Source citation ledger
Elements
Euclid; Thomas L. Heath (translation)
translation · c. 300 BCE; Heath English 1908
Euclid, The Thirteen Books of the Elements, trans. Thomas L. Heath (1908).
The Thirteen Books of Euclid’s Elements
Added 2026-10-18 for numbers-forms orphan leftovers. Keep apart from Yijing hexagram speech and modern set-theory dumps.
These are separate Atlas meetings that cite this source. Citation is not proof.
Hellenic religion
Equilateral is used in Triangle.
Heath’s Euclid Book I seats the equilateral triangle among the opening constructed figures — all sides equal — in the plane-geometry handbook. A named equilateral species of triangle in that Elements speech, not isosceles alone and not a bare three-side dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
used in · sourced · documented
Isosceles is used in Triangle.
Heath’s Euclid Book I defines the isosceles triangle as the figure with two equal sides and proves its base-angle equality. A named isosceles species in that handbook, not equilateral as all-three equal and not scalene.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
used in · sourced · documented
Heath’s Euclid Book I defines the scalene triangle as the figure with three unequal sides among the triangle species. A named scalene species in that handbook, not isosceles and not a modern inequality dump alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
used in · sourced · documented
Acute triangle is used in Triangle.
Heath’s Euclid Book I classifies triangles by angles and works with acute-angled cases among ordinary plane figures. A named acute-triangle species in that handbook, not the right-angled Pythagorean seat and not obtuse.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
used in · sourced · documented
Obtuse triangle is used in Triangle.
Heath’s Euclid Book I classifies obtuse-angled triangles among the angle species of plane triangles. A named obtuse-triangle species in that handbook, not right-triangle I.47 and not acute.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
used in · sourced · documented
Parallelogram appears in Hellenic religion.
Heath’s Euclid Book I builds parallelogram area and parallel theory as a working plane figure of the Elements. A named parallelogram in that handbook, not rhombus alone and not a modern vector dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Rectangle appears in Hellenic religion.
Heath’s Euclid seats the rectangle (right-angled oblong) among Book I–II plane figures and rectangular areas in geometric algebra. A named rectangle in that handbook, not the square already met and not a golden-rectangle design dump alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Rhombus appears in Hellenic religion.
Heath’s Euclid Book I defines the rhombus as an equilateral quadrilateral that is not right-angled, among named plane figures. A named rhombus in that handbook, not rhomboid and not a heraldry lozenge flatten.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Rhomboid appears in Hellenic religion.
Heath’s Euclid Book I names the rhomboid (ῥομβοειδές) as the quadrilateral with opposite sides and angles equal that is neither rectangle nor rhombus. A named rhomboid lemma in that handbook, not rhombus and not a casual parallelogram synonym dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Trapezoid appears in Hellenic religion.
Heath’s Euclid and commentary seat trapezium/trapezoid speech among irregular quadrilaterals neighboring the named parallelogram family in Book I figure lists. A named trapezoid gloss in that Elements neighborhood, not parallelogram and not a modern taxonomy dump alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Pentagon appears in Hellenic religion.
Heath’s Euclid Book IV constructs the regular pentagon inscribed in a circle and develops its diagonal ratios. A named pentagon in that handbook, not pentagram as the star alone and not pentadecagon.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Hexagon appears in Hellenic religion.
Heath’s Euclid IV.15 constructs the regular hexagon in a circle, with side equal to the radius. A named hexagon in that handbook, not hexagram as Yijing figure and not a honeycomb ornament dump alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Decagon appears in Hellenic religion.
Heath’s Euclid Book IV pentagon construction produces the regular decagon side as a working chord in the same circle geometry. A named decagon neighbor in that handbook, not pentagon alone and not a full star-polygon dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Pentadecagon appears in Hellenic religion.
Heath’s Euclid IV.16 constructs the regular fifteen-angled figure — the pentadecagon — in a circle from triangle and pentagon arcs. A named pentadecagon in that handbook, not pentagon alone and not a non-constructible polygon dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Dodecagon appears in Hellenic religion.
Heath’s Euclid regular-polygon constructions (hexagon and bisected arcs) make the regular dodecagon an ordinary neighbor of Book IV circle-polygon speech, even without a starred IV proposition of its own. A named dodecagon in that Elements neighborhood, not pentadecagon as the IV.16 star and not a full n-gon dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Pentagram appears in Hellenic religion.
Heath’s Euclid Book IV pentagon construction yields intersecting diagonals that form the pentagram star inside the pentagon, with extreme-and-mean ratios on those diagonals. A named pentagram figure in that Elements geometry, not an occult seal dump and not pentagon as the outer polygon alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Cube appears in Hellenic religion.
