OF THE

MATHEMATICAL

REPOSITORY.

BY THOMAS LEYBOURN,
Of the Royal Military College.

VOL III.

London:

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

HATTON GARDEN.

1814.

Art.

I.

If.

Art,

II.

Page.

viz, 271 to 290.. 53

I Solutions to Questions proposed in No. VIII. viz. 241 to 270... 1

Solutions to Questions proposed in No. IX.

III. Solutions to Questions proposed in No. X.

IV. Solutions to Questions proposed in No. XI.

Notices relating to Mathematics, pages 49, 97,

PART II.

viz. 291 to 310...105

viz, 311 to. 330...169

ORIGINAL ESSAYS.

Mr. GOUGH on Polygonal Numbers.............

Mr. Knight on the Binomial Theorem, and the Logarithmic

Series....

Page.

1

8

III.

An illustration of the 47th Prop. of the 2d Book of the Prin-

cipia, by A. B..................

A curious indeterminate problem, by Mr. CUNLIFFE............

Solutions to a curious problem in dynamics, by J. L....................

Mr. KNIGHT on the Expansion of a formula connected with

Physical Astronomy..........

VII. Mr. KNIGHT on the sine and cosine of Multiple arcs....... ..............

VII. Mr. NOBLE on Magic Squares..............

IX.

Baron Maseres on the mutual attraction of all the particles of

matter.......

X.

Mr. BARLOW on Polygonal Numbers.

03-27-43 WE

58

60

XI. Mr. BARLow on the irreducible Case of Cubic Equations........ 46

XII, New Properties of the Conic Sections, by Mr. J.F.W. HERSCHEL

XIII. Indeterminate Problems, by Mr. CUNLIFFE........................................

XIV. Mr. CUNLIFFE on the Ellipse and Hyperbola

XV. Mr BARLOW on the approximation of the roots of Equations. 97

XVI. Properties of the right-angled triangle, by Mr. BRANSÈY........

XVII. Mathematical Scraps by Mr. WHITE....

I. Legendre's Memoir on Elliptic Transcendentals concluded.... 1 to 45
II. A formula for the length of a circular arc, by Euler....

Cambridge Problems, for 1811, 1812 and 1813, pages 1 to 38.

46