This section is from the book "An Illustrated Flora Of The Northern United States, Canada And The British Possessions Vol3", by Nathaniel Lord Britton, Addison Brown. Also available from Amazon: An Illustrated Flora of the Northern United States, Canada and the British Possessions. 3 Volume Set..
Coreopsis tripteris L. Sp. Pl. 908. 1753.
Perennial; stem glabrous, much branched above, 4°-8° high. Leaves petioled, glabrous, or very nearly so, firm, the lower all divided into lanceolate, entire, acute, rough-margined segments, which are 2'-5' long, 1/4'-1' wide and pinnately veined; uppermost leaves lanceolate, entire; heads numerous, slender-peduncled, l'-l 1/2' broad; outer bracts of the involucre linear, obtusish, much narrower and somewhat shorter than the ovate-oval or ovate-lanceolate, acute inner ones; rays 6-10, yellow, obtuse, entire; achenes oblong to obovate, narrowly winged, emarginate; pappus none.
Coreopsis palmata Nutt. Gen. 2: 180. 1818.
Perennial; stems rigid, glabrous, simple, or little branched, very leafy, 1°-3° high. Leaves sessile, 2'-3 long, palmately deeply 3-lobed at or below the middle, or the uppermost entire, thick, rigid, the lobes linear-oblong, obtusish, entire, or with 1-3 lateral lobes, their margins rough; heads few or solitary, short-peduncled, 1 -2' broad; involucre hemispheric, its bracts somewhat united at the base, those of the outer series narrower and nearly as long as the inner ones; rays 6-10, bright yellow, oblong or obovate, mostly 3-toothed; achenes oblong, narrowly winged, slightly incurved; pappus of 2 short tips, or none.
On dry prairies and in thickets, Indiana to Missouri, Louisiana, Minnesota, Manitoba, Nebraska and Texas. June-July.
Coreopsis major Walt. Fl. Car. 214. 1788. Coreopsis senifolia Michx. Fl. Bor. Am. 2: 138. 1803. Coreopsis Oemleri Ell. Bot. S. C. & Ga. 2: 435. 1824. Coreopsis stella a Nutt. Journ. Acad. Phil. 7:76. 1834. Coreopsis senifolia var. stellata T. & G. Fl. N. A. 2: 342. 1842.
Perennial; stem pubescent or glabrous, branched above, 2°-3° high. Leaves sessile, more or less pubescent, or glabrous, divided to the base into 3, lanceolate, linear, ovate-lanceolate or oblong, acute, entire segments 2'-4' long, 2"-12" wide, which appear as if in verticils of 6; upper and lower leaves (rarely all of them), undivided and entire; heads several or numerous, slender-peduncled, 1'-2' broad; bracts of the hemispheric involucre all united at the base, the outer ones linear-oblong, obtuse, equalling or shorter than the broader inner ones, all pubescent; rays 6-10, yellow, oblong, entire; disk yellow; achenes oblong to elliptic, winged, 1/2'-2' long; pappus of 2 short deciduous teeth.
In dry sandy woods, Virginia to Kentucky, Florida and Alabama. July-Aug. Consists of several races, differing in pubescence and in shape and width of the leaf-segments.