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• This is a mathematics by a guy who was missed by a lot of people on his name was Hippocrates.

• But not the medic lived at the same time.

• But this was Hippocrates of CCI us.

• The island years medic was hip properties of costs.

• I think Hippocrates, a mathematician, deserves an even bigger place in history.

• And he was missed, and I explained one of the things he did.

• So this is called a mess.

• So laid compass on what he did.

• He took two lines at an angle.

• And you might say, but what angle?

• It absolutely doesn't matter.

• But way afternoons you have to be accurate.

• This you got a mark them off like a ruler, and now you do the same.

• Here it is now possible to multiply any two numbers or divide any two numbers just using lines.

• So say they won't they multiply.

• 34,690 Dubai three.

• No, hang on.

• Hang on.

• Three times four.

• What you do is you find three on this line and one on the bottom line, and you draw lines for it and give you a picture off.

• 13 Now, this is well BC long before Christ and they're talking about massing pictures.

• Wouldn't it be wonderful?

• So we've got 13 but say we won't.

• Four threes.

• What you do?

• You find 1234 on the line and you need a set square.

• What you do places set square on that line accurately.

• That it?

• Yeah.

• And then you slide it along the ruler, it passes through the four and they've ever done this right?

• So that's a parallel line.

• That's a pearly line.

• They both parallel and this goes to the 12 and 34 to 12.

• Not only that, your parallel lines give you 13 23633943 Strove 53 15 Isn't it beautiful?

• Division University Your own right.

• 12 by four Land to the 12 of the four parallel lines through the one we'll give you the answer.

• Three.

• It's a Z Z is that and it works for any numbers.

• Oh, you need big lines.

• But it's the principle on the principle is so simple.

• No wonder the Greeks didn't spend any time at all in you Mercy.

• They were more interested in geometry.

• The shape of maths.

• This is the second idea from Hippocrates Mateos.

• And this is how to find the square.

• Root off any number.

• Any number.

• Wow.

• Yes.

• Using a few lines, a few curves is trying to say you want to find the square root of 32,000?

• No, nine, Thank goodness we know that one, don't we?

• Okay, let's find it.

• Okay.

• What you do, if you produce a line and you mark it off, sent to meet it, It's fine.

• That should be enough.

• We want the square root of nine.

• So starting them there you count.

• One, 23456789 Now what you do now is you add one And you might say why?

• Because that's what makes it work.

• So now you've got 10.

• So a line of 10 with five a center on fivers radius.

• You produce a semi circle.

• You can produce a complete circle every likes and tell it to you.

• And now with the set square, you raise the perpendicular from the nine.

• And where that line meets that point, that distance is the square root of nine.

• Or in this case, three centimeters.

• That's the length of that line of the length that line is three centimeters exactly.

• But that would have worked for any number you like on that would, of course, be infractions.

• If it was not a square number itself, I'd asked you to find the square root of a 1,000,000,000.

• You would have marked a 1,000,000,001 as you.

• So he gets impractical cause you got a line with a 1,000,000,000 unit.

• So it's impractical.

• But the theory works on the practice.

• It works, and I'll show you why we can doing that to that.

• And you can see because the radius of the circle is five on we chose nine.

• That's got to before, and that's got me three units.

• Okay?

• And that's the 345 tranq or famous pitcher Dorian Triangle five Square 25 equals four squared 16 plus feet.

• Where'd nine.

• But that wasn't the way this was discovered.

• And that isn't what used for the explanation.

• What I've got to do now is draw another one very quickly.

• Don't worry about the lines on the inspiration is this.

• If we draw the line there, we draw a line across here.

• What you produces Two triangles say lease was the first known Greek mathematician.

• And he told you that in a semi circle any two lines from a here and be here.

• If they meet, anyone occurred than the angle they create will be a right angle.

• Always on that is.

• So when we look at these two triangles, that angle there is equal to the angle there.

• That angle, they're equals that angle there because the Children at a right angle and that's a right and another right.

• So that means these two triangles are similar.

• There are different size, but their sights are always in the same proportion.

• So let's say, for example, that happened to be six units, and that happened to be three units.

• If that was three units and that was six, this would have to be 12 because 3 to 6 is a sick sister.

• 12.

• It's a simple is that if this was too, then it would be different.

• 2 to 6 is a sixes to 18.

• Yeah, 206 is 33 16 or 18.

• So that was, too.

• And that was six.

• That would have to be 18.

• But if this was one unit and that was six, this was have to be six sixes or 36 on the whole.

• Thanks.

• Of course there will be 37 and that's why it works for any number.

• Why does this willing to square rope?

• Because Because you go in that way, you're squaring.

• So coming back your square rooting.

• Okay, that's what you get.

• And that's where you get the square root on That works now.

• These two ideas have been missed by many, many mathematicians in many, many history books, in many collections off mathematicians here.

• History Hippocrates Cheers was missed, but he waas, seen by renegade, a car and a car, wrote a book called The Geometry and that Is It in French on those of the two designs.

• Okay, and that's him French.

• And that's a translation in English from the world of mathematics, Newman's world of mathematics, Volume one and what they Car said.

• Now do you see understanding these as an introduction to geometry, he said.

• If you understand you angles and few links of lines, you can calculate absolutely anything on.

• He was wrong because at his time we hadn't discovered calculus on calculus, a required to measure things that change even as they change, But that was the kicker on.

• He and Fermat started to look for ways of measuring things that even changed on Along Came Lightness and Isaac Newton on Need produced calculus On From then, you could measure anything using geometry, you know, when brilliant, good enough to sponsor one of our episodes.

• I always love searching their sight to see what they've got on the topic we just covered.

• And when it comes to square roots, they have a lot of stuff.

• And I mean ah, lot of stuff.

• Check it out, people.

• This is all amazing, intriguing content because brilliant is a treasure trove of courses and quizzes and all sorts of stuff just like this.

• Don't just sit there watching videos.

• The best way to learn to get smarter is to do stuff and brilliance.

• Interactive website is, well, brilliant for just that.

• You could go check out brilliant without any commitment.

• But if you do want to sign on for a premium membership on, unlock all the treasures they've got, go to brilliant door orc slash number file because that's gonna get you 20% off.

• There's a link down in the description.

This is a mathematics by a guy who was missed by a lot of people on his name was Hippocrates.

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# Mesolabe Compass and Square Roots - Numberphile

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林宜悉 posted on 2020/03/27
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