Mathematical Questions and Solutions, from the "Educational Times": With Many Papers and Solutions in Addition to Those Published in the "Educational Times", Volum 29W. J. C. Miller Hodgson, 1878 |
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Resultat 1-5 av 5
Side ix
... cusps and four nodes ; find their positions , and the length of the arc external to the ellipse between two real cusps ; and account fully for the apparent reduction of the curve to a circle and two parabolas respectively , in special ...
... cusps and four nodes ; find their positions , and the length of the arc external to the ellipse between two real cusps ; and account fully for the apparent reduction of the curve to a circle and two parabolas respectively , in special ...
Side 47
... cusps and four nodes ; find their positions , and the length of the arc external to the ellipse between two real cusps ; and account fully for the apparent reduction of the curve to a circle and two parabolas respectively , in special ...
... cusps and four nodes ; find their positions , and the length of the arc external to the ellipse between two real cusps ; and account fully for the apparent reduction of the curve to a circle and two parabolas respectively , in special ...
Side 48
... cusps are more easily found from the equation = P = b ( 1 - e2 sinλ ) ̄ * , [ BOOTH's New Geometrical Methods , Vol ... cusp sign . dP Now αλ therefore = e2 62 be2 sin λ cos A ( 1 - e2 sin2 x ) ; = P3 sin A cos λ ; ( P3 sin x cos x ) + P ...
... cusps are more easily found from the equation = P = b ( 1 - e2 sinλ ) ̄ * , [ BOOTH's New Geometrical Methods , Vol ... cusp sign . dP Now αλ therefore = e2 62 be2 sin λ cos A ( 1 - e2 sin2 x ) ; = P3 sin A cos λ ; ( P3 sin x cos x ) + P ...
Side 49
... cusps situated symmetrically one in each quadrant . The length of the curve is 8 = = С Pax + dP = b αλ of dλ be2 sin Ʌ cos A + ( 1 − e2 sin2λ ) ( 1 - e2 sin2x ) . ( 3 ) , and at the point midway between two cusps λ = T . Taking then ...
... cusps situated symmetrically one in each quadrant . The length of the curve is 8 = = С Pax + dP = b αλ of dλ be2 sin Ʌ cos A + ( 1 − e2 sin2λ ) ( 1 - e2 sin2x ) . ( 3 ) , and at the point midway between two cusps λ = T . Taking then ...
Side 50
... cusps . The points of contact of the double tangents CI and CJ are easily found by putting R = 0 in ( 2 ) , whence it is seen that they lie on the imaginary ellipse Q1 = 0 , the other points where they cut the curve lying on the ellipse ...
... cusps . The points of contact of the double tangents CI and CJ are easily found by putting R = 0 in ( 2 ) , whence it is seen that they lie on the imaginary ellipse Q1 = 0 , the other points where they cut the curve lying on the ellipse ...
Vanlige uttrykk og setninger
a₁ angles asymptotes axis centre cerchio chance circumference circumscribed circle coefficient common points common tangents comune conic cos² cubic cubic curve curve cusps directrix distance divide harmonically drawn ellipse envelop equal fixed points focus four common G. S. CARR given Hence hyperbola infinity inflexion inscribed integral intersection inverse J. J. WALKER line at infinity locus negative pedal nine-point circle nodes pairs parabola parallel parallelepiped passes perpendicular plane points of contact polar Prof Professor WOLSTENHOLME prove punti punto question radius random chords random lines random points reciprocal respective probabilities retta semiperimeter sides SIMSON line sin² sin³ Solution by E. B. sphere straight line subtend tangential equation tangents TEBAY theorem triangle ABC triangolo vertex vertical whence WOOLHOUSE
Populære avsnitt
Side 58 - Between 1° and 2". Between 2° and 3°. Between 3° and 4°. Between 4° and S°_ More than 5°..
Side 66 - The chief use of the method, as far as I have yet carried it, is to determine the new limits of integration when we change the order of integration or the variables in a multiple integral, and also to determine the limits of integration in questions relating to probability.
Side 80 - Again, the well-known result that the feet of the perpendiculars on the sides of a triangle from any point on the circumscribing circle are cottinear follows from example 7, p.
Side 106 - ... 32.2 Use a fine needle point to make a pin prick about 0.005 in. (0.13 mm) in diameter at about the center of each of the marks in 32.1. 32.3 Mount the specimen flat with the apparatus of 30.2 and obtain distance measurements with the apparatus of 30.
Side x - Find the centre of a circle cutting off three equal chords from the sides of a triangle. 6. The triangle whose vertices are the three points of contact of the inscribed circle with the sides of a triangle, is always acuteangled.
Side 34 - The enunciation of a Theorem consists of two parts, — the hypothesis, or that which is assumed, and the conclusion, or that which is asserted to follow therefrom. Thus in the typical Theorem, If A is B, then C is D, (i), the hypothesis is that A is B, and the conclusion, that C is D. From this Theorem it necessarily follows that : If C is not D, then A is not B, (ii).
Side 21 - The highest point of the wheel of a carriage, rolling on a horizontal road, moves twice as fast as each of two points in the rim, whose distance from the ground is half the radius of the wheel.