Glossarium Technicum (Technical Glossary)

Lexicon of Pisan Agrarian Metrology, Euclidean Geometry, and Graeco-Arabic Algebra

Every inline :term: tag across geometor-fibonacci links directly to its #term-<slug> anchor below.

pertica (pertica pisana) — Pisan surveying rod

  • Tradition: Medieval Latin (Pisan Metrology)

  • English Rendering: Pisan surveying rod (linear or superficial)

Fundamental Pisan unit of land measurement: $1$ linear pertica $= 6$ linear pedes $= 108$ unciae (puncta); $1$ superficial (square) pertica $= 6$ superficial pedes $= 36$ denarii $= 108$ superficial unciae (Practica Geometriae, Introductoria, p. 3).

pes (linealis / superficialis) — Pisan foot

  • Tradition: Medieval Latin (Pisan Metrology)

  • English Rendering: Pisan foot ($1/6$ of a pertica)

As a linear measure, $1/6$ of a pertica ($= 18$ unciae). As a superficial strip (pes terrae), a rectangle $1$ pertica ($6$ linear pedes) long by $1$ linear pes wide, equal to $1/6$ of a square pertica or $6$ denarii (Introductoria, p. 3).

uncia / punctum — inch or point

  • Tradition: Medieval Latin (Pisan Metrology)

  • English Rendering: inch or point ($1/18$ of a Pisan pes; $1/108$ of a pertica)

Fine subdivision of the Pisan rod: $18$ linear unciae make $1$ linear pes, and $108$ linear unciae make $1$ pertica. Superficially, $18$ superficial unciae make $1$ superficial pes (Introductoria, p. 3).

denarius de mensura — measuring denarius

  • Tradition: Medieval Latin (Pisan Metrology)

  • English Rendering: measuring denarius ($1$ square pes $= 1/36$ square pertica)

Unit square of side $1$ linear pes inside the $6 \times 6$ grid of the square pertica, so that $6$ denarii equal $1$ superficial pes and $36$ denarii equal $1$ superficial pertica (Distinctio I, pp. 3–5).

panorum — Pisan panorum ($5\frac{1}{2}$ square perticae)

  • Tradition: Medieval Latin (Pisan Metrology)

  • English Rendering: panorum ($5\frac{1}{2}$ square perticae)

Pisan agrarian land measure equal to $5\frac{1}{2}$ superficial perticae ($= 1/12$ of a stariorum), used throughout the episcopate of Pisa (Introductoria, p. 3).

stariorum — Pisan stariorum ($66$ square perticae)

  • Tradition: Medieval Latin (Pisan Metrology)

  • English Rendering: stariorum ($12$ panora $= 66$ square perticae)

Principal Pisan grain-seeding field area equal to $12$ panora or $66$ superficial perticae; $24$ stariora constitute $1$ modiorum ($= 1584$ square perticae) (Introductoria, pp. 3–5).

embadum — planar area / surface content

  • Tradition: Medieval Latin (from Greek embadon via Arabic/Hebrew)

  • English Rendering: planar area / surface content (or squared side)

Standard Graeco-Latin technical term across Savasorda and Fibonacci for the superficial content (area) of a plane figure, and by extension the square built on the edge of a polyhedron (embadum lateris, Distinctio III & VI).

cathetus — perpendicular altitude

  • Tradition: Latin (from Greek kathetos)

  • English Rendering: perpendicular altitude

Perpendicular line dropped from a vertex of a triangle, pyramid, or cone onto the opposite base line or base plane (linea perpendicularis, quae cathetus appellatur, Distinctio III, p. 39).

casus (maior / minor) — base projection segment

  • Tradition: Medieval Latin

  • English Rendering: projection segment cut on the base by the altitude

Each of the two segments into which the foot of the cathetus divides the base of a triangle; on the $(13, 14, 15)$ triangle with base $14$, the minor casus is $5$, the major casus is $9$, and the cathetus is $12$ (Distinctio III, p. 39).

consortes — co-heirs / landholding partners

  • Tradition: Latin (Legal & Agrarian)

