Suggestions

[MarcinCiura]

Propositions I.XXVII, I.XXVIII and I.XXIX (Russian):

• Rename the angles so that their sides are marked with G and H rather than E and F.

Proposition I.XXXV (Russian):

• Rename <BAC to <EAC, <EBD to <FBD, and <AFD to <BFD to match the vertices of the triangles that are proven to be equal.
• Optional: draw EFDG byred so that <AEC is anchored.
• Very optional: don't draw AC, which is only implicitly mentioned in the text.

[MarcinCiura]

Proposition I.XXXVI (Russian):
[Both my suggestions were wrong.]

[MarcinCiura]

Proposition I.XXXVII:

• The labels A and F in the diagram are positioned too low.
• "равными между собой" should better say "равными по площади между собой".
• Where parallelograms "= дважды" triangles, the left-hand side is bottom-aligned while the right-hand side is middle-aligned.

[MarcinCiura]

Proposition I.XXXVIII:

• Nit: label D is positioned a bit higher than label G. draw byLabelsOnPolygon(A, B, E, F, H, G, D, C)(0, 0); instead of two separate draws fixed this for me.

[MarcinCiura]

Proposition I.XLI:

• Typo in the title: missing "I".
• Optional: add inax[ax:VI] at the end.

[MarcinCiura]

Proposition I.XLII:

• Optional: add inax[ax:VI] at the end.

[MarcinCiura]

Proposition I.XLVI (Russian):

• Optional: make use of \drawRightAngle.

[MarcinCiura]

Proposition I.XLVII (Russian):

• Instead of ,\\$\drawUnitLine{BC} = \drawUnitLine{CI}$ и $\drawUnitLine{CA} = \drawUnitLine{CF}$;, write .\\Но $ etc.
• Optional: draw angles <BCI and <ACF inside triangles ACI and BCF (with startTempAngleScale(angleScale*3/4);).
• Optional: refer to \inprop[prop:I.IV] where triangle ACI = triangle BCF.
• Optional: refer to \inprop[prop:I.XLI] where squares = дважды triangles.
• Optional: refer to \inax[ax:VI] where ACFG = KICJ.
• Optional: refer to \inax[ax:II] at the end of the proof.

[jemmybutton]

Thank you! Mostly done: ab0381e

About this one:

Nit: the line $\drawUnitLine{CD} = \drawUnitLine{GH} = \drawUnitLine{EF}$ could better say $\drawUnitLine{CD} = \drawUnitLine{EF} = \drawUnitLine{GH}$
The line$\therefore \drawUnitLine{CD} = \mbox{ и } \parallel \drawUnitLine{EF}$; is misleading. It should say, e.g. но \drawUnitLine{CD} = \mbox{ и } \parallel \drawUnitLine{EF}$ (гип.);

I think there's some logic to the original: parallelograms are said to be on equal bases, so CD = GH by hyp. and GH = EF by pr.1.34, so the order CD = GH = EF seems more natural in this context. And the next line follows from this one via ax.II (that CD and EF are equal) and pr.1.33 (that they are parallel), and therefore \therefore seems appropriate.

[MarcinCiura]

In propositions I.XXXIX and I.XL, the line segments that end at A end too far.
I hacked a fix by adding byLineDefine(A, C, byyellow, 0, 0); and pushing AC it at the second position in draw byNamedLineSeq(0)(...); but it is not ideal. Maybe there are better solutions.

[MarcinCiura]

in proposition I.XLVI, def. 30 should be referenced instead of def. 27.

[MarcinCiura]

Optional: use \inpropN in propositions I.XLV, I.XLVI, and I.XLVIII.

[jemmybutton]

Fixed! As for

In propositions I.XXXIX and I.XL, the line segments that end at A end too far.
I hacked a fix by adding byLineDefine(A, C, byyellow, 0, 0); and pushing AC it at the second position in draw byNamedLineSeq(0)(...); but it is not ideal. Maybe there are better solutions.

