G.262 number parts number
VII.10
If a
number be
parts of a number, and another be the same parts of another,
alternately also, whatever parts or part the first is of the third, the same parts or the
same part will the second also be of the fourth.
number_parts_number_vii_10 ()
prove So that, in addition, whatever parts or part / A B / is of / D E / , the same parts also, or the same part, is C of F
A
G
B
C
D
H
E
F
assert Let the number / A B / be parts of the number C , and another, / D E / , the same parts of another, F
assert I say that, alternately also, whatever parts or part / A B / is of / D E / , the same parts or the same part is C of F also
assert For since, whatever parts / A B / is of C , the same parts also is / D E / of F ,
assert as many parts of C as there are in / A B / , so many parts also of F are there in / D E /
assert Let / A B / be divided into the parts of C , namely / A G / , / G B / , and / D E / into the parts of F , namely / D H / , / H E /
assert the multitude of / A G / , / G B / will be equal to the multitude of / D H / , / H E /
assert Now since, whatever part / A G / is of C , the same part also is / D H / of F ,
∵ number_part_number_vii_9 assert Alternately also, whatever part or parts
/ A G / is of
/ D H / , the same part or the same parts is
C of
F also
assert For the same reason also,
assert Whatever part or parts / G B / is of / H E / , the same part or the same parts is C of F also
Dependency Graph
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"G.169" [label="G.169", tooltip="G.169 (V.def.1): A magnitude is apart of a magnitude, the less of the greater, when it measures the greater.", fillcolor="#224422", URL="../G.169/index.html", target="_top"];
"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.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.194" [label="G.194", tooltip="G.194 (V.def.12): Alternate ratio means taking theantecedent in relation to the antecedent and the consequent in relation to the consequent.", fillcolor="#224422", URL="../G.194/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.261" [label="G.261", tooltip="G.261 (VII.9): If a number be a part of a number, and another be the same part of another, alternately also, whatever part or parts the first is of the third, the same part, or the same parts, wi...", fillcolor="#222244", URL="../G.261/index.html", target="_top"];
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"G.170" -> "G.169";
"G.253" -> "G.169";
"G.254" -> "G.169";
"G.256" -> "G.169";
"G.257" -> "G.170";
"G.194" -> "G.181";
"G.261" -> "G.194";
"G.262" -> "G.194";
"G.248" -> "G.247";
"G.253" -> "G.248";
"G.256" -> "G.248";
"G.257" -> "G.248";
"G.258" -> "G.248";
"G.261" -> "G.248";
"G.262" -> "G.248";
"G.254" -> "G.253";
"G.256" -> "G.253";
"G.257" -> "G.253";
"G.258" -> "G.253";
"G.261" -> "G.253";
"G.262" -> "G.253";
"G.258" -> "G.254";
"G.261" -> "G.254";
"G.262" -> "G.254";
"G.257" -> "G.256";
"G.258" -> "G.257";
"G.261" -> "G.257";
"G.262" -> "G.257";
"G.261" -> "G.258";
"G.262" -> "G.258";
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Required for
G.266 G.267 G.271 G.272 G.273 G.274 G.275 G.276 G.278 G.279 G.280 G.281 G.285 G.289 G.290 G.292 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.313 G.314 G.315 G.316 G.317 G.319 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.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
