Inventor of logarithms in 1614. Logarithms were attained by looking them up in a table.

Designed the "line of numbers" wherein the logarithm of a number is expressed inherently by spacing the digits, e.g. 1, 2, 3, ..., 10, in a manner proportional to the logarithm of the number. Many scales useful for navigation and other engineering problems were laid out and used. A common example is the Gunter Scale

Cajori contended Oughtred was an independent inventor of the rectilinear slide rule and the first one to propose the circular type slide rule.

Various spellings Coggeshall, Cogshall, & Coggleshall
Described slide rule as in Bion. Three double lines of numbers A, B, C are figured 1, 2, 3, 4, 5, 6, 7, 8, 9 and then 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ... [The] single line of numbers D whose radius is exactly equal to two radius's of A, B, C is broke for the easier measuring of timber and figured thus 4, 5, 6, 7, 8, 9, 10, 20, 30, 40 this line is called the Girt Line. This variations of this are known as the Carpenters Rules

Both Josiah and Joshua have been seen as first name.

Combined a two-fold two-foot measuring rule on side, incorporating a brass slide with a logarithmic scale on one 12 inch leg inscribing on the other leg various constants enabling the quick calculation of engineering problems. This became known as Routledge's Engineer's Slide Rule . See the Ken Roberts reprint titled "Instructions for the use of the Practical Engineers' & Mechanics' Improved Slide Rule"

References
• Bion, Nicholas. The Construction and Principal Uses of Mathematical Instruments. 1758 Paris, reprinted 1995. Translated from the French of M. Bion by Edmond Stone. Mendham, New Jersey: Astragal Press.
• Cajori, Florian. A History of Logarithmic Slide Rule and Allied Instruments and On the History of Gunter's Scale and the Slide Rule During the Seventeenth Century. Originally 1910, republished 1994. Mendham, New Jersey: Astragal Press.
• Rabone, John & Sons 1880. The Carpenter's Slide Rule - Its History and Use. Reprinted by Ken Roberts, Fitzwilliam, New Hampshire.
• Routledge, Joshua. ca. 1867. Instructions for the use of the Practical Engineers' & Mechanics' Improved Slide Rule. Reprinted by Ken Roberts, Fitzwilliam, New Hampshire.
• Stanley, Philip. 1984. Boxwood & Ivory. Westbourough, Mass.: The Stanley Publising Co.