G.328 similar plane numbers

VIII.26

Similar plane numbers have to one another the ratio which a square number has to a square number.
similar_plane_numbers_viii_26(A, B)
given A, B be similar plane numbers
prove A has to B the ratio which a square number has to a square number
A B C D E F
given A, B be similar plane numbers
assert A, B are similar plane numbers,
∵ similar_plane_numbersassert one mean proportional number falls between A, B
assert Let it so fall, and let it be C
construct many_numbers_please: And let D, E, F, the least numbers of those which have the same ratio with A, C, B, be taken
∵ find_numbers_continuedassert the extremes of them D, F are square
assert Since, as D is to F, so is A to B, and D, F are square,
∴ A has to B the ratio which a square number has to a square number

Dependency Graph

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"G.251" -> "G.169"; "G.252" -> "G.169"; "G.253" -> "G.169"; "G.254" -> "G.169"; "G.255" -> "G.169"; "G.256" -> "G.169"; "G.268" -> "G.169"; "G.270" -> "G.169"; "G.271" -> "G.169"; "G.274" -> "G.169"; "G.275" -> "G.169"; "G.276" -> "G.169"; "G.277" -> "G.169"; "G.278" -> "G.169"; "G.283" -> "G.169"; "G.289" -> "G.169"; "G.171" -> "G.170"; "G.176" -> "G.170"; "G.183" -> "G.170"; "G.185" -> "G.170"; "G.186" -> "G.170"; "G.257" -> "G.170"; "G.186" -> "G.171"; "G.174" -> "G.173"; "G.289" -> "G.173"; "G.297" -> "G.173"; "G.319" -> "G.173"; "G.328" -> "G.173"; "G.267" -> "G.174"; "G.296" -> "G.174"; "G.180" -> "G.176"; "G.183" -> "G.176"; "G.187" -> "G.176"; "G.267" -> "G.176"; "G.271" -> "G.176"; "G.272" -> "G.176"; "G.274" -> "G.176"; "G.275" -> "G.176"; "G.276" -> "G.176"; "G.289" -> "G.176"; "G.296" -> "G.176"; "G.297" -> "G.176"; "G.183" -> "G.180"; "G.230" -> "G.180"; "G.263" -> "G.180"; "G.266" -> "G.180"; "G.273" -> "G.180"; "G.278" -> "G.180"; "G.296" -> "G.180"; "G.297" -> "G.180"; "G.318" -> "G.180"; "G.319" -> "G.180"; "G.328" -> "G.180"; "G.182" -> "G.181"; "G.194" -> "G.181"; "G.265" -> "G.181"; "G.268" -> "G.181"; "G.274" -> "G.181"; "G.275" -> "G.181"; "G.278" -> "G.181"; "G.183" -> "G.182"; "G.273" -> "G.183"; "G.186" -> "G.184"; "G.186" -> "G.185"; "G.187" -> "G.186"; "G.273" -> "G.187"; "G.261" -> "G.194"; "G.262" -> "G.194"; "G.266" -> "G.194"; "G.267" -> "G.194"; "G.268" -> "G.194"; "G.270" -> "G.194"; "G.271" -> "G.194"; "G.319" -> "G.194"; "G.319" -> "G.230"; "G.248" -> "G.247"; "G.249" -> "G.247"; "G.250" -> "G.247"; "G.251" -> "G.247"; "G.255" -> "G.247"; "G.268" -> "G.247"; "G.269" -> "G.247"; "G.270" -> "G.247"; "G.271" -> "G.247"; "G.275" -> "G.247"; "G.276" -> "G.247"; "G.278" -> "G.247"; "G.283" -> "G.247"; "G.289" -> "G.247"; "G.250" -> "G.248"; "G.251" -> "G.248"; "G.252" -> "G.248"; "G.253" -> "G.248"; "G.255" -> "G.248"; "G.256" -> "G.248"; "G.257" -> "G.248"; "G.258" -> "G.248"; "G.261" -> "G.248"; "G.262" -> "G.248"; "G.265" -> "G.248"; "G.266" -> "G.248"; "G.267" -> "G.248"; "G.268" -> "G.248"; "G.269" -> "G.248"; "G.270" -> "G.248"; "G.271" -> "G.248"; "G