The first argument to byNamedLineSeq, which is 0, is responsible for shifting all lines in a sequence to the left (negative values) or to the right (positive values) of the sequence axis. 1 or -1 is for shifting it half line width. So changing it to byNamedLineSeq(1)(...) would make external angle of AB and AF exactly coincide with point A. But I'd rather make it something like byNamedLineSeq(4/5)(...). ab3820a#diff-ce29b5befc0686b45157d97a74d17263R3059

[MarcinCiura]

1. I.XL is not fixed yet.
2. You have seen my early version. FYI, I based it on B5 paper with bleed, i.e. 165+6x230+6 mm because your dimensions (153x210 mm) would lead to large losses of paper. For mass printing in A5 format, one has to make the pages 146x206 mm when printing, 140x200 mm after cutting. Source: a printing house I talked to.
3. To give you proper credit, is your surname ...рев or ...рёв?

[jemmybutton]

1. Fixed now: 89775f3#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R3095 (but I have no solution for such problems in general, maybe I should add something to shift points on line sequence one by one, not all at once)
2. In the beginning I thought to make the first version just A5 (to be able to print on any A4 printer to proofread), but it turns out that A* is a little too narrow to comfortably put something on the margins (at first I tried to inset figures like in the original, but besides the fact that that requires more manual tweaking, that doesn't look very good to me, so I gave up for now and that's why macro for problem is called \problemNP: simply \problem is automatically inset and you still can find it in one proposition https://github.com/jemmybutton/byrne-euclid/blob/master/byrne_context.tex#L12269 ) and printing for proofreading is not that necessary, so I made it 153×210 to decide on actual format some time later (maybe something like 70×90/16, which is 170×215). But of course it's subject to change and your format seems nice.
3. -рев

[MarcinCiura]

I.XLVIII (Byrne's bug in the formulation of the proposition): то угол \drawAngle{DAB} -> то угол \drawAngle{BAC}.

[MarcinCiura]

Introduction (obviously my proposals may be unidiomatic):
"по общему мнению" -> "по общему согласию"
"в виде слов" -> "буквами"
"пространное определение" -> "обманчивое определение" (specious != spacious)
"Линия суть длина" -> I may be wrong but "суть" means "they are", not "it is" to me.

Definition 1 (Russian): missing period.
Definition 8 (Russian), optional: "по одной прямой" is so-so even though I know this is what the original says. I like Byrne's "direction" better.

[MarcinCiura]

Definition 34 (Russian): "прямоугольники" -> "четырехугольники".

[MarcinCiura]

Axiom 10 (Russian), not sure: doesn't "пространство" mean 3D space?

[MarcinCiura]

Nit (both versions): The first word in the introductions is not typeset in \sc.

[MarcinCiura]

Def. 33: It's actually not a definition of a parallelogram as Euclid's parallelograms include rhombi and rectangles. Here, it's a rhomboid, never ever used again (https://archive.org/stream/euclid_heath_2nd_ed/1_euclid_heath_2nd_ed#page/n201/mode/2up).

[jemmybutton]

Thank you!

I.XLVIII (Byrne's bug in the formulation of the proposition): то угол \drawAngle{DAB} -> то угол \drawAngle{BAC}.

Fixed: a2ae3c0#diff-ce29b5befc0686b45157d97a74d17263R3629 and a2ae3c0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R3610

"по общему мнению" -> "по общему согласию"

It would be a more precise translation, but "по общему согласию" doesn't sound right to me, maybe something like "по общему признанию" would be better, but "по общему мнению" doesn't change the meaning too much either.

"пространное определение" -> "обманчивое определение" (specious != spacious)

"Линия суть длина" -> I may be wrong but "суть" means "they are", not "it is" to me.

Shame on me! You're absolutely right, fixed: a2ae3c0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R229 and a2ae3c0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R244%3E

Definition 1 (Russian): missing period.

