The question asks about the historical figure credited with calculating the Earth's circumference to be approximately 25,000 miles. This is a significant achievement in the history of science and geography.

Calculating Earth's Circumference: Eratosthenes' Method

The most famous early calculation of the Earth's circumference was performed by the ancient Greek scholar Eratosthenes of Cyrene. He lived in the 3rd century BCE and was the chief librarian at the Library of Alexandria.

Eratosthenes' method was ingenious and relied on simple geometric principles and astronomical observations. He observed the sun's position at noon on the summer solstice in two different Egyptian cities: Syene (modern Aswan) and Alexandria.

• In Syene, located close to the Tropic of Cancer, the sun was directly overhead at noon on the summer solstice. This meant a vertical object would cast no shadow.
• In Alexandria, located north of Syene, a vertical object cast a noticeable shadow at noon on the same day.

Eratosthenes reasoned that the difference in the shadow angle in Alexandria was due to the curvature of the Earth, assuming the sun's rays were parallel upon reaching Earth. By measuring the angle of the shadow in Alexandria (he found it to be about 7.2 degrees) and knowing the distance between Syene and Alexandria, he could calculate the Earth's circumference.

The angle of the shadow in Alexandria is equal to the angle subtended by the arc connecting Syene and Alexandria at the Earth's center. This is because the sun's rays are considered parallel. If the angle is $\theta$ and the distance between the cities is $d$, and the Earth's circumference is $C$, the relationship is:

$\frac{\theta}{360^\circ} = \frac{d}{C}$

He estimated the distance between Syene and Alexandria to be 5000 stadia. Using his measured angle of 7.2 degrees (which is $360 / 50 = 7.2$), he calculated the circumference:

$C = \frac{d \times 360^\circ}{\theta} = \frac{5000 \text{ stadia} \times 360^\circ}{7.2^\circ} = 5000 \times 50 \text{ stadia} = 250,000 \text{ stadia}$

The exact length of the 'stade' unit used by Eratosthenes is debated, but if we use a common conversion that places the result around 24,000 to 28,000 miles, it was remarkably close to the actual circumference (which is about 24,901 miles around the equator and 24,859 miles around the poles). The figure of 25,000 miles is often cited as a rounded or approximate value derived from his calculation.

Analyzing the Options

Let's look at the other options provided:

• Thales of Miletus: An earlier Greek philosopher and mathematician known for foundational geometric theorems, but not for this specific calculation of Earth's circumference.
• Poseidonius: Another Greek scholar who also attempted to calculate the Earth's circumference later, using a different method based on the star Canopus's position observed from different latitudes. His results were less accurate than Eratosthenes'.
• Hipparchus: A prominent Greek astronomer and mathematician known for developing trigonometry and cataloging stars, but not primarily for this circumference calculation.

Based on historical accounts of the calculation involving shadow angles in Syene and Alexandria yielding a result close to 25,000 miles, Eratosthenes is the correct figure.

Therefore, the scholar who calculated the circumference of the Earth to be approximately 25,000 miles using his famous method was Eratosthenes.

Revision Table: Earth Circumference Calculation

Additional Information: Ancient Astronomy and Geography

The work of Eratosthenes is part of a rich tradition of ancient Greek science. Scholars like him combined mathematics, astronomy, and geography to understand the world. His method demonstrated a sophisticated understanding of geometry and the relationship between angles and distances on a sphere. While his distance measurement between cities was an estimate (based on travel time or surveys), his geometrical approach was sound and formed the basis for future geodetic measurements.

The approximation of the Earth's circumference was crucial for understanding the scale of the world and for cartography (map-making). This early scientific inquiry laid the groundwork for later discoveries and advancements in astronomy and geography.