Negative Numbers: The Unimaginable

“Many persons rise up against these negative magnitudes, as if they were objects difficult to conceive, yet there is nothing at the same time more simple nor more natural.” (L'Abbé Deidier, 1739)

 "[negative numbers] darken the very whole doctrines of the equations and to make dark of the things which are in their nature excessively obvious and simple. It would have been desirable in consequence that the negative roots were never allowed in algebra or that they were discarded." (Francis Meseres, 1759)

“One must admit that it is not a simple matter to accurately outline the idea of negative numbers, and that some capable people have added to the confusion by their inexact pronouncements. To say that the negative numbers are below nothing is to assert an unimaginable thing.” (Jean le Rond d'Alembert, "Negatif”, Encyclopédie [1751 – 1772])

“[…] the algebraic rules of operation with negative numbers are generally admitted by everyone and acknowledged as exact, whatever idea we may have about this quantities. “ (Jean Le Rond d'Alembert, Encyclopédie, [1751 – 1772])

“It is very inaccurate to say that a negative number is less than 0, which is what many authors claim. A negative number is a positive number, but in another sense, and therefore relative. “ (Van Swinden, cca 1800)

„Every negative quantity standing by itself is a mere creature of the mind and [...] those which are met with in calculations are only mere algebraical forms, incapable of representing any thing real and effective.“ (Lazare Carnot, “Geometrie de Position”, 1803)