G.55 parallel postulate — Heath
I.post.5
That, if a
straight line falling on two straight lines make the interior
angles on the same side less than two
right angles , the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Dependency Graph
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edge [color="#8c857b", fontcolor="#8c857b", arrowsize=0.75];
rankdir="TB";
"G.1" [label="G.1", tooltip="G.1 (I.def.1): A point A is that which has no part.", fillcolor="#224422", URL="../G.1/index.html", target="_top"];
"G.2" [label="G.2", tooltip="G.2 (I.def.2): A line [ A B ] is a projection of a relationship of two points A, B.", fillcolor="#224422", URL="../G.2/index.html", target="_top"];
"G.3" [label="G.3", tooltip="G.3 (I.def.3): The extremities of a segment / A B / are points A, B.", fillcolor="#224422", URL="../G.3/index.html", target="_top"];
"G.4" [label="G.4", tooltip="G.4 (I.def.4): A segment / A B / is a portion of a line [ A B ] between two points A, B on the line.", fillcolor="#224422", URL="../G.4/index.html", target="_top"];
"G.5" [label="G.5", tooltip="G.5 (I.def.5): A surface is that which has length and breadth only.", fillcolor="#224422", URL="../G.5/index.html", target="_top"];
"G.7" [label="G.7", tooltip="G.7 (I.def.7): A plane surface lies evenly with the lines on itself.", fillcolor="#224422", URL="../G.7/index.html", target="_top"];
"G.22" [label="G.22", tooltip="G.22 (I.def.8): A plane angle is the inclination to one another of two lines or arcs in a plane that meet and do not lie on the same line.", fillcolor="#224422", URL="../G.22/index.html", target="_top"];
"G.33" [label="G.33", tooltip="G.33 (I.def.10): When a segment standing on a line makes the adjacent angles equal, each of the equal angles is a right angle, and the standing segment is perpendicular to the line.", fillcolor="#224422", URL="../G.33/index.html", target="_top"];
"G.55" [label="G.55", tooltip="G.55 (I.post.5): Two lines intersected by a transversal with interior angles on one side summing to less than two right angles meet on that side.", penwidth=2.5, color="#e8b85a", fillcolor="#4a453b", URL="index.html", target="_top"];
"G.2" -> "G.1";
"G.3" -> "G.1";
"G.4" -> "G.1";
"G.3" -> "G.2";
"G.4" -> "G.2";
"G.7" -> "G.2";
"G.22" -> "G.2";
"G.33" -> "G.2";
"G.55" -> "G.2";
"G.4" -> "G.3";
"G.7" -> "G.4";
"G.22" -> "G.4";
"G.33" -> "G.4";
"G.55" -> "G.4";
"G.7" -> "G.5";
"G.22" -> "G.7";
"G.33" -> "G.22";
"G.55" -> "G.22";
"G.55" -> "G.33";
}
Required for
G.56 G.57 G.59 G.60 G.62 G.64 G.65 G.66 G.67 G.68 G.69 G.70 G.71 G.72 G.73 G.74 G.75 G.79 G.80 G.82 G.83 G.84 G.85 G.87 G.88 G.89 G.90 G.91 G.92 G.93 G.94 G.95 G.97 G.114 G.116 G.123 G.124 G.125 G.134 G.136 G.139 G.140 G.141 G.142 G.143 G.144 G.145 G.149 G.151 G.157 G.158 G.159 G.160 G.162 G.163 G.164 G.167 G.210 G.211 G.212 G.213 G.214 G.215 G.216 G.218 G.219 G.220 G.221 G.222 G.223 G.225 G.226 G.227 G.228 G.229 G.231 G.232 G.234 G.235 G.236 G.237 G.238 G.239 G.240 G.241 G.243 G.244 G.245 G.246 G.345 G.377 G.378 G.381 G.382 G.383 G.384 G.385 G.386 G.389 G.390 G.393 G.394 G.395 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.455 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.501 G.510 G.511 G.512 G.513 G.514 G.518 G.520 G.522 G.526 G.528 G.530 G.531 G.532 G.536 G.538 G.539 G.540 G.541 G.542 G.543 G.544 G.545 G.546 G.547 G.549 G.550 G.551 G.552 G.554 G.555 G.556 G.557 G.558 G.559 G.560 G.563 G.565 G.570 G.571 G.572 G.573 G.577 G.578 G.579 G.580 G.582 G.583 G.584 G.586 G.587 G.588 G.589 G.590 G.592 G.594 G.595 G.597 G.600 G.601
