There is a useful moment in Voynich research when we stop asking what a diagram represents and ask a more physical question.
How was it drawn?
Not symbolically.
Mechanically.
A large circle does not simply appear on parchment.
Somebody chooses a centre.
Chooses a radius.
Moves a tool or hand around that centre.
A radial diagram requires divisions.
A repeated star requires angle decisions.
Concentric rings require one centre to survive several passes.
A straight connector crossing a crowded diagram has to be aimed.
The Voynich Manuscript contains enough geometry that construction itself deserves to become evidence.
Before a circle is cosmology, astronomy, medicine or memory, it is a circle somebody had to construct.
Quick Read
- The Voynich Manuscript contains many circular and radial diagrams, especially in its astronomical and cosmological-looking pages.
- Some pages use multiple concentric rings, repeated sectors, radial lines and star-like constructions.
- These forms are compatible with the use of ordinary drafting aids such as a compass/dividers and straightedge, but the existence of a specific tool should not be asserted without physical trace evidence.
- A diagram can reveal a centre, radius, symmetry, subdivision method and construction sequence even when its subject remains unknown.
- f57v uses four concentric circular text bands with aligned start markers and a repeated 17-unit sequence.
- f67–70 contain numerous radial and circular layouts with inward/outward text, stars and repeated sectors.
- f69r contains a central six-pointed star, numerous radiating lines and an outer circular system divided into text segments.
- The Rosettes foldout scales the problem up: nine major circular regions are connected across a six-panel sheet.
- The geometry is not perfectly machine-precise. Unequal sectors, irregular rays and hand variation can themselves reveal how construction was executed.
- The strongest method is to describe geometric operations before assigning cosmological, geographical or medical meaning.
The Tool Question Is Not the Meaning Question
Suppose a circle was drawn with a compass.
That does not make it astronomical.
Suppose a line was made against a straightedge.
That does not make it a road.
Suppose eight rays were laid out from one centre.
That does not make them eight winds.
Construction and semantics occupy different levels.
The advantage of studying construction first is that physical geometry is often easier to verify.
We can measure:
- whether rings share a centre;
- whether radii are equal;
- whether sectors are evenly divided;
- whether lines converge;
- whether repeated shapes share templates;
- whether drawing order is visible at intersections.
None of those observations requires a translation.
Compass, Dividers or Freehand?
A good geometric study should not begin by declaring a compass.
It should ask which drawing mechanism best explains the trace.
A circle can be produced by:
- freehand drawing;
- rotating a cord or thread around a fixed point;
- using dividers or a compass-like instrument;
- tracing a circular object;
- copying through transfer or template;
Different mechanisms predict different imperfections.
A fixed-radius instrument tends to preserve distance from the centre.
Freehand drawing tends to drift.
A template may produce repeated near-identical radii across separate diagrams.
A physical pin or compass point might leave a centre trace—but absence of a visible puncture in a scan does not prove no such tool was used.
The correct claim is not “Voynich used a compass” until the object supports that. The correct research question is “which construction process best explains the geometry we can measure?”
Concentric Circles Preserve a Construction History
Several Voynich diagrams use rings inside rings.
If those rings share a centre closely, the page preserves a construction constraint.
One centre was likely established and reused.
The radius changed.
The centre did not.
This matters because a later text band can be positioned relative to an earlier circle.
The geometry therefore contributes to the Order of Making problem.
Was the outer ring drawn first?
Were radial divisions added before text?
Did labels fill predetermined sectors?
A circle is no longer only a shape.
It is a sequence of actions.
f57v: Four Rings, One Centre, Repeated Sequence
f57v is useful because geometry and notation meet unusually tightly.
The page contains four concentric circular text bands, four radial text items and four small human figures near the centre.
The rings appear to share aligned start cues.
One ring contains the famous 17-unit sequence repeated four times.
This means the page can be studied at several levels:
- geometric centre;
- ring spacing;
- sector alignment;
- start-point alignment;
- sequence repetition;
- relation of four cycles to four central figures.
