PRINTED AND SOLD BY W. GLENDINNING, NO. 25,

HATTON GARDEN.

1809.

Art.

1.

OF THE

SECOND VOLUME.

PART I.

MATHEMATICAL QUESTIONS.

Page.

Solutions to Questions proposed in No. IV. viz. 121 to 150. 1

JI. Solutions to Questions proposed in No. V. viz. 151 to 180. 65

III. Solutions to Questions proposed in No. VI. viz. 181 to 210. 145

IV. Solutions to Questions proposed in No. VII. viz. 211 to 240. 197

Notices relating to Mathematics, pages 63, 193, 257.

Art.

1.

PART II.

ORIGINAL ESSAYS.

......

Demonstration of a Proposition in Mechanics. By A. B.

II. On the Motion of a Pendulum whose points of suspension are
moveable. By Mr. JOHN GOUGH.

III. An Occular Demonstration of the Forty-seventh proposition of
the first book of Euclid. By Mr. H. DOUGLAS.
IV. Theorems for finding the Sums of certain Infinite Series by means
of Circular Arcs. By Mr. JAMES CUNLIFFE, of the Royal
Military College.

V. Theorems for finding the Sums of certain Infinite Series by means
of Hyperbolic Logarithims. By Mr. CUNLIFFE.

Page.

13

14

31

VI. Solution of a Dynamical Question. By Mr. JOHN BARRY.

VII. Some Properties of Parallelograms, with the application of them

to the moments of Forces. By Mr. JOHN GOUGH.

VIII. Solutions of some Mechanical Problems. By A. B.

IX. A Diophantine Problem. By Mr. CUNLIFFE.

X. The Theory of Amicable Numbers. By Mr. JOHN GOUGH

XI. A New Solution of a Problem in Insurance of Money on Lives.

By PHILALETHES CANTABRIGIENSIS.

XII. Theorems for finding the Sums of certain Infinite Series. By

Mr. CUNLIFFE

XIII. On the Attraction of an infinite solid elliptic cylinder. By

Mr, THOMAS KNIGHT.

XIV. Two Indeterminate Problems. By Mr. CUNLIFFE.

XV. Mr. KNIGHT on the Proportionality of the Force to the Velo-

city, and on the Composition of Forces.

50

54

58

XVI. On the Composition of rotatory Motions. By Mr. KNIGHT....

XVII. On the Expansion of certain Functions. By Mr. KNIGHT. 64

XVIII. Mr, KNIGHT on the Expansion of any Function of a Mul-
tinomial.

62

XIX. Demonstration of a.Theorem in the Diophantine Analysis. By

Mr BARLOW, of the Royal Military Academy, Woolwich, 70

XX. Mr. KNIGHT on the Binomial Theorem."

I. A Dynamical Principle, with its application,. By Mr. BAZLEY. 77

PART III.

74

MATHEMATICAL MEMOIRS EXTRACTED

FROM WORKS OF EMINENCE.

A Memoir on Elliptic Transcendentals. By ADRIEN MARIE LE

GENDRE, Member of the National Institute of France, and