### Contents

 GLOSSARY OF TERMS xi INTRODUCTION xvi THE INVERSE METHOD OF FLUXIONS xvi HYDRAULICS xvi ASTRONOMY xxvi LOGARITHMS 19 ON FUNCTIONS 97 FACTORIALS 108
 Of Vanishing Fractions 464 ON THE RECTIFICATION OF CURVES 502 ON THE CUBATURE OF SOLIDS 512 PRACTICAL GEOMETRY 520 page 526 PERSPECTIVE Part I 542 PROJECTION OF A SPHERE IN PLANO 547 GNOMONICAL PROJECTION OF THE SPHERE 564

 ON LIFE ANNUITIES 120 CONVERGENCY OF SERIES 149 ELEMENTS OF EUCLIDBook I 159 PLANE TRIGONOMETRY 344 SPHERICAL TRIGONOMETRY 367 TWO HUNDRED MISCELLANEOUS QUESTIONS 387 CONIC SECTIONS 397 Origin and General Equation of the Conic Sections 404 OF THE ELLIPSE 410 PERSPECTIVE Plate 1 to face 417 OF THE HYPERBOLA 418 OF SEVERAL OTHER CURVES 426 FLUXIONS 437 Application of Fluxions to the Theory of Curves 447
 5 576 PRACTICAL CONSTRUCTION OF MAPS 577 512 588 MENSURATION 607 Mensuration of Solids 627 Of Specific Gravity 637 LAND SURVEYING 651 GAUGING 663 MECHANICS 673 Of the Composition and Resolution of Forces 687 On the Collision of Elastic Bodies 694 On the Wheel and Axle 703 On the Screw 709

### Popular passages

Page 172 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Page 191 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 190 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Page 196 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 192 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Page 177 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 209 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 284 - The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram.
Page 286 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 179 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.