None of those measurements tells us what the diagram means.
Together they tell us that the page was not casually filled with circles.
Its geometry and notation were coordinated.
f67: Geometry Begins to Organise Direction
The folios around f67 contain several circular astronomical/cosmological-looking designs.
On f67r1, a central moon face and a twelve-pointed star are surrounded by circular writing and twelve inward radial text items.
On f67v1, a sun face sits at the centre of a circular design subdivided by seventeen outward text radii.
On f67v2, eight radiating lines divide between four inward and four outward textual paths.
Here construction geometry and reading geometry become inseparable.
A radial line is simultaneously:
- a geometric element;
- a possible divider;
- a text baseline;
- a relationship between centre and perimeter.
Which Way Does Voynich Read? owns the reading-direction, rotation and sequence question.
This article asks how the radial scaffold itself was produced.
f69r: A Construction That Can Be Counted
f69r presents a large circular design around a six-pointed central star.
From the centre radiate numerous lines. Eight are painted blue in paired cardinal orientations and four green lines divide intermediate quadrants. Twenty-two radiating text items occupy the diagram, and the outer circular system contains additional segmented text.
The page has been compared with historical wind diagrams, which is a useful comparator because it shows that similarly organised radial geometry existed in medieval manuscript culture.
But the construction question comes first.
How was the central star laid out?
Were cardinal lines established before intermediate lines?
Were the coloured rays planned geometrically or painted after freehand line placement?
Are the angular divisions equal enough to imply measured subdivision?
These questions can discriminate construction methods before the wind-diagram comparison is asked to carry historical meaning.
Unequal Geometry Is Evidence Too
Perfect symmetry can suggest measured construction.
Imperfect symmetry can be even more informative.
An unequal six-pointed star tells us the maker was not drawing with modern CAD precision.
Unequal sectors can show where estimation replaced measurement.
A centre slightly off-axis can reveal that concentricity was approximate rather than exact.
Repeated drift in one direction can reflect page posture or tool reach.
Therefore “imperfect” should not be treated as noise.
Construction error is one of the few places where the page can preserve the movement of the hand.
Straightedge-Like Lines Are a Different Problem From Circles
A straightedge solves a different geometric task from a compass.
It aligns points.
It establishes diameters.
It divides fields.
It can connect centres.
Voynich contains numerous radiating lines and some connector-like structures that look straighter than surrounding organic drawings.
But “straight line” does not automatically mean “straightedge”.
A trained hand can draw a short straight segment freehand.
The question becomes quantitative:
- how straight is the line;
- over what distance;
- does it pass exactly through intended points;
- does it share direction with other lines;
- does its edge show the uniformity expected from a guide?
The Rosettes Foldout: Geometry at Architectural Scale
The Rosettes sheet expands the drafting problem from one circle to a network.
Nine major circular regions are arranged approximately in a three-by-three field and connected across a six-panel foldout.
The geometry involves:
- relative circle size;
- centre placement;
- inter-circle connectors;
- corner elements;
- paths and tubes;
- writing around perimeters;
- features crossing fold boundaries.
This is the kind of page where construction planning becomes unavoidable.
Did the maker mark the nine centres first?
Did folds exist before the drawing?
Were connector paths established before local detail?
Was the entire sheet visible during drafting?
The Rosettes Foldout owns the topology and interpretation problem. The Foldouts article owns handling. Here the focus is the construction sequence itself.
Could Fold Creases Have Served as Guides?
A fold is already a straight line on parchment.
It can divide a sheet.
It can establish symmetry.
It can act as a construction axis.
On a large foldout, it is therefore worth asking whether important geometric features align with folds.
If they do, several causal histories are possible:
- the sheet was folded first and the crease used as a guide;
- the diagram was drawn first and later folding followed its architecture;
- both were planned together.
Again, alignment creates a question, not an automatic sequence.
Did the Makers Use Templates?
Repeated diagram forms can arise from memory, measurement or templates.
If two circles on distant pages have exactly the same diameter, perhaps the same tool setting or physical template was reused.
