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Horst Steinke


themes, […] of contemplation

sub specie aeternitatis,


amor Dei intellectualis



Vico e la tradizione “platonica”. “La filosofia dell’umanità e la storia universale delle


, in «BCSV», XXII-XXIII, 1992-1993, pp. 65-102, p. 102).


G. Vico,

Liber metaphysicus

, Chapter VII, § IV, according to

On the Most

Ancient Wisdom of the Italians

, trans. by J. Taylor, with an introduction by R.

Miner, New Haven-London, Yale University Press, 2010, p. 121.



, chapter III, p. 53. The reference is to Section IV of

De ratione


found in

On the Study Methods of Our Time

, cit., p. 23, which reads: «We are able

to demonstrate geometrical propositions because we create them; were it pos-

sible for us to supply demonstrations of propositions of physics, we would be

capable of creating them

ex nihilo

as well».


Liber metaphysicus

, Chapter I, § I,

On the Most Ancient Wisdom of the Ital-


, cit., p. 25. The originality of defining the


as an entitity that is “sim-

ple” in that it has no parts can be seen by remembering that it was not con-

sidered the only definition possible. Vico himself referred to the competing

view that «even the smallest particles […] are infinitely divisible”, and of «a

geometry which defines the point as a minimal particle divided endlessly»



, pp. 61, 63).


An important means of devising such constructions are so-called “aux-

iliary constructions”, such as bisecting an angle, bisecting a line, drawing a line

at a right angle from a given point, and drawing a straight line perpendicular

to another line, as outlined in Book I, Propositions 9-12, of Euclid’s



See Euclid,

The Thirteen Books of Euclid’s Elements

, trans. by T. L. Heath, Cam-

bridge, Cambridge University Press, 1908, vol. 1, pp. 264-275. A specific ex-

ample of an important auxiliary construction, to prove the Triangle Sum Con-

jecture, can be found in M. Serra,

Discovering Geometry: An Investigative Approach


Emeryville, Key Curriculum Press, 3


edition, 2003, p. 200. On the crucial

heuristic role of auxiliary constructions, see also J. Hintikka - U. Remes,


Method of Analysis: Its Geometrical Origin and Its General Significance

, Dordrecht-

Boston, D. Reidel, 1974, pp. 41-48.


§ 349 is discussed in some detail by Remaud (

Vico lector de Espinosa

, cit.,

pp. 198-201), and Otto (

“Contextualidad” científica y “convertibilidad” filosófica

, cit.,

p. 173), but without drawing a distinction between geometrical method and



See T. Crilly with D. Johnson,

The Emergence of Topological Dimension The-


, in

History of Topology

, ed. by I. M. James, Amsterdam, Elsevier, 1999, pp. 1-

24, pp. 1, 20-22. Actually, there are several “dimension theories” which under-

lines the “creative” rather than “constructive” nature of the process of



. Each “dimension theory” has been “composed”, to use a Vichian

term, in a different way, according to its own logic.