I have since been able to identify the edition, though it turns out my initial identification was only half correct.
One of the prospectuses is indeed for the Cyclopaedia (fig. 1), advertising the first revised London edition (London: Printed for W. Strahan, J. F. and C. Rivington, A. Hamilton, J. Hinton, T. Payne [and 31 others], 1778–88; ESTC T136235), issued in parts.
The edition was identified by the conditions of sale, made visible thanks to some very delicate peeling. Condition IV notes that the first part of the Cyclopaedia was to be issued on 10 January 1778 (fig. 2).
Chambers's Cyclopaedia was first published in 1728 and went through numerous editions throughout the eighteenth century. It was one of the first general encyclopaedias published in English and a precursor to the great Encyclopédie of Denis Diderot and Jean le Rond d'Alembert.
Abraham Rees's revised edition added much new material to Chambers, and his scholarly efforts garnered Rees fellowships in the Royal Society and the Linnean Society. Rees went on to published his New Cyclopaedia in parts between 1802 and 1820. The complete work consists of thirty-nine text volumes accompanied by five volumes of plates and an atlas.
The Second Prospectus
The second prospectus turned out to be a surprise. It was not for Chambers's Cyclopaedia at all, but for Thomas Theodore Middleton's A New and Complete System of Geography (London: Printed for J. Cooke, 1778–79; ESTC N5096).
'[A] bibliographical nightmare. The title-pages in similar volumes by Thomas Bankes, q.v., closely resemble in both wording and lay-out those in Middleton and may well have been intended as successors to Middleton's work. [Thirteen] map plates first used here in Middleton later make their appearance in Bankes's publications. Some of the Middleton title-pages carry dates; some do not. But they seem to have been published within a fairly short span of years, 1772–1782. The title-pages of the numerous copies seen frequently vary. The initial wording is the same, but type-setting, lay-out, and dates are not. Most copies were undated; on dated copies, dates ranged from 1777–1779; often [the] vol. I date was later than vol. II'.
For McCorckle's full analysis of Middleton's System of Geography see entry 280 in her Carto-Bibliography, available online thanks to the Bibliographical Society of America.
Samuel Johnson. A Dictionary of the English Language .... London: Printed for J. F. and C. Rivington, L. Davis, T. Payne and Son, W. Owen, T. Longman [and 21 others], 1785. Seventh edition (shelfmark: RJJ Dic 1785 OS). ESTC T116652; Fleeman 55.4D/9.