.272" -> "G.248"; "G.273" -> "G.248"; "G.274" -> "G.248"; "G.275" -> "G.248"; "G.276" -> "G.248"; "G.277" -> "G.248"; "G.278" -> "G.248"; "G.279" -> "G.248"; "G.280" -> "G.248"; "G.281" -> "G.248"; "G.289" -> "G.248"; "G.296" -> "G.248"; "G.297" -> "G.248"; "G.300" -> "G.248"; "G.308" -> "G.248"; "G.319" -> "G.248"; "G.328" -> "G.248"; "G.250" -> "G.249"; "G.251" -> "G.249"; "G.252" -> "G.249"; "G.255" -> "G.249"; "G.275" -> "G.249"; "G.276" -> "G.249"; "G.277" -> "G.249"; "G.278" -> "G.249"; "G.279" -> "G.249"; "G.280" -> "G.249"; "G.281" -> "G.249"; "G.289" -> "G.249"; "G.296" -> "G.249"; "G.297" -> "G.249"; "G.251" -> "G.250"; "G.252" -> "G.251"; "G.255" -> "G.251"; "G.289" -> "G.252"; "G.254" -> "G.253"; "G.255" -> "G.253"; "G.256" -> "G.253"; "G.257" -> "G.253"; "G.258" -> "G.253"; "G.261" -> "G.253"; "G.262" -> "G.253"; "G.263" -> "G.253"; "G.265" -> "G.253"; "G.266" -> "G.253"; "G.283" -> "G.253"; "G.255" -> "G.254"; "G.258" -> "G.254"; "G.261" -> "G.254"; "G.262" -> "G.254"; "G.263" -> "G.254"; "G.265" -> "G.254"; "G.266" -> "G.254"; "G.274" -> "G.254"; "G.274" -> "G.255"; "G.257" -> "G.256"; "G.263" -> "G.256"; "G.258" -> "G.257"; "G.261" -> "G.257"; "G.262" -> "G.257"; "G.265" -> "G.257"; "G.261" -> "G.258"; "G.262" -> "G.258"; "G.265" -> "G.258"; "G.262" -> "G.261"; "G.266" -> "G.262"; "G.265" -> "G.263"; "G.266" -> "G.263"; "G.271" -> "G.263"; "G.274" -> "G.263"; "G.289" -> "G.263"; "G.268" -> "G.265"; "G.274" -> "G.265"; "G.267" -> "G.266"; "G.271" -> "G.266"; "G.274" -> "G.266"; "G.319" -> "G.266"; "G.296" -> "G.267"; "G.270" -> "G.268"; "G.270" -> "G.269"; "G.271" -> "G.269"; "G.272" -> "G.269"; "G.273" -> "G.269"; "G.276" -> "G.269"; "G.278" -> "G.269"; "G.280" -> "G.269"; "G.281" -> "G.269"; "G.289" -> "G.269"; "G.297" -> "G.269"; "G.300" -> "G.269"; "G.308" -> "G.269"; "G.319" -> "G.269"; "G.272" -> "G.270"; "G.275" -> "G.270"; "G.278" -> "G.270"; "G.289" -> "G.270"; "G.272" -> "G.271"; "G.273" -> "G.271"; "G.276" -> "G.271"; "G.297" -> "G.271"; "G.319" -> "G.271"; "G.273" -> "G.272"; "G.297" -> "G.272"; "G.278" -> "G.273"; "G.289" -> "G.273"; "G.275" -> "G.274"; "G.278" -> "G.274"; "G.296" -> "G.274"; "G.278" -> "G.275"; "G.289" -> "G.275"; "G.296" -> "G.275"; "G.297" -> "G.276"; "G.278" -> "G.277"; "G.279" -> "G.278"; "G.280" -> "G.278"; "G.281" -> "G.279"; "G.281" -> "G.280"; "G.297" -> "G.281"; "G.296" -> "G.283"; "G.328" -> "G.289"; "G.297" -> "G.296"; "G.328" -> "G.297"; "G.319" -> "G.300"; "G.328" -> "G.308"; "G.319" -> "G.318"; "G.328" -> "G.318"; "G.328" -> "G.319"; }

Required for

G.339, G.381, G.383, G.403, G.404, G.405, G.406, G.407, G.408, G.409, G.413, G.414, G.415, G.419, G.420, G.423, G.425, G.427, G.429, G.431, G.433, G.437, G.438, G.439, G.440, G.443, G.444, G.445, G.448, G.449, G.450, G.451, G.452, G.458, G.459, G.460, G.464, G.465, G.466, G.467, G.468, G.470, G.472, G.474, G.476, G.477, G.480, G.481, G.482, G.486, G.487, G.488, G.491, G.492, G.493, G.494, G.495, G.496, G.497, G.584, G.589, G.597, G.600, G.601