Fixed: a2ae3c0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R388

Definition 8 (Russian), optional: "по одной прямой" is so-so even though I know this is what the original says. I like Byrne's "direction" better.

For definitions and axioms I took Morduhai-Boltovskoi's translation of the Elements, but I agree, Byrne's definitions is easier to understand. Fixed: a2ae3c0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R430

Definition 34 (Russian): "прямоугольники" -> "четырехугольники".

Fixed: a2ae3c0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R806

Axiom 10 (Russian), not sure: doesn't "пространство" mean 3D space?

It does, in most cases, but it's ok to say "двумерное пространство", and M.-B. have translated it this way, so I'll leave it be.

Nit (both versions): The first word in the introductions is not typeset in \sc.

Fixed (by hand for now): a2ae3c0#diff-ce29b5befc0686b45157d97a74d17263R118 and a2ae3c0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R125

Def. 33: It's actually not a definition of a parallelogram as Euclid's parallelograms include rhombi and rectangles. Here, it's a rhomboid, never ever used again (https://archive.org/stream/euclid_heath_2nd_ed/1_euclid_heath_2nd_ed#page/n201/mode/2up).

Strictly speaking, yes, and fixed: a2ae3c0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R800
Although M.-B. writes "ромбоид (параллелограмм)" in his translation of def. 22. Since there's no reason (except for being faithful to the original original, which is not the case in Byrne's book anyway) to keep definitions like that, it makes sense to introduce some definition for parallelogram instead.

[jemmybutton]

@mciura both books fit within A5 now: 145 by 200 ( e9d5cba ). That's still somewhat wider than 140 by 200, that you mentioned, but still, it should be possible to print everything on regular A4 printer, and with A3plus format printing (which is quite common, afaik) it should be possible to print it with all the cutting. Lettrines are now a little bit smaller, and font size is 10 instead of 11.

[MarcinCiura]

1. Lines 982 and 983 in the Russian version express twice the same thought about figures that lie in one plane.
2. In line 985 of the Russian version, it might help to mention that the Euclidean compass collapses once lifted from the surface so it cannot be used to transfer distance (https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI2.html).
3. Somewhere around line 975 of the Russian version, a diagram like at https://www.mathsisfun.com/definitions/corresponding-angles.html and its explanation might help the reader. The names of the angles are not so intuitive.
4. In my Polish translation of Proposition I.5, I marked the angles BCE and CBD with black arcs. I think that failing to mark them was an error on Byrne's part.

[jemmybutton]

Thank you! Mostly fixed 42338c0
2. This addition is important, but maybe it's better to be placed alongside the postulates as a comment?
3. For some reason Byrne didn't use diagrams in the introduction extensively. I think, adding some more in the future would also help.
4. The only doubt i have about these black arcs is that this proposition is one of the most well known in Byrne's book and black arcs make it look very different from the original. Maybe change arc color to something less eye-catching, say, yellow?

[MarcinCiura]

Thank you!
2. Let us both think more about the placement of this comment. I have not yet finished reading and translating the "Elucidations" supersection.
3. Although your addition helps the reader, too, I meant "восемь углов трансверсали: односторонние углы, соответственные углы и накрестлежащие углы."
4. I fully agree.

[jemmybutton]

I didn't do anything on 2. and 3. yet (hopefully, I'll do something some time soon), 4. is fixed in both places (a9ec3f0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R312 and a9ec3f0#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R1388 )
Note that the typeface in the book is changed to EB Garamond as suggested here #34 . It shouldn't be a problem at this stage, but it will take some time to take care of all the widows and orphans.

[jemmybutton]

Hi Marcin!
2. As the book has wide enough margins, I suggest using them to place all the necessary notes, like this e440f81#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R838 . This way translation won't deviate too far from the original in its bulk.
The same thing could be done somewhere with respect to 3.

[MarcinCiura]

2. Marginal notes look very good to me — thank you!
   A little suggestion: maybe a more explicit text along the lines of "переносить расстояния ним невозможно" (but idiomatic) instead of "и ни для чего больше"?

