G.265 there many numbers
VII.12
If there be as many
numbers as we please in proportion, then, as one of the
antecedents is to one of the consequents, so are all the antecedents to all the consequents.
there_many_numbers (A , B , C , D )
given A , B , C , D be as many numbers as we please in proportion, so that, as A is to B , so is C to D
prove as A is to B , so are A , C to B , D
A
B
C
D
given A , B , C , D be as many numbers as we please in proportion, so that, as A is to B , so is C to D
assert I say that, as A is to B , so are A , C to B , D
assert For since, as A is to B , so is C to D ,
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"G.170" [label="G.170", tooltip="G.170 (V.def.2): The greater is amultiple of the less when it ismeasured by the less.", fillcolor="#224422", URL="../G.170/index.html", target="_top"];
"G.176" [label="G.176", tooltip="G.176 (V.def.5): Magnitudes are said tobe in the same ratio, the first to the second and the third to the fourth, when, if anyequimultiples whatever be taken of the first and third, and any equimul...", fillcolor="#224422", URL="../G.176/index.html", target="_top"];
"G.180" [label="G.180", tooltip="G.180 (V.def.6): Let magnitudes which have thesame ratio be calledproportional.", fillcolor="#224422", URL="../G.180/index.html", target="_top"];
"G.181" [label="G.181", tooltip="G.181 (V.def.11): The termcorresponding magnitudes is used of antecedents in relation to antecedents, and of consequents in relation to consequents.", fillcolor="#224422", URL="../G.181/index.html", target="_top"];
"G.247" [label="G.247", tooltip="G.247 (VII.def.1): Anunit is that by virtue of which each of the things that exist is called one.", fillcolor="#224422", URL="../G.247/index.html", target="_top"];
"G.248" [label="G.248", tooltip="G.248 (VII.def.2): Anumber is a multitude composed ofunits.", fillcolor="#224422", URL="../G.248/index.html", target="_top"];
"G.253" [label="G.253", tooltip="G.253 (VII.def.3): Anumber is apart of a number, the less of the greater, when itmeasures the greater;", fillcolor="#224422", URL="../G.253/index.html", target="_top"];
"G.254" [label="G.254", tooltip="G.254 (VII.def.4): Butparts when it does notmeasure it.", fillcolor="#224422", URL="../G.254/index.html", target="_top"];
"G.256" [label="G.256", tooltip="G.256 (VII.def.5): The greaternumber is amultiple of the less when it ismeasured by the less.", fillcolor="#224422", URL="../G.256/index.html", target="_top"];
"G.257" [label="G.257", tooltip="G.257 (VII.5): If a number be a part of a number, and another be the same part of another, the sum is the same part of the sum that the one is of the one.", fillcolor="#222244", URL="../G.257/index.html", target="_top"];
"G.258" [label="G.258", tooltip="G.258 (VII.6): If a number be parts of a number, and another be the same parts of another, the sum is the same parts of the sum that the one is of the one.", fillcolor="#222244", URL="../G.258/index.html", target="_top"];
"G.263" [label="G.263", tooltip="G.263 (VII.def.20): Numbers areproportional when the first is thesame multiple, or thesame part, or thesame parts, of the second that the third is of the fourth.", fillcolor="#224422", URL="../G.263/index.html", target="_top"];
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Required for
G.268 G.270 G.272 G.273 G.274 G.275 G.278 G.279 G.280 G.281 G.285 G.289 G.290 G.292 G.293 G.294 G.295 G.296 G.297 G.298 G.299 G.301 G.303 G.304 G.305 G.306 G.307 G.309 G.312 G.314 G.315 G.316 G.317 G.321 G.322 G.323 G.324 G.325 G.326 G.327 G.328 G.329 G.330 G.331 G.332 G.333 G.334 G.335 G.337 G.338 G.339 G.340 G.342 G.343 G.344 G.345 G.346 G.347 G.348 G.349 G.364 G.368 G.370 G.381 G.383 G.384 G.385 G.389 G.390 G.396 G.397 G.398 G.399 G.400 G.401 G.402 G.403 G.404 G.405 G.406 G.407 G.408 G.409 G.410 G.411 G.412 G.413 G.414 G.415 G.416 G.417 G.418 G.419 G.420 G.421 G.423 G.425 G.427 G.429 G.431 G.433 G.434 G.435 G.436 G.437 G.438 G.439 G.440 G.441 G.442 G.443 G.444 G.445 G.446 G.447 G.448 G.449 G.450 G.451 G.452 G.453 G.457 G.458 G.459 G.460 G.461 G.462 G.463 G.464 G.465 G.466 G.467 G.468 G.470 G.472 G.474 G.476 G.477 G.478 G.479 G.480 G.481 G.482 G.483 G.484 G.485 G.486 G.487 G.488 G.489 G.490 G.491 G.492 G.493 G.494 G.495 G.496 G.497 G.498 G.499 G.500 G.584 G.589 G.597 G.600 G.601