Heath’s Euclid Book XIII constructs the cube among the five regular solids and treats cubic measure in the solid books. A named cube in that handbook, not cuboid as rectangular parallelepiped alone and not a Timaeus element-represents dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Tetrahedron appears in Hellenic religion.
Heath’s Euclid Book XIII constructs the regular tetrahedron (pyramid with four equilateral faces) among the five solids. A named tetrahedron in that handbook, not square-pyramid alone and not a Timaeus fire-element represents dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Octahedron appears in Hellenic religion.
Heath’s Euclid Book XIII constructs the regular octahedron among the five solids. A named octahedron in that handbook, not cube dual mystique alone and not a Timaeus air-element represents dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Dodecahedron appears in Hellenic religion.
Heath’s Euclid Book XIII constructs the regular dodecahedron of twelve pentagons among the five solids. A named dodecahedron in that handbook, not dodecagon as the plane twelve-gon and not a Timaeus cosmos-element represents dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Icosahedron appears in Hellenic religion.
Heath’s Euclid Book XIII constructs the regular icosahedron of twenty triangles among the five solids. A named icosahedron in that handbook, not icosagon as the plane twenty-gon and not a Timaeus water-element represents dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Cone appears in Hellenic religion.
Heath’s Euclid Books XI–XII define the cone and prove volume relations for cones beside cylinders and pyramids. A named cone in that solid handbook, not conical-frustum as Archimedes pad and not a pottery kiln-cone wrong lemma.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Cylinder appears in Hellenic religion.
Heath’s Euclid Books XI–XII define the cylinder and prove its volume relations beside the cone. A named cylinder in that solid handbook, not cylinder-seal as the Near Eastern object and not a modern engine dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Sphere appears in Hellenic religion.
Heath’s Euclid Book XII treats the sphere’s volumes and relations after Book XI’s solid definitions. A named sphere in that handbook, not celestial-sphere as the sky instrument and not a spheroid dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Prism appears in Hellenic religion.
Heath’s Euclid Book XI defines the prism as a solid with parallel opposite bases and parallelogram faces, among working solid figures. A named prism in that handbook, not optical prism glass and not a full n-gonal prism taxonomy dump alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Parallelepiped appears in Hellenic religion.
Heath’s Euclid Book XI develops parallelepiped solids — faces parallelograms in parallel pairs — as a core solid-geometry figure. A named parallelepiped in that handbook, not cuboid alone and not a modern packing dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Cuboid appears in Hellenic religion.
Heath’s Euclid Book XI treats rectangular parallelepipeds — right-angled box solids — among parallelepiped cases. A named cuboid gloss on that rectangular solid, not the cube as equal-edge regular solid and not a furniture dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Square pyramid appears in Hellenic religion.
Heath’s Euclid Books XI–XII treat pyramids on polygonal bases, including square-base cases among ordinary pyramid volume speech. A named square pyramid in that handbook, not Egyptian step-pyramid architecture and not tetrahedron as the regular triangular pyramid alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Triangular prism appears in Hellenic religion.
Heath’s Euclid Book XI prism definition covers solids with triangular bases among ordinary prism cases. A named triangular prism species in that handbook, not tetrahedron and not optical prism glass.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Pentagonal prism appears in Hellenic religion.
Heath’s Euclid Book XI prism speech covers polygonal bases; a pentagonal prism is an ordinary species under that definition beside the pentagon plane figure. A named pentagonal prism in that Elements neighborhood, not dodecahedron and not a Johnson-solid dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Hexagonal prism appears in Hellenic religion.
Heath’s Euclid Book XI prism speech covers polygonal bases; a hexagonal prism is an ordinary species under that definition beside the hexagon plane figure. A named hexagonal prism in that Elements neighborhood, not honeycomb ornament and not an Archimedean solid dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Proportion is historically related to Ratio.
Heath’s Euclid Book V is the Eudoxan theory of proportion — equality of ratios (a:b = c:d) — foundational to later similarity books. A named proportion doctrine historically kin to ratio in that handbook, not golden-ratio as one extreme-mean case alone and not Vitruvius temple-mystique proportion.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
historically related to · sourced · documented
Golden ratio is historically related to Ratio.
Heath’s Euclid seats extreme and mean ratio (Book II.11; VI Def. 3; VI.30) — a segment cut so whole to greater equals greater to lesser — the geometric ancestor of later golden-ratio speech. A named extreme-mean ratio kinship to ratio in that handbook, not temple sacred-ratio mystique and not golden-rectangle as a design label alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
historically related to · sourced · documented
Geometric Mean Form is historically related to Ratio.
Heath’s Euclid Book VI finds mean proportionals between magnitudes — geometric means in ratio speech — as working constructions of the similarity books. A named geometric-mean form historically kin to ratio in that handbook, not arithmetic/harmonic means as Pythagorean triad dump and not a statistics average dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
historically related to · sourced · documented
Golden Rectangle is historically related to Ratio.
