The legend of three-element lens : Brief Introduction of Cooke Triplet
In 1983, British lens designer Harold Dennis Taylor (1862–1943) (hereafter “Taylor”) designed a 3-element lens consisting of two convex lenses and a concave lens (Cooke Triplet), opening a new page in modern design of photographic lenses.
Features of the Cooke Triplet lens
The triplet designed by Taylor are arranged in order of postive – negative – postitive. The focal power of the negative lens must be more or less equals to the focal power of the two postive lenses. The triplet has enough degrees of freedom for the lens designer to correct monochromatic aberrations(spherical, coma, astigmatism, field curvature) and chromatic aberrations(axial and lateral). Alternatively, apart from the simplest three-element design, the lens designer can replace any of the element with a glue doublet or splitting any of the element into multiple elements.
When Taylor published his design in The Royal Photographic Society Journal, the maximum aperture was F3.7. Taylor mentioned that the lens designed was basically free of spherical aberration at F8, and the lens achieves best sharpness at F11. 
Because the company, T. Cooke and Sons, Taylor is working for were not interested in producing the triplet lens, Taylor bring his design to lens Taylor, Taylor & Hobson(“TTH”). TTH manufactured and sold the lenses under the name of “Cooke” which is the trademark of T. Cooke and Sons. Two series of Cooke Triplet were avalaible at the time of introdcution: Series II (Portrait lenses) and Series V (Process lenses). 
List of Cooke Triplet lenses for photography cameras
When Taylor’s patent expired, other companies started to made their own triplet lenses. Here is a list of the lens series name made with Cooke Triplet design:
Agfa: Agnar, Apotar
Carl Zeiss Jena: Triotar
Carl Zeiss Oberkochen: Pantar
Hugo Meyer/Meyer: Trioplan, Domiplan
Ludwig: Victar, Meritar
Minolta: Rokkor TC
Steinheil: Cassar, Cassarit
Other than photographic lenses, Cooke Triplet can also be found on enlargers such as Rodenstock Trinar/Rogonar and Schneider Componar/Componar-C. Moreover, the design were used on some projection lenses too such as Meyer Diaplan/Pentacon AV.
Character of the common Cooke Trirplets
The two photos below are taken with Steinheil Cassarit 50mm F2.8 at s Sony NEX-5N. At F4.0, the contrast and sharpness are much better than at F2.8.
Here are the list of Cooke Triplet lenses which will be posted:
Meyer Trioplan 100mm F2.8
Leica Elmar 90/4.0 3e
British APO triplet
 Brit. Pat. 22,607 and US Pat. 568052
 “A Simplified Form and Improved Type of Photographic Lens.” by H. Dennis Taylor https://archive.rps.org/archive/volume-35
 Cooke Compendium – Cooke Optics