[jemmybutton]

Thank you, I'll think a bit about this phrase, переносить расстояния is correct, but it feels like it needs some context to be clearly understood.

[MarcinCiura]

In Proposition I.XIII (Russian), lines 1892-1893:

Если \drawUnitLine{ED} $\perp$ к~\drawUnitLine{BC} тогда,\\
\drawAngle{ADB,EDA} и~$\drawAngle{CDE} = \drawTwoRightAngles$ \indef[def:I.X].

can be rewritten as

Если $\drawUnitLine{ED} \perp \drawUnitLine{BC}$, тогда\\
$\drawAngle{ADB,EDA} + \drawAngle{CDE} = \drawTwoRightAngles$ \indef[def:I.X].

(Optionally remove "к" after \perp, although it can stay for consistency with line 1895; fix the position of the comma; use + for addition rather than и).

[jemmybutton]

Thank you, your variant looks much better to me. I will apply it with the next commit.
UPD: done c716c04#diff-5a8eec69ed8a2717ec1a6d8ee3f6ac94R1892

[MarcinCiura]

Proposition XI.1: s/There then will be/There will then be/ (https://archive.org/details/in.ernet.dli.2015.84160/page/n283)

I have thought about the issue of point C in that proposition. IMHO, it would be better to keep the diagram as before, with a longer line AC, and name the point at the intersection of AC with the circle. Recall that "straight line" means "line segment" for Euclid. With the new diagram, "Let it be BD" implicitly requires BD to have the same length as BC.

[jemmybutton]

@mciura both fixed abaef57
I don't remember exactly why i left the possibility for arc labels to be at respective points rather that on an arc itself, but it seems to be used nowhere, so arc labels are now placed precisely on arc ends, no matter where the point is.

[MarcinCiura]

Two very pedantic comments:

As for the marginal note "А циркуль пригоден только для построения окружностей, то есть измерять и откладывать расстояния с его помощью также нельзя." it seems to me that one can measure distances with compasses but cannot move distances after the leg of compasses is raised.

As for the note "Аксиомы XI и XII обычно включаются в качестве IV и V в состав постулатов.", the change occurs in later editions than Byrne's, which follow Heiberg's 1883-1884 critical edition in using codex Vaticanus Graecus 190. Unlike the text of earlier editions, the text of the codex is thought to predate Theon of Alexandria's changes to the Elements.

[MarcinCiura]

I have just learned that ConTeXt has italic correction turned off by default: https://tex.stackexchange.com/questions/255021/no-italic-correction-in-context
What do you think about turning it on?

[MarcinCiura]

It seems to me that the fragment "The twelfth axiom may be expressed..." belongs below the 12th axiom, and the Elucidations begin after it: https://archive.org/details/firstsixbooksofe00eucl/page/n27

[jemmybutton]

@mciura Thank you! Agreed. Fixed af5c529

[MarcinCiura]

Proposition II.9: rectangle CDFG accidentally looks like a square.

[MarcinCiura]

Even though you do not need \inpostL, I added it to my file as I use it in Proposition II.10:

draw ... and {EB,BG} (\inpostL[post:I.I] and \inpropN[post:I.II])

I am neutral on the question whether it should be added to preamble_be.tex.

Edit: I do not need \inpostL anymore, following the real Euclid who separates the drawing of {EB} from producing it to {G} by a mini-proof that {EB,BG} meets {FD,FG}.

[jemmybutton]

@mciura

Proposition II.9: rectangle CDFG accidentally looks like a square.

fixed a864325#diff-ce29b5befc0686b45157d97a74d17263R4291

I do not need \inpostL anymore

added anyway a864325#diff-b44801cabf4c040d727c2524313832c6R240 just in case

[MarcinCiura]

The italic correction does not seem to work. I am getting exactly the same bad results with itlc=yes commented out in type-ebgaramond-be.tex.

