Sandy Bultena, I LOVE how the computer takes so long to follow though the steps. I just keep pausing to analyze every step the computer makes. It's awesome.
Good, but ekthesis (the stage of construction) is as equally important as the proof stage. I suggest that you explain the construction algorithm step by step instead of saying "we're goin' and we're goin". Apart from that, everything is very good. Thanks for your effort in making these videos.
All the individual steps of construction have been detailed in previous propositions, which are identified on the right hand side. I am trying as much as possible to stay true to the Heath's translation of Euclids book, where he does NOT repeat the construction methods that have already been described in previous propositions.
I am not sure what you mean? Remember that it is necessary to have a length that is equal to half the length of one of the sides. This makes it easier to construct if we do this ON the triangle side itself.
sorry i think my question was not clear.. i was thinking, what if i simply extended the line BC (or the other sides of the triangle)?.. it wasn't part of the postulate right, which is to draw the one side of the parallelogram on the triangle?
No, the postulate was to show how to draw a parallelogram with equal area, but with a predefined angle (which is shown near the bottom of page). So, if we have a specific angle, we could draw it anywhere along one of the triangle's sides, or an extension of it. But wherever we draw it, we then need to mark off a length that is half the width of the triangles side, and then determine the triangles height. I think the way Euclid did it was simple, but it is definitely not the only way to do it. There are usually many solutions to the same problem. One may (or may not be) better than another. I am following Euclid because I am assuming he was smarter than me. :)
Sandy Bultena, I LOVE how the computer takes so long to follow though the steps. I just keep pausing to analyze every step the computer makes. It's awesome.
New favourite Euclid video.
Thank you!
Good, but ekthesis (the stage of construction) is as equally important as the proof stage. I suggest that you explain the construction algorithm step by step instead of saying "we're goin' and we're goin".
Apart from that, everything is very good. Thanks for your effort in making these videos.
All the individual steps of construction have been detailed in previous propositions, which are identified on the right hand side.
I am trying as much as possible to stay true to the Heath's translation of Euclids book, where he does NOT repeat the construction methods that have already been described in previous propositions.
why was the angle copied on the line EC? why not the other sides?
It doesn't matter which line you copy the angle to. Any side would do
why on the triangle maam? why not extend any of the line of the triangle?
I am not sure what you mean? Remember that it is necessary to have a length that is equal to half the length of one of the sides. This makes it easier to construct if we do this ON the triangle side itself.
sorry i think my question was not clear.. i was thinking, what if i simply extended the line BC (or the other sides of the triangle)?.. it wasn't part of the postulate right, which is to draw the one side of the parallelogram on the triangle?
No, the postulate was to show how to draw a parallelogram with equal area, but with a predefined angle (which is shown near the bottom of page). So, if we have a specific angle, we could draw it anywhere along one of the triangle's sides, or an extension of it. But wherever we draw it, we then need to mark off a length that is half the width of the triangles side, and then determine the triangles height. I think the way Euclid did it was simple, but it is definitely not the only way to do it.
There are usually many solutions to the same problem. One may (or may not be) better than another. I am following Euclid because I am assuming he was smarter than me. :)
"Draw line AC" should read "Draw line AE".