Proposition Replicated
Proposition VI.20
Similar polygons are divided into similar triangles, equal in multitude and in the same ratio as the wholes; and the polygon has to the polygon a ratio duplicate of that which the corresponding side has to the corresponding side.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:VI.20
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
Neighborhood at a glance
Full neighborhood
Depends on (3)
- VI.18Proposition VI.18On a given straight line to describe a rectilineal figure similar and similarly situated to a given rectilineal figure.
- VI.19Proposition VI.19Similar triangles are to one another in the duplicate ratio of the corresponding sides.
- V.12Proposition V.12If any number of magnitudes be proportional, as one of the antecedents is to one of the consequents, so will all the…
Required by (dependents) (6)
- VI.22Proposition VI.22If four straight lines be proportional, the rectilineal figures similar and similarly described upon them will also be…
- VI.25Proposition VI.25To construct one and the same figure similar to a given rectilineal figure and equal to another given rectilineal…
- VI.27Proposition VI.27Of all parallelograms applied to the same straight line and deficient by parallelogrammic figures similar and similarly…
- VI.31Proposition VI.31In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly…
- XI.33Proposition XI.33Similar parallelepipedal solids are to one another in the triplicate ratio of their corresponding sides.
- XII.1Proposition XII.1Similar polygons inscribed in circles are to one another as the squares on the diameters.
Discussion
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