Heath’s Euclid extreme-and-mean constructions produce rectangles whose sides stand in that ratio — later English golden-rectangle design speech on an Elements geometric seat. A named golden-rectangle kinship to ratio in that neighborhood, not Vitruvius temple mystique and not golden-ratio as the bare ratio lemma alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
historically related to · sourced · documented
Congruence Form appears in Hellenic religion.
Heath’s Euclid treats figures as equal by superposition and matching sides and angles (Common Notions; triangle congruence propositions) — the Elements seat later English calls congruence. A named congruence-form gloss on that equal-figures speech, not modern modular arithmetic and not similarity alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Square number appears in Hellenic religion.
Heath’s Euclid Books VII–IX treat square numbers among plane numbers built from equal factors in the number books. A named square-number in that handbook, not the geometric square already met and not a figurate triangular-number dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Cubic number appears in Hellenic religion.
Heath’s Euclid Books VII–IX treat solid (cube) numbers among numbers composed in three equal factors. A named cubic-number in that handbook, not the geometric cube solid alone and not a modern algebra dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Irrational number appears in Hellenic religion.
Heath’s Euclid Book X classifies incommensurable magnitudes — ἄλογοι lines and areas — the Elements seat later English calls irrational. A named irrational-number gloss on that incommensurable theory, not a modern real-analysis dump and not rational as commensurable twin alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Rational number appears in Hellenic religion.
Heath’s Euclid contrasts commensurable magnitudes with incommensurables in Book X — the Elements seat later English calls rational numbers. A named rational-number gloss on commensurable magnitude speech, not modern ℚ set theory and not irrational twin alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Prime number appears in Hellenic religion.
Heath’s Euclid Books VII–IX define prime numbers and prove there are more primes than any assigned finite multitude (IX.20). A named prime-number in that handbook, not composite alone and not a modern cryptography dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Composite number appears in Hellenic religion.
Heath’s Euclid Book VII defines composite numbers as those measured by some number, opposite primes in the number books. A named composite-number in that handbook, not prime alone and not a modern factoring dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Circumcircle is used in Circle.
Heath’s Euclid Book IV repeatedly circumscribes circles about triangles and regular polygons — the circumcircle as working construction around a figure. A named circumcircle use of circle in that handbook, not incircle as the inscribed twin and not a modern triangle-center dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
used in · sourced · documented
Heath’s Euclid Book IV inscribes circles in triangles and regular polygons — the incircle as working construction inside a figure. A named incircle use of circle in that handbook, not circumcircle as the outer twin and not excircle as later tangent lore.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
used in · sourced · documented
Reciprocal is historically related to Ratio.
Heath’s Euclid Book V treats inverse (reciprocal) ratios among proportion operations — when ratios are taken inversely. A named reciprocal kinship to ratio in that handbook, not a modern fraction-button dump and not unit-fraction alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
historically related to · sourced · documented
Divisor appears in Hellenic religion.
Heath’s Euclid Book VII speaks of numbers that measure other numbers — the Elements seat later English calls a divisor. A named divisor gloss on measuring-number speech, not dividend/quotient school-pad alone and not modern modular residue dumps.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Unit fraction appears in Hellenic religion.
Heath’s Euclid Book VII defines a part of a number as the unit-aliquot measure — the Elements seat later English calls a unit fraction (1/n). A named unit-fraction gloss on VII parts speech, not Egyptian Rhind unit-fraction tables and not modern numerator/denominator school chrome alone.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
appears in · sourced · documented
Pythagoreanism
Right triangle is historically related to Pythagoreanism.
Heath’s Euclid I.47 proves that in a right-angled triangle the square on the hypotenuse equals the squares on the other two sides — the Pythagorean theorem as Elements seats it. A named right-triangle proposition historically kin to Pythagorean number-geometry, not acute/obtuse classification alone and not a numerology dump.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
historically related to · sourced · documented
Perfect number is historically related to Pythagoreanism.
Heath’s Euclid IX.36 proves the generation of even perfect numbers from prime (Mersenne) forms — the Elements theorem historically kin to Pythagorean perfect-number lore without dumping amicable/abundant/deficient pads.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
historically related to · sourced · documented
Platonism
Platonic solid is historically related to Platonism.
Heath’s Euclid Book XIII constructs exactly the five regular solids later called Platonic — tetrahedron, octahedron, cube, icosahedron, dodecahedron — in a geometry handbook historically kin to Plato’s Academy solid speech without restating Timaeus element assignments as represents edges.
from Euclid; Thomas L. Heath (translation) · Elements, c. 300 BCE; Heath English 1908
historically related to · sourced · documented