“In mechanics Pappus shewed that the centre of mass of a triangular lamina is the same as that of an inscribed triangular lamina whose vertices divide each of the sides of the original triangle in the same ratio. He also discovered the two theorems on the surface and volume of a solid of revolution which are still quoted in text-books under his name: these are that the volume generated by the revolution of a curve about an axis is equal to the product of the area of the curve and the length of the path described by its centre of mass; and the surface is equal to the product of the perimeter of the curve and the length of the path described by its centre of mass.”
“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