"The great Cartesian invention had its roots in those famous problems of antiquity which originated in the days of Plato. In endeavoring to solve the problems of the trisection of an angle, of the duplication of the cube and of the squaring of the circle, the ruler and compass having failed them, the Greek geometers sought new curves. They stumbled on the conic sections...There we find the nucleus of the method which Descartes later erected into a principle. Thus Apollonius referred the parabola to its axis and principal tangent, and showed that the semichord was the mean propotional between the latus rectum and the height of the segment. Today we express this relation by x2 = Ly, calling the height the ordinate (y) and the semichord the abscissa (x); the latus rectum being... L. ...the Greeks named these curves and many others... loci... Thus the ellipse was the locus of a point the sum of the distances of which from two fixed points was constant. Such a description was a rhetorical equation of the curve..."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Tobias Dantzig, Number: The Language of Science (1930).
https://en.wikiquote.org/wiki/History_of_mathematics
Revision History
No revisions have been submitted for this quote.
Categories
History of mathematics
159 quotes on TrueQuotesView all quotes by History of mathematics →
Related Quotes
"The authors hope by publishing this work to demonstrate that the Arabs were not only transmitters of other cultures, …"
"In England, where it originated, the calculus fared less well. ...by siding completely with Newton in the priority di…"
"The evolution of number into the 'transfinite' was included only to emphasize the power of the forces acting within m…"
"The excellent work of Tropfke is an example of the tendency to break away from the mere chronological recital of facts."
"The mathematical genius can only carry on from the point which mathematical knowledge within his culture has already …"
"The Greeks studied the conic sections from a purely geometric point of view. But the invention of in the seventeenth …"
"The field of mathematics is now so extensive that no one can [any] longer pretend to cover it, least of all the speci…"
"Those people who do mathematics—the 'mathematicians'—are not only the possessors of the cultural element known as mat…"
"The fact that arithmetic and geometry took such a notable step forward... was due in no small measure to the introduc…"
"If the Greeks had had a mind to reduce mathematics to one field... their only choice would have been to reduce arithm…"