Talk:Thābit ibn Qurra

Clarifications needed for recent edit

Hello TheVictorGoesTheSpoils, thanks for your recent contribution to this article. I corrected a few things and tried to improve the prose a little. However, some things you wrote remain unclear, and not having checked the sources myself I dare not make any more changes to them. You wrote (refs left out):

He provided a strengthened extension of Phythoras' proof which included the knowledge of Euclid's Fifth Postulate, which states that the intersection between two straight line segments combine to create two interior angles which are less than 180 degrees. These method of reduction and composition result in a combination and extension of contemporary and ancient knowledge on this famous proof. Thābit believed that geometry was tied with the equality and differences of magnitudes of lines and angles, also that ideas of motion should be included in geometry and more widely physics.

After my copy-edit, this became (again, refs left out):

He provided a strengthened extension of Pythagoras' proof which included the knowledge of Euclid's fifth postulate. This postulate states that the intersection between two straight line segments combine to create two interior angles which are less than 180 degrees. The method of reduction and composition used by Thābit resulted in a combination and extension of contemporary and ancient knowledge on this famous proof. Thābit believed that geometry was tied with the equality and differences of magnitudes of lines and angles, as well as that ideas of motion (and ideas taken from physics more widely) should be integrated in geometry.

My questions:

1. What do you mean by 'strengthened extension'? Do you mean that Thābit improved upon existing proofs of the Pythagorean theorem? If so, whose proofs exactly did he improve upon (as is well known, Pythagoras himself left no writings, so presumably we're speaking about early Greek mathematicians, but who exactly?), and how exactly did he improve them? By using Euclid's fifth postulate in his proof? If so, how did he use it and why was this an improvement?
2. What is the 'method of reduction and composition'?
3. Is the study of 'the equality and differences of magnitudes of lines and angles' some sort of traditional definition of (Eucledian) geometry in Thābit's time? If so, that should probably be made explicit. Am I right to interpret your original edit 'ideas of motion should be included in geometry and more widely physics' as a statement that Thābit that believed theories of motion and other ideas taken from physics should be integrated into geometry? What exactly are 'ideas of motion' anyway, and what role did Thābit precisely envision for them in geometry?

As you see, there are a lot of questions here, which might be difficult to answer. If you too don't know the answers, it would probably better to simply remove your additions again. One should never write about what one doesn't fully understand: it only confuses the readers. If you believe you do understand, please elaborate the paragraph a bit and make sure the readers also understand.

Thanks, ☿ Apaugasma (talk ☉) 11:22, 19 November 2022 (UTC)

Hi Apaugasma,

After alot of thought and some review on my sources, I think I am ready to address some of the concerns you raised. The clarity of my revisions on this page is mainly due to the prose that I adopted, and was trying to implement what I learned about neutral language. So I will answer your questions in order.

1. Strengthened extension is a literary choice I made, which honestly can be clarified to Generalizing Pythagoras' theorem, using Euclid's Elements as a vector to approach the problem, specifically focusing on Euclids 5th postulate to improve on the proof. The generalization of Euclids 5th postulate came about Algebraically, which is coincidentally the explanation to question 1 and 2. So, to summarize, Thabit used Euclid's postulates on the Pythagorean Theorem, and Al-Khwarizmi's Al-Jabr concepts on simplification and notation to improve upon and ultimately generate many of the proofs we use today to describe right triangles, not just geometrically, but also mathematically.
2. Method of reduction and composition is a fancy way of saying algebraic simplification. I will likely link it to the Reduction page in order to clarify that.
3. Something that I did not make too clear which I shall fix, is how proficient a Euclidian Geometer Thabit was. He was only able to generalize Pythagoras' Theory because he was so well versed as a geometer, and was familiar with all of his postulates. The 5th postulate which is roughly the idea that "the equality and differences of magnitudes of lines and angles' in a triangle will always sum to 180 degrees. This phenomenon was already observed and categorized. Thabit took this axiom and combined it with Al-Khwarizmi's Al-Jabr. His work combined the Euclidian ideas of geometry with algebra, to solve other pressing issues in his research such as Physics problems. Many physics problems or how I phrased it, "ideas of motion" require a geometric analysis in order to properly prove the motion of objects, combined with Algebra this idea is able to take the form of a generalized formula, and proof. Although it needs to be noted that Thabit was more well versed with Statics and the analysis of objects that do not move. The ideas of motion and static physics do mesh together. The forces and phenomena seen in the 9th century are consistent with the same observations made by newton, and this framework allowed him use calculus to prove and generalize further the ideas of motion and static physics. Saying precisely what Thabit believed is hard due to the lack of accessible primary documentation. It is however definitive for us to interpret his mathematic works as a clear indicator that he was a proponent of merging these two fields.

I hope this is a good answer to your questions posited to me. I am working in my sandbox to remedy and clarify the sections you asked for clarification on. I will post my clarifications later this afternoon here on the talk page.

Thanks for the help,

TheVictorGoesTheSpoils TheVictorGoesTheSpoils (talk) 20:02, 9 December 2022 (UTC)

@TheVictorGoesTheSpoils: I'm going to be honest with you, as I see it you are using a lot of words here to say very little. Thabit applied both Euclid's (fl. 300 BCE) geometry and al-Khwarizmi's (died c. 850 CE) recently introduced system of algebra to work out new and more generalized proofs of the Pythagorean theorem. In physics, he also applied geometry and algebra to the analysis of motion. Is that it? If it is, I strongly advise you to just write two sentences of that length, possibly the exact two sentences I just wrote, and nothing more. How exactly Thabit applied geometry and algebra to these problems appears too difficult to explain for you, and to be entirely honest my impression is that you yourself do not fully understand. Again, do not write about what you do not fully understand, but instead summarize and try to capture the essence of what you do understand. ☿ Apaugasma (talk ☉) 00:02, 10 December 2022 (UTC)