  • English Rendering: co-heirs / joint landholding partners

Partners or co-owners sharing a field, orchard, well, or boundary access in fixed rational shares (e.g. halves, thirds, or $p : q$), motivating the exact Euclidean division constructions of Distinctio IV (de divisione camporum inter consortes, p. 110).

media et extrema proportio — extreme and mean ratio ($\phi$)

  • Tradition: Latin (Euclid VI.def.3 / II.11 / XIII.1–18)

  • English Rendering: extreme and mean ratio (the golden section $\phi$)

Division of a segment $BE$ at $G$ so that the whole $BE$ is to the greater part $BG$ as $BG$ is to the lesser part $GE$ ($BE : BG = BG : GE = \phi = \frac{1 + \sqrt{5}}{2}$). Used by Fibonacci in Distinctio VI (pp. 196–202) to construct the dodecahedron and icosahedron and in Distinctio VIII (pp. 207–208) for the pentagon and decagon.

res / radix — algebraic unknown ($x$)

  • Tradition: Medieval Latin (from Arabic shayʾ / jidhr)

  • English Rendering: the unknown quantity $x$ (‘thing’ or ‘root’)

First-degree algebraic unknown $x$ in al-Khwārizmī’s and Fibonacci’s rhetorical algebra (Distinctio VIII, pp. 207–224; Liber Abaci Cap. XV).

census — square of the unknown ($x^2$)

  • Tradition: Medieval Latin (from Arabic māl)

  • English Rendering: the square of the unknown ($x^2$)

Second-degree algebraic power $x^2$ (‘wealth/square’); doubled in Distinctio VIII as census census for the fourth power $x^4$ in biquadratic polygon problems such as $x^4 + 3125 = 125 x^2$ (pp. 207–208).

linea binomialis / binomiale — binomial irrational

  • Tradition: Medieval Latin (Euclid Book X.36)

  • English Rendering: binomial irrational line ($a + \sqrt{b}$ or $\sqrt{a} + \sqrt{b}$)

Compound irrational magnitude formed by adding two lines commensurable in square only, classified into six species in Euclid Book X and tested systematically by Fibonacci in Distinctio VIII and Flos.

recisum (apotome) — apotome / residual irrational

  • Tradition: Medieval Latin (from Gerard of Cremona’s Euclid Book X.73)

  • English Rendering: apotome / residual irrational line ($a - \sqrt{b}$ or $\sqrt{a} - \sqrt{b}$)

Irrational difference of two lines commensurable in square only—exemplified by the dodecahedron edge $\sqrt{15} - \sqrt{3}$ (a fourth apotome in a sphere of rational diameter $6$, Distinctio VI, p. 196) and the decagon chord $\sqrt{31\frac{1}{4}} - 2\frac{1}{2}$ (Distinctio VIII, p. 208).

congruum — common step of three squares in arithmetic progression

  • Tradition: Medieval Latin (Fibonacci, Flos & Liber Quadratorum, 1225)

  • English Rendering: congruum (common difference of three squares in arithmetic progression)

An integer $D = 4ab(a^2 - b^2)$ (always divisible by $24$) such that $z^2 - D$, $z^2$, and $z^2 + D$ are simultaneously squares. Dividing by $12^2$ yields the rational triple $(\frac{31}{12})^2, (\frac{41}{12})^2, (\frac{49}{12})^2$ with common difference $5$ (Flos, p. 227), and connects geometrically to trapezoid bisection $c^2 = (a^2 + b^2)/2$ in Distinctio IV.

quadrans (oroscopus) — surveyor’s quadrant with shadow square

  • Tradition: Medieval Latin

  • English Rendering: surveyor’s and astronomer’s quadrant with shadow square

Quarter-circle sighting instrument equipped with two pinnules (tabulae perforatae), a plumb bob (perpendiculum), a 90-degree arc, and an inscribed $12 \times 12$ shadow square (umbra recta / umbra versa) used in Distinctio VII (p. 204) to measure inaccessible tower heights and valley widths by similar right triangles.