of the analytical geometry of his time. Monge ( ) gave the modern ‘point-slope’ form of equation of a line as y – y ′ = a ( x – x ′ ) and the condition of perpendicularity of two lines as aa ′ + = . S.F. Lacroix ( – ) was a prolific textbook writer, but his contributions to analytical geometry are found scattered.
He gave the ‘two-point’ form of equation of a line as β β β = α ) α α – y – x – – ′ ′ and the length of the perpendicular from ( α , β ) on y = ax + b as ( β – a – b His formula for finding angle between two lines was tan θ a – a aa ′ = ′ . It is, of course, surprising that one has to wait for more than years after the invention of analytical geometry before finding such essential basic formula. In , C. Lame, a civil engineer, gave m E + m ′ E ′ = as the curve passing through the points of intersection of two loci E = and E ′ = .
Many important discoveries, both in Mathematics and Science, have been linked to the conic sections. The Greeks particularly Archimedes ( – B.C.) and Apollonius ( B.C.) studied conic sections for their own beauty. These curves are important tools for present day exploration of outer space and also for research into behaviour of atomic particles.