; and, by resolving similar polygons into similar triangles, the same proposition was extended to these polygons also.
Side 13 - ... all their theorems of this kind. It is often said, that curve lines have been considered by them as polygons of an infinite number of sides. But this principle no where appears in their writings. We never find them resolving any figure, or solid, into infinitely small elements.
Side 57 - Whatfoever politive ideas we have in our minds of any fpace, duration, or number, let them be ever fo great, they are ftill finite ; but when we fuppofe an inexhauftible remainder, from which we remove all bounds, and wherein we allow the mind an endlefs...
Side 205 - ... time approach to each other within less than any given difference, become ultimately equal. If you deny it, let them be ultimately unequal, and let their ultimate difference be D, then they cannot approach nearer to equality than quantities having a difference D: which is against the hypothesis.
Side 193 - I consider mathematical quantities in this place not as consisting of very small parts, but as described by a continued motion. Lines are described, and therefore generated not by the apposition of parts, but by the continued motion of points ; superficies by the motion of lines ; solids by the motion of superficies ; angles by the rotation of the sides ; portions of time by a continual flux ; and so in other quantities. These geneses really take place in the nature of things, and are daily seen...
Side 65 - ... of the simple addition of rising Moments, or of the continual flux of one Moment, and for that reason ascribe only length to it, and determine its quantity by the length of the line passed over : As a line, I say, is looked upon to be the trace of a point moving forward, being in some sort divisible by a point, and may be divided by Motion one way, viz. as to length ; so Time may be conceived as the trace of a Moment continually flowing, having some kind of divisibility from an Instant, and from...
Side 192 - ... flowing quantities." For example: I don't here consider Mathematical Quantities as composed of Parts extremely small, but as generated by a continual motion. Lines are described, and by describing are generated, not by any apposition of Parts, but by a continual motion of Points. Surfaces are generated by the motion of Lines, Solids by the motion of Surfaces, Angles by the Rotation of their Legs, Time by a continual flux...
Side 6 - ... objections that have been made to it. But, before we proceed, it may be of use to consider the...