Analysis and Intervention in Intellectual and Developmental Disabilities

Ask a wise man to dinner and he'll upset everyone by his gloomy silence or tiresome questions. Invite him to a dance and you'll have a camel prancing about. Haul him off to a public entertainment and his face will be enough to spoil the people's entertainment.

Analysis and synthesis, though commonly treated as two different methods, are, if properly understood, only the two necessary parts of the same method. Each is the relative and correlative of the other.

Vieta presented his analytic art as "the new algebra" and took its name from the ancient mathematical method of "analysis", which he understood to have been first discovered by Plato and so named by Theon of Smyrna. Ancient analysis is the 'general' half of a method of discovering the unknown in geometry; the other half, "synthesis", being particular in character. The method was defined by Theon like this: analysis is the "taking of the thing sought as granted and proceeding by means of what follows to a truth that is uncontested"'. Synthesis, in turn, is "taking the thing that is granted and proceeding by means of what follows to the conculsion and comprehension of the thing sought" (Vietae 1992: 320). The transition from analysis to synthesis was called "conversion", depending on whether the discovery of the truth of a geometrical theorem or the solution ("construction") to a geometrical problem was being demonstrated, the analysis was called respectively "theoretical" or "problematical".