[jemmybutton]

@mciura It does work (at least with the examples provided in that SE answer), but not in this case. The reason is in the way i made upright parentheses in italic text. They are simply characters from roman font forced into italics and they are treated respectively (as if they were italics), i.e. no correction is applied. Curiously, it doesn't work in such a case either:

(\emph{á})

but it works in this case:

({\em á})

Replacing the definition:

%\definehighlight[emph][style=italic]
 \def\emph#1{{\em #1}}

works.

But still, I don't know how to combine italics correction and upright parentheses yet. I'll try to figure it out

[MarcinCiura]

A small nit: consider adding some vertical space after subpropositions.
However, my putting after={\blank[medium]} (or any other \blank[...]) into \setuphead[subproposition] did not change anything in the look.

[jemmybutton]

@mciura I didn't do \setuphead correctly, so it didn't work well (and even broke everything in TeX Live 2019), but recently i somewhat fixed this and added a little vertical space too 0d756a0#diff-b44801cabf4c040d727c2524313832c6R288 . Is it ok now?

[MarcinCiura]

Some minor suggestions about triangles. Except I.22, all are very easy to fix.
I.10 and I.11: you can substitute 97/56 for 7/4 as an approximation to sqrt(3).
Byrne shows scalene (or isosceles but not equilateral) triangles in these diagrams:
I.6: triangle ABD accidentally looks like equilateral.
I.12: triangle ABC accidentally looks like equilateral.
I.16: triangle ABC accidentally looks like equilateral.
I.18: triangle ABD accidentally looks like isosceles (to be fair, Byrne has it like this, too)
I.22: triangle ABC accidentally looks like right-angled, suggesting that AC and CB must be tangent to circles ADC and BEC.
I.24: AC accidentally bisects BD.
I.26: triangle DEG in Case I accidentally looks like isosceles; triangle DGF in Case II too (Byrne has this one, too).
I.32: triangle ABC accidentally looks almost like equilateral.
I.37 triangle BCD accidentally looks like isosceles (this one does not hurt much).
I.38: triangles BCD and EGH accidentally look like mirror images.
I.39: triangle BCD accidentally looks like equilateral (this one also does not hurt much).
I.40: triangles ACD and BEF accidentally look like mirror images.
I.48: triangle BDC accidentally looks like equilateral.
II def. 2: parallelograms AEIG and DFIH accidentally look like rhombi.

[jemmybutton]

@mciura Thank you! fixed 8444c83

[MarcinCiura]

Thank you, now the triangles look much better. One nit: in I.24, AD should be equal to AC.

[jemmybutton]

@mciura Done! 4f43748

[MarcinCiura]

I know that this suggestion is controversial as it asks for modifying Byrne's showcase proof of I.47 but the proof in its current form is incomprehensible. It implies that ICJK = 2 AIC follows from AB || CF while in fact it follows from AK || CI, omitted from the proof.

Since Byrne (always?) makes both premises of axiom I immediately precede the conclusion, I suggest to format the Russian version as follows:

Теперь, поскольку \left{
AB || CF [optional: (prop. I.14)]
AK || CI [optional: (construction)]
\right},
\left{
ACFG = дважды BCF
ICJK = дважды AIC
\right} \inprop[prop:I.XLI].
\therefore ACFG = ICJK \inax[ax:I.VI].

[MarcinCiura]

Another suggestion about triangles:
I.42 — AF accidentally equals FG.

[jemmybutton]

@mciura Thank you! Done 0a1521f
On I.47 I agree, Byrne's proof is unclear. I didn't use curly brackets though (their presence would be too conspicuous, imo) and simply broke the argument in two parts.
I assume that in I.42 you meant what's BE and EC in my version?

[MarcinCiura]

Yes, I accidentally quoted my symbols in I.42, and I agree that braces in I.47 would look ugly.
A small nit: now in I.47 "И поскольку" starts with a capital letter yet is not preceded by a period.