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中文摘要：
在古巴比伦数学中，正四棱台体积公式的表现形式和现代形式相比十分复杂。奎内斯（Ivor Grattan-Guinness）在解释该公式时，对分割图形的拼合方法不太合理。有鉴于此，基于平面情形与空间情形类比的思想对该公式进行了古证复原，这一方面能加深对古巴比伦几何学思想的理解，另一方面也为正四棱台体积公式的教学提供了有益的借鉴。
英文摘要：
In ancient Babylonian mathematics, the expression of volume formula for the frustum of a square pyramid is much more complicated than its modern form. Many works of the history of mathematics just list the formula without explaining. Ivor Grattan-Guinness gave an explanation about the formula by means of the segmentation method used by the ancient Chinese mathematician Liu Hui. This paper points out that Guinness＇ combination of the segments is not quite reasonable and reconstructs the proof for the Babylonian volume formula by analogizing the plane case to the space case, i. e. , by analogizing intermediate segment of the trapezoid to the intermediate plane of the frustum of a square pyramid. The frustum volume of a square pyramid is eventually resolved into the volumes of a regular prism and special upright slices. The reconstruction of the proof of this volume formula can not only deepen the understanding of Babylonian geometrical thoughts, but also benefit the teaching of this volume formula.
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