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some typos fixed, minor improvements in lettrines
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@jemmybutton
jemmybutton committed Apr 10, 2019
1 parent 6bc5c5d commit 8a02bdf
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6 changes: 3 additions & 3 deletions byrne_ru_context.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -11778,7 +11778,7 @@
И, присоединив \inprop[prop:V.XVIII],\\
$\drawSizedLine{AF,FB} : \drawSizedLine{AF} :: \drawSizedLine{AD,DC,CE} : \drawSizedLine{AD}$.

Ио есть \drawSizedLine{AD,DC,CE} содержит \drawSizedLine{AD} столько раз, сколько \drawSizedLine{AF,FB} содержит требуемую часть (\conststr).
То есть \drawSizedLine{AD,DC,CE} содержит \drawSizedLine{AD} столько раз, сколько \drawSizedLine{AF,FB} содержит требуемую часть (\conststr).

$\therefore$ \drawSizedLine{AF} и~есть требуемая часть.
\stopCenterAlign
Expand Down Expand Up @@ -13381,7 +13381,7 @@
draw byNamedArc(EF);
stopAutoLabeling;
stopGlobalRotation;
}$, как и~сектора.}
}$, как и~секторы.}

Возьмем на окружности \circleG\ любое количество дуг
\drawFromCurrentPicture[middle][arcCK]{
Expand Down Expand Up @@ -13436,7 +13436,7 @@

$\therefore \drawAngle{BC} : \drawAngle{EF} :: \arcBC\ : \arcEF$ \indef[def:V.V], или углы в~центре относятся так же, как дуги, на которых они стоят, но углы на окружности вдвое меньше углов в~центре \inprop[prop:III.XX] и~относятся так же \inprop[prop:V.XV], и~следовательно так же, как дуги, на которых они стоят.

Очевидно, что сектора в~равных кругах и~на равных дугах равны (\inpropL[prop:I.IV], \inpropN[prop:III.XXIV], \inpropN[prop:III.XXVII], и~\indefL[def:III.IX]). Значит, если выше углы заменить на сектора, получим доказательство второй части, то есть, что в~равных кругах сектора относятся друг к~другу как дуги, на которых они стоят.
Очевидно, что секторы в~равных кругах и~на равных дугах равны (\inpropL[prop:I.IV], \inpropN[prop:III.XXIV], \inpropN[prop:III.XXVII], и~\indefL[def:III.IX]). Значит, если выше углы заменить на секторы, получим доказательство второй части, то есть, что в~равных кругах секторы относятся друг к~другу как дуги, на которых они стоят.

\qed
\stopProposition
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43 changes: 31 additions & 12 deletions lettrines/lettrines.mp
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Original file line number Diff line number Diff line change
Expand Up @@ -88,23 +88,27 @@ numeric branchNumber, branchAngle[], branchScale[], meristemOrientation[], meris
boolean branchActive[], branchFlipped[];

vardef makeBranchPath@#(expr brOrigin, brAngle, brScale, brFlipped) =
applyBranchTransform(branchTemplate@#, brOrigin, brAngle, brScale, brFlipped)
applyBranchTransform(branchTemplate@#, brOrigin, brAngle, brScale, brFlipped, stemVector@#)
enddef;

vardef applyBranchTransform (expr p, brOrigin, brAngle, brScale, brFlipped) =
save somePath;
vardef applyBranchTransform (expr p, brOrigin, brAngle, brScale, brFlipped, brStem) =
save somePath, someStem;
path somePath;
pair someStem;
if brFlipped:
somePath := p yscaled -1;
if cycle p:
somePath := reverse somePath;
fi;
someStem := brStem yscaled -1;
else:
somePath := p;
someStem := brStem;
fi;
if brScale > 0:
somePath := somePath scaled (brScale*scaleFactor);
fi;
somePath := somePath shifted (someStem*outlineThickness);
(somePath rotated brAngle) shifted brOrigin
enddef;

