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Equal arcs along a circle subtend equal angles along that circle. Therefore, certain triangles within a circle can be shown to have the same shape, with their sides forming ratio equalities. Cyclic quadrilaterals can then describe equalities with multiple ratios, and these multivariable relationships can be used to find triangles with other triangles. This plane geometry approach was used by Isaac Barrow in 1667 to describe tangential refraction along a line and at a circle, without trigonometry, algebra, or calculus. It is particularly suited for clinicians in the field of low vision and ophthalmic optics, since it requires no math background beyond high school plane geometry, and encourages a spatial understanding devoid of sign convention and jargon.

For those clinicians wishing to have more than a working knowledge of the subject of axial magnification, I have drawn a progression of geometric figures to cover the necessary preliminary concepts, each building on the previous, with labeled points maintaining their significance until noted otherwise.

Axial magnification is presented only after a thorough spatial representation of tangential refraction along a line and a circle. In order to then visualize the relevant axial ratio equalities involved using triangles, the optic axis is then represented as a circle of infinite radius, and the sign convention remains unnecessary.

Please see the attached document and provide feedback.

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