# How the heck did people do geometry before the Descartes?
**URL:** https://boards.straightdope.com/t/how-the-heck-did-people-do-geometry-before-the-descartes/480425
**Category:** Factual Questions
**Created:** [January 8, 2009, 9:25pm UTC](https://boards.straightdope.com/t/how-the-heck-did-people-do-geometry-before-the-descartes/480425 "2009-01-08T21:25:44Z")
**Posts on this page:** 3
**Page:** 2
### Author:  [@Fish](https://boards.straightdope.com/u/Fish)
#### Post date: [January 9, 2009, 12:15am UTC](https://boards.straightdope.com/t/how-the-heck-did-people-do-geometry-before-the-descartes/480425/21 "2009-01-09T00:15:39Z")
> [@WoodenTaco](#):
>
> Euclidean geometry is difficult too. How do you calculate stuff without using x and y?
Classically, the ancient geometers used a limited number of abstract tools: a straightedge, a stylus, a nail or two, and a length of string. Before that they would use a very long, flat ferret, a sharpened parakeet, and some rocks. Before that, they would weave together some dirt until they had long strands of dirt, then braid the dirt together into a string.
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### Author:  [@njtt](https://boards.straightdope.com/u/njtt)
#### Post date: [January 9, 2009, 12:24am UTC](https://boards.straightdope.com/t/how-the-heck-did-people-do-geometry-before-the-descartes/480425/22 "2009-01-09T00:24:52Z")
> [@](#):
>
> I guess I mistitled my post - I want to know how you do engineering. Proofs are clear. I’m not sure how to do applied math if all you have is proofs.
Sorry for the misunderstanding. My guess would be that most engineering, before fairly recent times, relied mostly on trial-and-error and craft rules-of-thumb, and did not make much use of math at all (beyond simple arithmetic, and perhaps some Euclid geometry to figure out what lengths or angles needed to be equal and such). However, if I am right about the _Principia_, that suggests that at least some of an engineer’s more advanced mathematical needs might be met by Euclid style geometry.
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### Author:  [@WoodenTaco](https://boards.straightdope.com/u/WoodenTaco)
#### Post date: [January 9, 2009, 12:39am UTC](https://boards.straightdope.com/t/how-the-heck-did-people-do-geometry-before-the-descartes/480425/23 "2009-01-09T00:39:12Z")
> [@Indistinguishable](#):
>
> Following up on my previous post, the other misconflation is possible, I suppose: thinking that “directly geometric” reasoning is just good for proofs and not calculations, as such. You can reason directly geometrically to calculate lengths and angles in just the same way as you might reason directly geometrically to establish a conjecture, without having to switch over to some imposed system of Cartesian coordinates and work purely numerically. It’s just the same sort of thing.
>
> What’s a specific engineering-inspired math problem which perplexes you?
I’d like to mention that I know that these problems are, of course, all solvable. Aqueducts and the Pantheon were built. I guess it just seems so hard to do without coordinates - and the answer seems like “Yes.”
And as I typed each problem I was going to propose, I realized that the Cartesian plane is definitely just something that assists in making the steps quicker, but isn’t strictly necessary. I was first thinking of posting asking about medieval astrology, the main area of pursuit of mathematicians - and then I remembered that the main tools like sextants are indeed particularly useful for geometric reasoning.
Now I’m wondering how you do stuff without trigonometry! But then I realize, trigonometry is provable using just Euclid. Makes sense.
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