**ALGEBRA**, or the Doctrine of EQUATIONS ;

Simple, Quadratic, Cubic, &c.

Operations thereof, as Reduction, Construction, &c.

**ANALYTICS**, or the Resolution of PROBLEMS by Species or Symbolical Expressions :

Rules or Operations hereof, Addition, Subtraction, Multiplication, &c.

Application thereof, in Combinations, Permutations, Magic Squares, Chances, Gaming, &c.

Series, Progressions, &c.

Methods de Maximis, Fluxions, Exponentials, Tangents, &c.

**ARITHMETIC**, including the Doctrine of DISCRETE or Discontinuous QUANTITY,

viz. Number, Ratio, Proportion,&c.

Kinds, as Integer, Fraction, Decimal, Surd, &c.

Relations, as Root, Power, Square, Cube, &c.

Rules or Operations thereof, as Notation, Numeration, Addition, Subtraction, &c.

Reduction, Practice, Position, &c.

Extraction, Approximation, &c.

Instruments subservient thereto, as Logarithms, Nepair's Bones, &c.

**GEOMETRY**,or the Doctrine of EXTENDED, or Continuous QUANTITY,

viz. l°, Lines, Right, Perpendicular, Parallel, Oblique, &c.

Angles, Acute, Scalenous, Vertical, Opposite, &c.

z°, Figures, or Surfaces, Triangle, Square, Parallelogram, Trapezium, Polygon, &c.

Circumstances hereof, as Perimeter, Area, &c.

Operations relating hereto, as Bissecting, Dividing, Multiplying, Measuring, &c.

Instruments used therein, as Compasses, Ruler, Square, Parallelism, Scale, &c.

Curves, as Circle, Cycloid, Cissoid, Catenaria, Caustic, Evolute, quadratrix, &c.

Circumstances thereof, as Axis, Diameter, Radius, Centre, Circumference, Absciss, Ordinate, &c.

Arch, Chord, Sine, Tangent, Secant, &c.

Instruments used herein, as Artificial Lines, Canons, &c.

Operations arising herefrom, as Surveying, taking Angles or Bearings, &c.

with Quadrant, Plain-Table, Semicircle, Circumferentor, &c.

taking Distances, with Chain, Perambulator, &c.

Plotting into Draught, Map, &c.

with Protractor, &c.

3°, Solids or Bodies, as Cube, Parallelepiped, Prism, Pyramid, Cylinder, Polyhedron, &c.

Their Surface, Solidity, &c.

Operations relating hereto, as Cubature, measuring of Timber, Gauging, &c.

Instruments used herein, as Carpenters Rule, Sector, Sliding Rule, Gauging Rod, &c.----

The Sphere, its Doctrine, Projection, &c.

Application thereof, in Planisphere, Analemma, &c.----

The Cone, its Sections, Ellipsis, Parabola, Hyperbola, &c.

Their Asymptotes, Foci, &c.

Their Construction, Quadrature, Rectification, &c.