Geometrical Solutions Derived from Mechanics; a Treatise of Archimedes

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By Abil Kile Posted on Nov 15, 2025
In Category - History
Archimedes, 281? BCE-212? BCE Archimedes, 281? BCE-212? BCE
English
Hey, have you ever tried to move a couch and thought, 'Man, this is heavy'? Archimedes basically wrote the ancient world's ultimate guide to that feeling, but for moving planets. This book isn't just old math; it's the record of a genius figuring out how to use simple machines to solve impossible problems, like calculating the volume of a sphere or the area under a curve, over 2,000 years before calculus was invented. It's like finding the original blueprint for the modern world, scribbled on a piece of papyrus. The real mystery is how someone could think this way so long ago.
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aquarium fish way back when I was just nine and studying in Class V. Under his guidance then, I experimented with breeding guppies, platties and mollies, fairly simple types of fish to breed. However, it was a matter of great excitement for me at that time to be successful in my experiments and Ashok was generous enough to even buy back from me the baby fish I reared just to encourage me. Later I developed sufficient confidence to experiment with and breed more difficult types of fish, like Siamese Fighting Fish and Blue Guramies-all under the expert tutelage of Ashok. So it was to Ashok's shop that I went every morning at 9.00 a.m., speeding on my bicycle to be on time. I would stay there until lunch time, a regular hands on, doing whatever I was asked to do. Ashok's shop is not very large. It is a two-roomed shop on the ground floor of the Gomes Catao complex. It has a display section in front and a store room at the back. The showroom has about twenty fish tanks on display with a variety of fish that Ashok purchases mainly from Mumbai. Each tank stores a particular species of fish. Ashok's shop is located away from the main market area so he does not have the advantage of casual customers dropping by. However Ashok has his regular customers and there are always at least twenty to thirty customers daily. During my first few days at his shop, my work was only to watch the tanks, clean those which were dirty, remove the dead fish and do some other small jobs. I also fed the fish and treated the wounded and diseased fish. Sometimes, I also attended to customers. Gradually, I began to accompany Ashok on his rounds to various places. A gentleman in Moira wanted to set up an aquarium at his home. He had a tank. He also had definite ideas about how he wanted it to finally look and Ashok was called to see how it could all be done. The man sent his car for us. At his house we discussed the location of the tank, lighting arrangements, the water filters, the kind and quantity of fish he would like to have, and maintenance. After we were fully satisfied that we had everything right and had noted down his requirements, we returned to Mapusa. Later he came for the material which we kept ready for him. Another time I accompanied Ashok to a client's office to put a pair of Dwarf Guramies in the fish tank and to fix a picture as a backdrop for the tank. On such visits I watched care fully what Ashok did and soon enough Ashok started sending me on my own to visit some of his clients who had small or simple problems. I went to clients to fix aquarium equipment such as air pumps and filters, to fix toys in the tanks, to check fish for diseases or if there was a sudden crisis such as fish dying in numbers, or if a client wished to add more fish to his collection. I was sent to collect overdue payments or simply to enquire the aquariums were doing. Sometimes I went on my own to visit some of the places where we had set up tanks and enjoyed watching the fish swimming happily in their new homes. One day my employer decided to send me as a spy to find out the prices of fish and fish food at a competitive fish shop. I tried to behave like a...

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This isn't a novel with characters, but the story is still thrilling. It's the story of a single, powerful idea: that the physical world follows mathematical rules we can discover and use. Archimedes shows how you can figure out complex areas and volumes—things that seem to require advanced calculus—by imagining them as objects with weight and balance. He uses levers, scales, and centers of gravity as his tools. The 'plot' is him proving his theorems by pretending to weigh shapes against each other on a theoretical balance beam. It's a clever workaround that feels like a magic trick.

Why You Should Read It

Reading this is a direct line to one of the greatest minds ever. You get to see his thought process, not just his results. When he 'weighs' a parabola against a triangle to find its area, it's a 'Eureka!' moment you can share. It makes abstract geometry feel tangible and physical. It’s a reminder that groundbreaking ideas often start with simple, almost playful, observations about the world around us.

Final Verdict

Perfect for anyone curious about the foundations of science and engineering, or for readers who love a good intellectual puzzle. If you've ever enjoyed a 'popular science' book, this is the original source material. It’s short, surprisingly approachable in its core concepts, and leaves you with a deep appreciation for how one person's curiosity can echo for millennia. It’s not light reading, but it’s profoundly rewarding.



📢 Open Access

This text is dedicated to the public domain. Access is open to everyone around the world.

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