"Let AB be taken as unity, and let it be required to multiply BD by BC. I have only to join the points A and C, and dr…"

"If the square root of GH is desired, I add, along the same straight line, FG equal to unity; then, bisecting FH at K,…"

"Often it is not necessary thus to draw the lines on paper, but it is sufficient to designate each by a single letter.…"

"If... we wish to solve any problem, we first suppose the solution already affected, and give names to all the lines t…"

"Thus, all unknown quantities can be expressed in terms if a single quantity, whenever the problem can be constructed …"

"I have given these very simple [methods] to show that it is possible to construct all the problems of ordinary geomet…"

"This is also evident from what Pappus has done in the beginning of his seventh book, where... he refers to a question…"

"The considerations that forced ancient writers to use arithmetical terms in geometry, thus making it impossible for t…"

"The question, then, the solution of which... was completed by no one, is this: Having three, four or more lines given…"

"Any problem in geometry can be reduced to such terms that a knowledge of the lengths of certain straight lines is suf…"