**Gregoire de Saint-Vincent**(1584-1667)- Born in Belgium.
- He discovered the expansion of
**log(1+x)**in ascending powers of**x**.

**Joseph Saurin**(1659-1737)- Born in France.
- he showed how the tangents at the multiple points of curves can be determined by analysis.

**Henry Smith**(1826-1882)- Born in England.
- He did research on linear indeterminate equations and congruences.
- He also researched on the orders and genera of ternary quadratic forms.
- He established the principles on which the extension to the general case of
indeterminates depends, and obtained the general formulae.**n**

**Willebrod Snell**(1581-1626)- Born in Netherlands.
- In geodesy, he stated the principles for determining the length of an arc of a meridian from the measurement of any base line.
- In spherical geometry, he discovered the properties of the polar or supplemental triangle.

**Karl Georg Christian von Staudt**(1798-1867)- Born in Germany.
- He constructed a system of geometry built up without any reference to number or magnitude.
- He established the non-metrical projective properties of figures, using his system.
- He obtained a geometrical definition of a number.

**Jacob Steiner**(1796-1863)- Born in Switzerland.
- He discovered the Steiner (Roman) surface, which has a double infinity of conic sections on it.
- His Steiner theorem states that two pencils (collections of geometric objects) by which a conic is projected from two of its points are projectively related.
- He proved that any Euclidean figure can be generated, using only a straight rule if the plane of construction has a circle with its centre marked on it.

**Simon Stevinius**(1548-1620)- Born in Netherlands.
- He suggested the use of fractional, but not negative, exponents.
- He introduced the triangle of force in statics.

**James Joseph Sylvester**(1814-1897)- Born in England.
- He wrote on canonical forms, on the theory of contavariants, on reciprocants, and on the theory of equations in higher algebra.