There are three states of the map: an undated proof, lacking the names of the continents; the present issue known in only three examples; and eight examples of a later state, dated 1686. These latter include three institutional examples, one at the National Library of Australia, another in the New York Public Library, bound into a Samuel Thornton sea atlas, and a cropped example at the British Library.

Greene’s map is possibly the earliest world map engraved and published in England to include a pair of polar projections and is one of the earliest to show the coastline of New Zealand. The cartography, drawn from contemporary Dutch sources, shows California as an island while Australia is described as ‘Hollandia Nova’. The conjectural east coast of Australia remains blank, as is the northwest part of America. 

Double-page engraved copperplate double-hemisphere map of the world, with contemporary hand-colour in outline.

This rare English double-hemisphere world map was published in London by 

. In a time when most decorative world maps were copied from one or two Dutch models, Greene's map stands out for its unusual iconography. Perhaps most interesting are the four scenes representing methods of hunting on each of the four continents, including a Cannibalism scene in America and a Centaur in Asia. The four corners of the map are further embellished with male and female royal figures representing the four continents, an unusual deviation from the normal female allegorical images of the continents employed by most other mapmakers. 

Greene's cartography is drawn from contemporary Dutch sources though significant areas remain uncharted, such as the northwest part of America. Green's map is possibly the earliest world map published in England to include polar hemispheric projections, as well as the earliest in England to show the coastline of New Zealand.

Greene’s earliest publications were maps of England and Germany (1673). This map was published separately and made an appearance in the ‘London Gazette’ for 17–20 April 1676, which wrote that it was accomplished '...by the best Observations and the latest Discoveries that hath been made with the North Poler Draught, and the South Poler Draught...'. The work was sold for 2 shillings and could be purchased in three locations in London.

First published issue of an extremely rare seventeenth century double hemisphere world map, known in only three examples; and the earliest world map engraved and published in England to include a pair of polar projections, and is one of the earliest to show the coastline of New Zealand.

Greene's World Map with Polar Projections