“The first important example solved by Descartes in his geometry is the "problem of Pappus"; viz. "Given several straight lines in a plane, to find the locus of a point such that the perpendiculars, or more generally, straight lines at given angles, drawn from the point to the given lines, shall satisfy the condition that the product of certain of them shall be in a given ratio to the product of the rest. Of this celebrated problem, the Greeks solved only the special case when the number of given lines is four, in which case the locus of the point turns out to be a conic section. By Descartes it was solved completely, and it afforded an excellent example of the use which can be made of his analytical method in the study of loci. Another solution was given later by Newton in the Principia.”
“The so called άναλυόμϵνος ('Treasury of Analysis') is... a special body of doctrine provided for the use of those who, after finishing the ordinary Elements, are desirous of acquiring the power of sol...”
Pappus of Alexandria
“Analysis... takes that which is sought as if it were admitted and passes from it through its successive consequences to something which is admitted as the result of synthesis: for in analysis we assum...”
Pappus of Alexandria
“But in synthesis, reversing the process, we take as already done that which was last arrived at in the analysis and, by arranging in their natural order as consequences what were before antecedents, a...”
Pappus of Alexandria
“Now analysis is of two kinds, the one directed to searching for the truth and called theoretical, the other directed to finding what we are told to find and called problematical. (1) In the theoretica...”
Pappus of Alexandria
“waives the customary distinction between a circle, and ellipse, a parabola, and a hyperbola; these curves are simply conics, all alike. Although conics were studied by , Euclid, Archimedes and Apollon...”
Pappus of Alexandria