Press n or j to go to the next uncovered block, b, p or k for the previous block.
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/**
* Recipe for Proposition I.2: Place at a given point a line equal to a given line.
*
* inputs: [B (seg-from), C (seg-to), A (target)]
* ops:
* join-AB: segment A → B (Post.1)
* apply-I1: apply I.1 on [A,B], outputs {C:'D'} (By I.1)
* circle-BC: circle center B, radiusPoint C (Post.3)
* produce-E: produce from D through B until circle-BC (Post.2+Def.15)
* circle-DE: circle center D, radiusPoint E (Post.3)
* produce-F: produce from D through A until circle-DE (Post.2+Def.15)
* seg-AF: segment A → F (Post.1, export-only)
*
* exports: F (point, key:'result'), seg-AF
*
* degenerate: when A ≡ B → simplified ops
*/
export const RECIPE_PROP_2: ConstructionRecipe = {
propId: 2,
label: 'Transfer distance (I.2)',
inputSlots: [
{ ref: 'B', role: 'seg-from', label: 'Segment start', givenId: 'pt-B' },
{ ref: 'C', role: 'seg-to', label: 'Segment end', givenId: 'pt-C' },
{ ref: 'A', role: 'target', label: 'Target point', givenId: 'pt-A' },
],
distinctInputPairs: [
[0, 1],
[0, 2],
[1, 2],
],
ops: [
{ kind: 'segment', id: 'join-AB', from: 'A', to: 'B' },
{ kind: 'apply', id: 'apply-I1', recipeId: 1, inputs: ['A', 'B'], outputs: { C: 'D' } },
{ kind: 'circle', id: 'circle-BC', center: 'B', radiusPoint: 'C' },
{ kind: 'produce', id: 'produce-E', from: 'D', through: 'B', until: 'circle-BC', output: 'E' },
{ kind: 'circle', id: 'circle-DE', center: 'D', radiusPoint: 'E' },
{ kind: 'produce', id: 'produce-F', from: 'D', through: 'A', until: 'circle-DE', output: 'F' },
{ kind: 'segment', id: 'seg-AF', from: 'A', to: 'F' },
],
exports: [
{ ref: 'F', kind: 'point', outputLabelKey: 'result' },
{ ref: 'seg-AF', kind: 'segment' },
],
facts: [
{
kind: 'distance',
left: { a: 'B', b: 'E' },
right: { a: 'B', b: 'C' },
citation: { type: 'def15', circleOpId: 'circle-BC' },
statementTemplate: '{B}{E} = {B}{C}',
justificationTemplate: 'Def.15: {E} lies on circle centered at {B} through {C}',
},
{
kind: 'distance',
left: { a: 'D', b: 'F' },
right: { a: 'D', b: 'E' },
citation: { type: 'def15', circleOpId: 'circle-DE' },
statementTemplate: '{D}{F} = {D}{E}',
justificationTemplate: 'Def.15: {F} lies on circle centered at {D} through {E}',
},
{
kind: 'distance',
left: { a: 'D', b: 'A' },
right: { a: 'D', b: 'B' },
citation: { type: 'prop', propId: 1 },
statementTemplate: '{D}{A} = {D}{B}',
justificationTemplate: 'I.1: equilateral triangle on {A}{B}',
},
{
kind: 'distance',
left: { a: 'A', b: 'F' },
right: { a: 'B', b: 'E' },
citation: { type: 'cn3', whole: { a: 'D', b: 'F' }, part: { a: 'D', b: 'A' } },
statementTemplate: '{A}{F} = {B}{E}',
justificationTemplate:
'C.N.3: If equals are subtracted from equals, the remainders are equal. Since {D}{F} = {D}{E} and {D}{A} = {D}{B}, {A}{F} = {B}{E}.',
},
{
kind: 'distance',
left: { a: 'A', b: 'F' },
right: { a: 'B', b: 'C' },
citation: { type: 'cn1', via: { a: 'B', b: 'E' } },
statementTemplate: '{A}{F} = {B}{C}',
justificationTemplate:
'C.N.1: Things which equal the same thing also equal one another. Since {A}{F} = {B}{E} and {B}{E} = {B}{C}, {A}{F} = {B}{C}.',
},
],
ceremony: {
revealGroups: [
['join-AB'],
['apply-I1', 'circle-BC', 'produce-E'],
['circle-DE'],
['produce-F', 'seg-AF'],
],
narrationTemplate:
'The segment at {A} now equals {B}{C} — that is what Proposition two proves.',
},
degenerateCases: [
{
condition: { coincident: ['A', 'B'] },
ops: [
// When target = segFrom, circle at B through C, then produce F using fallback direction
// (A=B so computeDirectionVector falls back to (0,1), matching old behavior)
{ kind: 'circle', id: 'circle-BC', center: 'B', radiusPoint: 'C' },
{
kind: 'produce',
id: 'produce-F-degen',
from: 'A',
through: 'B',
until: 'circle-BC',
output: 'F',
},
{ kind: 'segment', id: 'seg-AF', from: 'A', to: 'F' },
],
},
],
}
/**
* Annotations for I.2 steps — keyed by op ID.
* 'seg-AF' is export-only (no student action), so no annotation.
*/
export const PROP_2_ANNOTATIONS: OpAnnotations = {
'join-AB': {
instruction: 'Join point {pt:A} to point {pt:B}',
tool: 'straightedge',
citation: 'Post.1',
highlightIds: ['pt-A', 'pt-B'],
},
'apply-I1': {
instruction: 'Construct equilateral triangle on {seg:AB} ({prop:1|I.1})',
tool: 'macro',
citation: 'I.1',
highlightIds: ['pt-A', 'pt-B'],
},
'circle-BC': {
instruction: 'Draw a circle centered at {pt:B} through {pt:C}',
tool: 'compass',
citation: 'Post.3',
highlightIds: ['pt-B', 'pt-C'],
},
'produce-E': {
instruction: 'From {pt:D}, extend through {pt:B} to meet the circle at {pt:E}',
tool: 'straightedge',
citation: 'Post.2',
highlightIds: ['pt-D', 'pt-B'],
expectedOverride: {
type: 'extend',
baseId: 'pt-D',
throughId: 'pt-B',
label: 'E',
},
},
'circle-DE': {
instruction: 'Draw a circle centered at {pt:D} through {pt:E}',
tool: 'compass',
citation: 'Post.3',
highlightIds: ['pt-D', 'pt-E'],
},
'produce-F': {
instruction: 'From {pt:D}, extend through {pt:A} to meet the circle at {pt:F}',
tool: 'straightedge',
citation: 'Post.2',
highlightIds: ['pt-D', 'pt-A'],
expectedOverride: {
type: 'extend',
baseId: 'pt-D',
throughId: 'pt-A',
label: 'F',
},
},
// 'seg-AF' intentionally has NO annotation — it's an export-only op
}
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