Quote: can reduce any problem in geometry to a knowledge of the lengths of certain straight lines

Quotation Skeleton

Any problem in geometry can easily be reduced … its construction. … [p. 296] Often it is not necessary thus to … Thus, to add the lines BD and GH, … [p. 296] Finally, so that we may be sure … as names are assigned or changed. … If, then, we wish to solve any problem, … needful for its construction,--to those that are unknown … lines, we must unravel the difficulty in any … express a single quantity in two ways. This … to the terms of the other. We must … considering everything involved, so many cannot be found, … choose arbitrarily lines of known length for each … each in order … so as to obtain a value for each … [p. 297] I may express this as follows: z … That is, z, which I take for the … of b diminished by a multiplied by z …   Google-1   Google-2

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Additional Titles

Quote: solve a geometric problem by reducing it to a series of n equations in n unknowns

Quote: use 'x, y, z' for unknown lengths and 'a, b, c' for known lengths

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Topic: geometry (33 items)
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