Converse and ostensive proportion
Labelled line-segments testing proportion by conversion and by direct demonstration
This page of Paris Manuscript K continues Leonardo's study of the theory of proportion after Euclid. Two groups of labelled line-segments are drawn: the first, headed 'eversa,' pairs the magnitudes a 12, b 4 with c 6, d 3 for a proportion taken by conversion; the second, headed 'ostensiva,' sets out a 12, c 4, b 4, d 2 and e 6 for a direct (ostensive) demonstration. The figures are faint pencil gone over in pen, with the proportion terms written in mirror-script. A numeral, 281, stands at the head of the page.
On this page
Converse proportion (eversa): a 12, b 4; c 6, d 3
The upper group is headed 'eversa,' proportion taken by conversion. Four magnitudes are named as labelled segments: a is 12 and b is 4, c is 6 and d is 3, pairing the terms for a converted ratio.
Ostensive proportion (ostensiva): a 12, c 4; b 4, d 2; e 6
The second group, labelled 'ostensiva,' lists a 12 and c 4, b 4 and d 2, together with e 6. The same kind of magnitudes are arranged for an ostensive (direct) demonstration of the proportion.