This isn't a question of semantics, it is question of geometry and the definition of words.
For example,
convex = curved or rounded outward; (math) a continuous function with the property that a line joining any two points on its graph lies on or above the graph; from Latin convexus = carried out/away from.
"Convex" is defined as
away from flat, an alteration of
shape that can ONLY be accomplished by
an increase in angle, i.e. more obtuse, to a form which lies
outside or above the corresponding flat plain.
knifenut1013 is comparing
non-corresponding shapes/functions/figures. His base
premise is false.
Now, a key point of his problem seems to be what angle is being measured (or not measured, really) and what shapes are being compared.
In practice (sharpening, and other practices as well, like aerodynamics), the angle being measured is the "held angle" or "
angle of incidence" between hone surface (flat gray) and spine-center (red line).
NOTE: If this is NOT the angle you are using to grind your bevel, then you are very likely not using ANY angle measurement at all but instead merely extrapolating after-the-fact. For example, the violet-line in the diagram is presumed tangential to the precise apex-angle of the green convex... but the precise apex-angle of the green convex
cannot be measured without precision instruments or precise knowledge of the geometry of the curve(s) at the point of bevel intersection (the true apical angle of incidence of a curved shape). However, such measurements are unnecessary for the purpose of this discussion as the measured apex and tangent bevel do not produce a triangle of similar geometry beyond an infinitesimally short shoulder height (i.e. at the point of bevel intersection).
Draw a chord perpendicular to the hone surface that meets the spine-center line to form a triangle. This triangle is geometrically
"similar" to the smaller triangle formed by drawing a chord perpendicular to spine-center that intersects the
bevel shoulder (light blue triangle). These triangles are
similar because their dimensions are directly proportional, their angles equal - these triangles even share an apex!
Altering the shape of the triangle by increasing or decreasing the height of the bevel along the spine-center WITHOUT a proportional change in shoulder thickness (which necessarily changes the angle of incidence) produces NON-similar triangles. (For some reason,
knifenut1013 insists on comparing non-similar geometric shapes and thereby reaches a conclusion that contradicts geometric and mathematical definitions.
However, one can alter the shape of the triangles
without changing the angle of incidence, shoulder width, or bevel height by using a curved or flexible hone instead of a solid hone. How much the shape is altered is controlled by the amount of deformation and curvature (again, away from flat) of the hone. The result is a thicker bevel, one with more metal that it would have if ground flat
at the same angle of incidence.
To make a convex bevel thinner than a flat bevel, one MUST change the angle of incidence,
but the result is still thicker than the flat bevel ground at that new angle and it is the flat bevel
at that angle which informs the use of the term "convex" to describe the rounded out bevel - again,
"out". "Out" from what?
This is not about the elementary statement, "you can't add material, only remove it." Of course you cannot add material. This is about drawing the correct correlations when using the term "convex". "Convex" is defined by "out from the correlated flat". "Out" cannot be "in" at the same time in the same context.