New Series of The Mathematical Repository, Volum 4W. Glendinning, 1819 |
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Side
... Solutions to Questions proposed in No. XII . Solutions to Questions proposed in No. XIII . III . Solutions to Questions ... Solution of a Dynamical Problem by A.B ......... XV . XVI . XVII . XVIII . An Indeterminate Problem , by Mr ...
... Solutions to Questions proposed in No. XII . Solutions to Questions proposed in No. XIII . III . Solutions to Questions ... Solution of a Dynamical Problem by A.B ......... XV . XVI . XVII . XVIII . An Indeterminate Problem , by Mr ...
Side 1
... Solutions to Questions proposed in Number XII . I. QUESTION 331 , by Mr. JOHN HYNES , Dublin . To find any number of squares whose sum and product are equal . SOLUTION , by Mr. CUNLIFFE , R. M. College . In order to make the solution ...
... Solutions to Questions proposed in Number XII . I. QUESTION 331 , by Mr. JOHN HYNES , Dublin . To find any number of squares whose sum and product are equal . SOLUTION , by Mr. CUNLIFFE , R. M. College . In order to make the solution ...
Side 4
... results of the two preceding cases are atten- tively considered , there will be no difficulty in extending the solution to as many squares as we please , without any further calculation . For let w2 , u2 , v2 , ( 4 )
... results of the two preceding cases are atten- tively considered , there will be no difficulty in extending the solution to as many squares as we please , without any further calculation . For let w2 , u2 , v2 , ( 4 )
Side 7
... SOLUTION , by Mr. CALLOW , the Proposer . Put x and y for the required quantities ; then , by the question , x2 + y2 . ( x + y ) = a , and x * + y * + ( x + y ) -2 ( x3 + y3 ) = b ; adding these two equations , we have - x + + y1 — 2 ...
... SOLUTION , by Mr. CALLOW , the Proposer . Put x and y for the required quantities ; then , by the question , x2 + y2 . ( x + y ) = a , and x * + y * + ( x + y ) -2 ( x3 + y3 ) = b ; adding these two equations , we have - x + + y1 — 2 ...
Side 8
... solution of a general cubic to be known ? FIRST SOLUTION , by Mr. CALLOW , the Proposer . From the second equation we get y = x + m , which substi- tuted in the first , it becomes x + ( 4x3 + 4xm2 + 2qx + r ) m + ( 6x2 + q + m2 ) m2 + ...
... solution of a general cubic to be known ? FIRST SOLUTION , by Mr. CALLOW , the Proposer . From the second equation we get y = x + m , which substi- tuted in the first , it becomes x + ( 4x3 + 4xm2 + 2qx + r ) m + ( 6x2 + q + m2 ) m2 + ...
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Vanlige uttrykk og setninger
altitude attraction axis base bisecting body centre of gravity chord circumference cone conic section cosine CUNLIFFE curve cycloid denote described determine diameter difference distance draw drawn ellipse equal equation expression fluxion force formula given circle given point given ratio hence hyperbola inscribed John Pond latitude Lemma length logarithm Mathematical Olinthus Gregory orbit ordinate PALABA parabola parallel pendulum perpendicular plane prime numbers Proposer Prove quadrant quantities QUESTION R. M. College radius rectangle right angles right ascension roots Royal Military Academy segments shew sides sin² sin³ sine SOLUTION specific gravity sphere spherical reflector spheroid square straight line supposed surface tangent theorem triangle velocity vertex vertical whence wherefore
Populære avsnitt
Side 6 - 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. By Theorem II. we have a : b : : sin. A : sin. B.
Side 135 - Shew that the sum of the products of each body into the square of- its velocity is a minimum, when the velocities are reciprocally proportional to the quantities of matter in the bodies.
Side 122 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
Side 138 - If the circumference of a circle be divided into any number of equal parts, the chords joining the successive points of division form a regular polygon inscribed in the circle ; and the tangents drawn at the points of division form a regular polygon circumscribed about the circle.
Side 28 - In a triangle, having given the ratio of the two sides, together with both the segments of the base, made by a perpendicular from the vertical angle, to determine the sides of the triangle.
Side 98 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Side 50 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included...
Side 123 - CLASSES. 1. Shew from the principles of the fifth book of Euclid, that a ratio of greater inequality is diminished, and of less inequality increased, by adding a quantity to both its terms. 2. The time of day at a given place determined from observations of the sun's altitude is 9h. 10'.45"; and a chronometer set to Greenwich time shews 6h. 3'.
Side 40 - 16 . 24 1.3.5.7 6.7.9.11 9.11.13.15 to n terms by increments. to n terms. 21. If seven balls be drawn from a bag containing eleven in all, five of which are white and six black ; what is the probability that three white balls will be drawn?