CONTENTS TO VOL. I.

Tract i. The Principles of Bridges. 1

II. Queries concerning London-bridge, proposedin the year 1746, by the Magistrates of theCity. ------ T 115

hi. Experiments and Observations proposed tobe made on London-bridge, by the Committeeof the Royal Society. - - - - 120

iv. Consequences in the Tides in the RiverThames, by erecting Blackfriars-bridge. 122

v. Answers to Questions proposed by the Com-

mittee of Parliament, on a Bridge of one Archover the Thames at London. - 127

VI. History and Practice of Iron Bridges. - 144

VII. On the Nature and Value of Infinite Scries. 167

viii. New Method for the Value of Infinite Se-ries. ------- 176

ix. On summing the very slow series a + b.v +

ex* + &c. 203

x. General Rules for the Extraction of all Roots. 210

xi. On the Roots of the Equation x ” — px”~* +

y,r M -&c. = 0. -218

xn. Demonstration of the Binomial Theorem. 228

xiii. On the Common Sections of the Sphere and

Cone. 245

xiv. Division of Circles into any Parts of equal

Areas and Perimeters. - 254

xv. Geometrical Division of the Circumference

of a Circle. ------ 25S

xvi. Trigonometry without the Tables of Sines,

&c. ------- 260

xvii. Investigation of Machin’s Quadrature of

the Circle. 266

xviii. On quickly-converging Series for theCircle. - - - 268

xix. History of Trigonometrical Tables. - 278

xx. The History of Logarithms. - - 306