“We shall now cite the more important of those theorems in the Mathematical Collections which are supposed to be original with Pappus. First of all ranks the elegant theorem re-discovered by Guldin, over 1000 years later, that the volume generated by the revolution of a plane curve which lies wholly on one side of the axis, equals the area of the curve multiplied by the circumference described by its centre of gravity.”
“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