If repeated stars share unusually precise angles, perhaps a reusable construction procedure existed.
If every instance varies freely, memory or local construction becomes more plausible.
A useful template study would therefore compare:
- diameters;
- sector counts;
- angle distributions;
- centre-to-feature distances;
- repeatable construction errors.
Shared error can be particularly revealing because it may identify a reused model more strongly than generic similarity.
Geometry and the Exemplar Problem
A carefully organised diagram can be copied.
If the surviving Voynich page follows a lost exemplar, some construction work may already have been solved before the parchment was touched.
The scribe or illustrator could copy:
- overall circle placement;
- sector counts;
- relative proportions;
- label locations;
- connector topology.
In that case, geometric regularity tells us about faithful copying as much as original design.
The Exemplar Problem keeps those histories separate.
Geometry Can Identify Families Without Naming Them
Suppose f67, f68 and f69 share a construction grammar.
Central body.
Concentric bands.
Radial sectors.
Repeated labels.
That can establish a diagram family before we know whether the family is astronomical, calendrical, cosmological or medical.
Constructional similarity is especially useful because it can survive semantic uncertainty.
The method becomes:
- measure geometry;
- cluster construction features;
- compare page families;
- only then test historical functions.
This is geometry before cosmology.
Why Medieval Comparators Matter
Medieval astronomical, calendrical and cosmological manuscripts demonstrate that scribes and illustrators routinely constructed circles, wheels, wind diagrams and radial schemes.
One comparator discussed in Voynich research is the winds diagram in Oxford, St John’s College MS 17, whose radial organisation has useful similarities to f69r while differing significantly in text and detail.
The comparison proves historical capability.
It does not prove copying descent.
A comparator says:
people in manuscript culture knew how to construct and use diagrams of this broad geometric class.
It does not say:
this is the source of Voynich f69r.
The Unruled Page Creates a Useful Contrast
Most Voynich prose does not display ordinary page ruling.
Yet the circular diagrams can be highly organised geometrically.
That contrast is important.
The makers were apparently willing to tolerate wavy prose baselines while investing much more explicit geometric control in certain diagrams.
This suggests that different page functions demanded different kinds of precision.
Ordinary prose needed a stable left edge and readable line spacing.
A circular diagram needed centres, rings, sectors and alignment.
See The Unruled Page.
Could Geometric Accuracy Reveal Different Hands or Workshops?
Possibly.
One illustrator may divide circles more accurately than another.
One hand may consistently misplace centres.
One section may favour compass-like rings while another uses freer curves.
If these differences correlate with scribal hands, Currier regimes or bifolia, construction style may become another production classifier.
But the analysis must avoid circular reasoning.
Do not define a “different illustrator” because the geometry differs and then use the different illustrator to explain why the geometry differs.
Independent variables are required.
The Measurement Problem
Digital images tempt precision.
Click two points.
Measure an angle to one decimal place.
Declare the medieval maker precise to one decimal place.
That is not safe.
Images can be:
- perspectively distorted;
- slightly curved by parchment;
- cropped;
- stretched during digitisation;
- affected by folds;
- misaligned relative to the camera.
Geometry studies therefore need calibration and uncertainty.
A difference of several millimetres may be real.
A difference of a few pixels may not be.
The more precise the measurement claim, the more carefully the image pipeline must be controlled.
Tool Marks Versus Tool Effects
There is an important distinction.
A tool mark is a physical trace: puncture, score, indentation, ruled line.
A tool effect is a geometric pattern compatible with a tool: a near-perfect circle, a long straight line, equal radii.
Tool effects can suggest a mechanism.
Tool marks support it more directly.
High-resolution and multispectral examination may help separate these evidence levels, especially where faint construction lines or punctures are suspected.
Until then, “compass-compatible” is often safer than “compass-drawn”.
What a Construction Sequence Might Look Like
For a typical circular Voynich diagram, one plausible construction workflow is:
- select the diagram centre;
- draw one or more main circles;
- establish radial divisions;
- add central emblem;
- add repeated stars or figures;
- write radial and circular text into the available structure;
- add colour.