Expand Down Expand Up @@ -388,7 +392,7 @@ enddef;

path branchTemplate.curlA, branchMeristem.curlA[];
numeric branchMeristemOrientation.curlA[],branchMeristemCount.curlA, branchMazSize.curlA;

pair stemVector.curlA;
branchTemplate.curlA := ((1/2,0) for a := 60 step 60 until 360: .. (cosd(a), sind(a)) scaled 1/2(1-a/360) endfor) shifted (-1/2, 0);
branchTemplate.curlA := branchTemplate.curlA rotated 15;
branchMeristem.curlA0 := subpath (1/2, length(branchTemplate.curlA) - 2) of branchTemplate.curlA;
Expand All @@ -398,10 +402,11 @@ branchMeristemOrientation.curlA1 := -1;
branchMeristemCount.curlA := 2;
branchMinSize.curlA := 2mm;
branchMaxSize.curlA := 1cm;
stemVector.curlA := (0, 0);

path branchTemplate.curlB, branchMeristem.curlB[];
numeric branchMeristemOrientation.curlB[], branchMeristemCount.curlB, branchMazSize.curlB;

pair stemVector.curlB;
branchTemplate.curlB := ((1/2,0) for a := 60 step 60 until 630: .. (cosd(a), sind(a)) scaled 1/2(1-a/540) endfor) shifted (-1/2, 0);
branchTemplate.curlB := branchTemplate.curlB rotated 15;
branchMeristem.curlB0 := subpath (1/2, length(branchTemplate.curlB) - 3) of branchTemplate.curlB;
Expand All @@ -411,27 +416,41 @@ branchMeristemOrientation.curlB1 := -1;
branchMeristemCount.curlB := 2;
branchMinSize.curlB := 2mm;
branchMaxSize.curlB := 1cm;
stemVector.curlB := (0, 0);

path branchTemplate.leafA;
numeric branchMeristemCount.leafA, branchMinSize.leafA, branchMazSize.leafA;
pair stemVector.leafA;
branchTemplate.leafA := (0, 0){dir(90)} .. (subpath (2, 7) of (fullcircle scaled 2/3) shifted (-3/4, 2/3)) .. {dir(-90)} cycle;
branchTemplate.leafA := branchTemplate.leafA rotated 15;
branchMeristemCount.leafA := 0;
branchMinSize.leafA := 1/2mm;
branchMaxSize.leafA := 1/4cm;
branchMinSize.leafA := 2/3mm;
branchMaxSize.leafA := 1/6cm;
stemVector.leafA := (0, 0);

path branchTemplate.leafB;
numeric branchMeristemCount.leafB, branchMinSize.leafB, branchMazSize.leafB;
pair stemVector.leafB;
branchTemplate.leafB := (0, 0){dir(90)} .. (subpath (2, 5) of (fullcircle scaled 3/4) shifted (-4/5, 3/4)){dir(60)} .. {dir(-90)} cycle;
branchTemplate.leafB := branchTemplate.leafB rotated 15;
branchMeristemCount.leafB := 0;
branchMinSize.leafB := 1/2mm;
branchMaxSize.leafB := 1/4cm;
branchMinSize.leafB := 2/3mm;
branchMaxSize.leafB := 1/6cm;
stemVector.leafB := (0, 0);

path branchTemplate.berryA;
numeric branchMeristemCount.berryA, branchMinSize.berryA, branchMazSize.berryA;
pair stemVector.berryA;
branchTemplate.berryA := fullcircle shifted(-1/2, 0);
branchMeristemCount.berryA := 0;
branchMinSize.berryA := 1/2mm;
branchMaxSize.berryA := 1/4cm;
stemVector.berryA := (-1, 0);

branchMaxSize.common := infinity;

string branchTypesList;
branchTypesList := "common, curlA, curlB, leafA, leafB";
branchTypesList := "common, curlA, curlB, leafA, leafB, berryA";

vardef branchPic@#(expr brPath, brOrigin, brAngle, brScale, brFlipped) =
save brType, p;
Expand All @@ -441,7 +460,7 @@ vardef branchPic@#(expr brPath, brOrigin, brAngle, brScale, brFlipped) =
image(
if (brType = "curlA") or (brType = "curlB"):
p0 := makeBranchPath@#(brOrigin, brAngle, brScale, brFlipped);
p1 := ((fullcircle shifted (1/2, 0)) scaled 1/5mm) rotated (angle(direction 0 of reverse(p0)) - 90);
p1 := ((fullcircle shifted (1/2, 0)) scaled 1/2pt) rotated (angle(direction 0 of reverse(p0)) - 90);
if brFlipped:
p1 := p1 rotated 180;
fi;
Expand All @@ -454,7 +473,7 @@ vardef branchPic@#(expr brPath, brOrigin, brAngle, brScale, brFlipped) =
if brScale > 1mm:
p1 := applyBranchTransform(
((fullcircle scaled (3/4brScale*scaleFactor - 1/2mm)) shifted ((-3/4, 2/3) scaled brScale*scaleFactor)) rotated 15,
brOrigin, brAngle, -brScale, brFlipped);
brOrigin, brAngle, -brScale, brFlipped, stemVector@#);
fill p1 withcolor black;
fi;
elseif (brType = "leafB"):
Expand Down

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