Timeline for Fully worked straightedge-and-compass construction for Euclid I.31 (including I.23, I.22, I.3)?
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| when toggle format | what | by | license | comment | |
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| Feb 28 at 16:48 | comment | added | RobinSparrow | @Rrasco88: the angles you seem confused about are $\angle{DBC}$ and $\angle{D'B'C'}$ in my diagram. The point $B'$ is the "given point" through which the parallel line is constructed by Euclid. No part of the construct is omitted in the picture. You don't need to use I.3 to move line segments around - no one does that, that's what a compass is for. | |
| Feb 27 at 20:32 | answer | added | RobinSparrow | timeline score: 0 | |
| Feb 27 at 20:00 | comment | added | Rrasco88 | @SammyBlack I understand the symmetry. What I don't understand is how the angle is being copied at all. I know I have to do I.23 on point A, and I.22 with I.3, but I struggle to keep all the lines, intersections, and circles in my head at once. | |
| Feb 27 at 19:52 | comment | added | Sammy Black | The alternate interior angles are labeled in a way that respects the symmetry between them. Imagine putting a pin in the midpoint of segment $DA$ and rotating the diagram half way around $(180^\circ)$. Notice that $\angle DAE$ would land on $\angle ADC$ with labels in that order/orientation. | |
| Feb 27 at 19:25 | comment | added | Rrasco88 | @RobinSparrow The orientation of angles DAE and ADC is throwing me off, and I'm lost immediately after drawing DA | |
| Feb 27 at 17:16 | comment | added | RobinSparrow | aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html gives a standard translation of Elements. At what point, exactly, are you losing the thread of what to do? All you need to do is build an arbitrary triangle on a line, then make a copy of that triangle on one of its sides, extended. | |
| Feb 27 at 16:59 | comment | added | Rrasco88 | @RobinSparrow I don't know how to do all the constructions in I.31 myself. That is why I am outsourcing it to someone who knows how to do it. If I knew how to do the proof with all the constructions, I would've done that already. | |
| Feb 27 at 16:47 | comment | added | RobinSparrow | Why don't you just screenshot each step in Geogebra? | |
| Feb 27 at 15:18 | history | edited | Rrasco88 | CC BY-SA 4.0 |
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| Feb 27 at 15:11 | history | asked | Rrasco88 | CC BY-SA 4.0 |