The ramp was the last simple machine anyone admitted was a machine
Ancient Greek thinkers named five simple machines and left out the ramp, even though people had been dragging heavy loads up slopes since prehistory. As late as 1826 Karl von Langsdorf insisted an inclined plane was no more a machine than a mountainside. Getting its maths right took until the Renaissance.
The oversight probably came from the ramp's stillness. It has no moving parts; the load does the travelling, and nature supplies slopes and hills for free. Yet the device was everywhere. Roman roads and causeways survive as early examples, Egyptian pyramids rose with the help of ramps, siege armies built them to top fortress walls, and the stones of Stonehenge are thought to have been hauled up temporary earth slopes that left little trace. The Greeks even paved a 6-kilometre track, the Diolkos, so that crews could haul whole ships over the neck of land at Corinth.
Calculating the effort involved defeated Heron of Alexandria and Pappus of Alexandria, whose answers were wrong. Jordanus de Nemore found the correct analysis in the 13th century, but it seems not to have spread. Girolamo Cardano proposed in 1570 that the force needed rose in step with the angle, which was also mistaken. Then three right answers appeared within a decade: Michael Varro in 1584, Simon Stevin in 1586, and Galileo in 1592. Stevin's is the most famous, thanks to an original argument using a loop of beads draped over a slope. In 1600 Galileo's Le Meccaniche finally grouped the ramp with the other simple machines as a force amplifier.
The rule itself is tidy. Ignoring friction, the force saved equals the length of the slope divided by the height it climbs, so a gentler ramp needs less push but a longer walk; the total work stays the same. Leonardo da Vinci worked out basic laws of sliding friction on slopes but left them in his notebooks, and they were rediscovered by Guillaume Amontons in 1699. Leonhard Euler showed in 1750 that the tangent of the steepest angle at which a load stays put equals the friction coefficient.
Wedges and screws are cousins: a wedge is a moving ramp, and a screw is a narrow ramp wrapped around a cylinder.
Source: Inclined plane
