Force versus weight: the spring and the counterweight
The pyramidal power of a spring compared with the columnar-and-pyramidal power of a weight
A theoretical comparison of force and weight opening a section 'of the difference between force and weight, and first of force.' It argues that a spring and a counterweight of equal power are not equivalent: the spring's power is 'pyramidal,' greatest at the first instant of its motion, whereas the counterweight combines a 'columnar' power (constant weight, equal at beginning and end) with a 'pyramidal' one that gains magnitude and speed as the fall proceeds. In slow motion the pyramidal component ceases and only the steady columnar power of the weight remains. The page carries the argument alone, without a diagram.
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Spring versus counterweight: pyramidal and columnar power
Of a spring and a counterweight of equal power, the spring is always worth more, because its power is pyramidal and greatest at the beginning of its motion. The counterweight instead has a composite power: a columnar part, constant and equal throughout, and a pyramidal part that gains magnitude and velocity through free, swift fall. When the heavy body moves slowly the pyramidal power ceases and only the steady columnar power remains.