different between quantic vs facient

English

Etymology

From Latin quantus (“how much”).

Noun

quantic (plural quantics)

1. (mathematics) A homogeneous polynomial in two or more variables.
   • 1858, Arthur Cayley, A Fourth Memoir on Quantics, 1859, Philosophical Transactions of the Royal Society of London, Volume 148, page 421,

     When the two quantics are the first derived functions of the same quantic of any odd order, the lineo-linear invariant does not vanish, but it is not an invariant of the single quantic.

   • 1859, George Salmon, Modern Higher Algebra, page 52,

     74. The discriminant of a binary quantic, or the eliminant of a system of binary quantics, is an invariant.

     We can see a priori that this must be the case, for if a given quantic has a square factor, it will have a square factor still when it is linearly transformed; or if a system of quantics have a common factor, they will still have a common factor when the equations are transformed.

   • 1895, Edwin Bailey Elliott, An Introduction to the Algebra of Quantics, 2011, Facsimile Edition.

References

• quantic in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.

English

Etymology

From Latin faciens, facientis, present participle of facere (“do, make”).

Noun

facient (plural facients)

1. (obsolete) One who does something; a doer; an agent.

   (Can we find and add a quotation of Bishop Hacket to this entry?)

2. (mathematics) One of the variables of a quantic as distinguished from a coefficient.
3. A multiplier.

Usage notes

The terms facient, faciend, and factum may imply that the multiplication involved is not ordinary multiplication, but some specified operation or a placeholder for any mathematical operation.

Anagrams

• actifen

Latin

Verb

facient

1. third-person plural future active indicative of faci?