The Answer

To Pope’s ImpromptuTitle and Epigraph This poem is also known by a longer title: "To Mr. Pope In answer to a coppy of verses occasion'd by a little dispute upon four lines in the Rape of the Lock"

Finch is responding to these four lines from Pope's The Rape of the Lock (first published 1712, finished 1717):
Parent of vapors and of female wit,
Who give the hysteric or poetic fit,
On various tempers act by various ways,
Make some take physic, other scribble plays; (Canto 4, lines 59-62)
Alexander Pope's poem "Impromptu, To Lady Winchelsea Occasion'd by Four Satyrical Verses on Women-Wits, in The Rape of the Lock":
In vain you boast Poetic Names of yore,
And cite those Sapphos we admire no more:
Fate doom'd the Fall of ev'ry Female Wit;
But doom'd it then when first Ardelia writ.
Of all Examples by the World confess'd,
I knew Ardelia could not quote the best;
Who, like her Mistress on Britannia's Throne;
Fights and subdues in Quarrels not her own.
To write their Praise you but in vain essay;
Ev'n while you write, you take that Praise away:
Light to the Stars the Sun does thus restore,
But shines himself till they are seen no more.

"Ardelia" is Finch's pen-name. The poem was written around 1714, and published in Bayle's Dictionary in 1741.

Pope’s and Finch’s poem share the words "fate" and "world," and Pope's use of "admire" is echoed in Finch's use of "admiration."

Disarmed with so genteel an air,
   The contest I give o’er;
Yet, Alexander, have a care,
   And shock the sex no more.
We rule the world our life’s whole race,
   Men but assume that right;
First slaves to ev’ry tempting face,
   Then martyrs to our spite.
You of one Orpheus sure have read,
   Who would like you have writ
Had he in London town been bred,
   And polished too his wit;
But he poor soul thought all was well,
   And great should be his fame,
When he had left his wife in hell,
   And birds and beasts could tame.
Yet venturing then with scoffing rhymes
   The women to incense,
Resenting heroines of those times
   Soon punished his offense.
And as the Hebrus rolled his skull,
   And harp besmeared with blood,
They clashing as the waves grew full,
   Still harmonized the flood.
But you our follies gently treat,
   And spin so fine the thread,
You need not fear his awkward fate,
   The lock won’t cost the head.
Our admiration you command
   For all that’s gone before;
What next we look for at your hand
   Can only raise it more.
Yet sooth the ladies I advise
   (As me too pride has wrought)
We’re born to wit, but to be wise
   By admonitions taught.