There are many primary sources in Perkins that are reprints. They can be checked out.
Use the search terms "discovery and exploration--sources" (you may add a place or region to this)
Other useful terms: diaries, correspondence, personal narratives,
e.g. explorers personal narratives
The Indian and Pacific correspondence of Sir Joseph Banks, 1768-1820
3 vols. Perkins/Bostock QH31.B19 A4 2008
From India, Raj and Empire
Early English books online EEBO -- ProQuest
Early English Books Online reproduces over 125,000 books, pamphlets and broadsides published in English between 1475 and 1700. To find maps go to Advanced Search and choose Map from the Illustration drop-down menu.
Eighteenth Century Collections Online ECCO
Nearly 150,000 English-language books and other publications, such as pamphlets, published between 1701 and 1800 are included. You can limit to documents with a map.
State Papers Online: The Government of Britain, 1509-1714 State Papers Online is an online archive of original manuscript documents: the British State Papers from the period of Henry VIII to that of Queen Anne. It combines State Papers Domestic, Scotland, Borders, Ireland and Foreign. Can limit to documents with maps.
Collection of full-text documents on the British Empire from the 15th century to the 20th century. You can click on Topics under the search box then choose "exploration" to get a selection of documents on that topic.
Making of the Modern World
Primary source documents online on economic and business activity in the West, from the last half of the 15th century to the mid-19th century. Go to advanced search and choose documents containing maps.
Sabin Americana This collection contains works about the Americas published throughout the world from 1500 to the early 1900's. Go to advanced search and choose documents containing maps. You can also choose subject areas such as colonization or maritime. You can select map under Illustrations.
Colonial State Papers
provides access to thousands of papers concerning English activities in the American, Canadian, and West Indian colonies between the sixteenth and eighteenth centuries. This has nice maps but you have to use "map" as a keyword.
India, Raj and Empire India, Raj and Empire provides documents from the manuscript collections of the National Library of Scotland pertaining to the History of South Asia between the foundation of the East India Company in 1615.
Virginia Company Archives
Documents the founding and economic development of Virginia as seen through the papers of the Virginia Company of London, 1606-1624. There are maps under "Further Resources."
To find original maps and other primary sources in Special Collections (such as explorers' journals or correspondence) you can search the library catalog then limit to location/special collections or you can search the Special Collections finding aids.
Probably the best way is to go to the Special Collections Reading Room and ask the reference librarian!
Man of the Sandwich Islands in a mask, 1779 “A mask made of a large gourd with holes cut in it for the eyes and nose. The top was full of small green twigs”, from Captain Cook’s logbook.