That sequence is a hypothesis.
Intersections can test it.
If text crosses a radial line, which lies on top?
If paint covers text, paint is later locally.
If a label bends around a star, the star probably existed before that label.
Every overlap is a tiny chronological receipt.
What Geometry Does Not Prove
- A circle does not prove astronomy.
- A radial diagram does not prove a wind rose.
- A central star does not prove one specific celestial body.
- Concentricity does not prove cosmology.
- A straight connector does not prove a road or pipe.
- Compass-compatible geometry does not prove a compass without supporting evidence.
- Shared geometry does not prove shared provenance.
- One construction error does not identify a scribe.
What Geometry Can Give Us
- centres;
- radii;
- sector counts;
- symmetry and asymmetry;
- construction families;
- possible drafting order;
- possible tool effects;
- alignment with folds;
- relationship between diagram and text;
- repeatable production habits.
That is a substantial evidence layer.
It does not require semantic naming to be useful.
Primary School: Draw the Same Circle Three Ways
Ask a child to draw a circle:
- freehand;
- around a cup;
- with a compass.
Compare the results.
The child learns that a finished shape can contain clues about the process that made it.
Secondary School: Recover the Centre
Take a photographed circular diagram.
Estimate its centre using several diameters.
Ask whether different rings share that centre.
Then measure sector angles.
Students learn that geometry can test construction claims without requiring a translation.
JC and Adult Readers: Build a Construction Ledger
For each diagram, record:
- page/folio;
- physical sheet and foldout state;
- number of circles;
- estimated centres;
- radii;
- sector counts;
- radial directions;
- symmetry;
- visible guide marks;
- possible punctures;
- text/drawing overlap order;
- colour order;
- scribal hand;
- Currier regime.
Then compare families.
The result is not a map of meaning.
It is a map of making.
Reader Checklist: Before You Infer a Drafting Tool
- Is the shape actually circular after correcting image distortion?
- Do concentric rings share one centre?
- Is a centre puncture visible?
- Could the circle have been traced from a template?
- Could it be freehand?
- Are straight lines long and uniform enough to suggest a guide?
- Do sector angles imply measured subdivision?
- Are irregularities systematic?
- Does geometry align with folds?
- Can drawing order be established at intersections?
- Does the same construction grammar recur elsewhere?
- Does a proposed tool explain more than one feature?
- Is the claim “compatible with” or “proven by” the physical trace?
Frequently Asked Questions
Were Voynich circles drawn with a compass?
Compass or divider use is a plausible construction mechanism for many regular circular diagrams, but a specific tool should not be treated as proven without supporting physical traces or sufficiently diagnostic geometry.
Were straightedges used?
Some long radial and connector lines are compatible with guided construction. Straightness alone is not enough to prove a straightedge, especially for short segments.
Why study drawing tools?
Because construction method can reveal planning, production sequence, repeated templates and workshop habits independently of semantic interpretation.
Do imperfect circles argue against tools?
Not necessarily. Parchment movement, imperfect instruments, freehand corrections and copying can all introduce irregularity. The pattern of error is more informative than perfection alone.
Does geometric resemblance prove two manuscripts are related?
No. Similar construction can arise from shared diagram traditions. A comparator demonstrates historical possibility, not direct descent.
Research Foundations
- René Zandbergen — Voynich illustrations and cosmological diagrams
- Quire 8 — f57v circular construction
- Quire 9 — f67 and f68 circular/radial designs
- Quire 10 — f69/f70 geometry
- Quire 14 — the Rosettes foldout
- Voynich illustration comparators, including the f69r wind-diagram comparison
The Final Idea
A diagram is an idea made physical.
Before the idea reached us, somebody had to choose a centre.
A radius.
A division.
A line.
A sequence of construction.
Those choices remain partly visible even when the subject is not.
Geometry cannot tell us what the Voynich diagrams mean by itself. It can tell us how much deliberate making occurred before meaning ever reached the page.