1805 encyclopedia defines America as encompassing the entire hemisphere.
The New and Complete American Encyclopedia (New York: John Low, 1805), 280–81
AMERICA, [so named from Americus Vespusius, the pretended discoverer,] one of the four quarters or grand divisions of the globe, universally allowed to be the largest of the whole, and from its discovery, frequently denominated the New World. This vast continent is washed by the two great oceans; being bounded on the E. by the Atlantic, which divides it from Europe and Africa; and on the W. by the Pacific, or Great South Sea, which separates it from Asia. It extends from Cape Horn, its most southerly extremity, in Lat. 56° S., to the North Pole; and spreads between the 40th degree E. and the 100th W. Long. from Philadelphia. It is nearly 10,000 miles in length from N. to S.. Its average breadth, from E. to W., is about 1,400 or 1,500 miles; but at its broadest part, it measures 5,690 miles. It is said to contain upwards of 14,000,000 square miles. As America lies in both hemispheres, it possesses all the varieties of soil, climate, and productions which the earth affords. It stretches through all the five zones and has two summers, as well as two winters in the year.