G.422 first binomial

X.def.ii.1

Given a:term:rational <G.392>segment and a binomial, divided into its terms, such that the:term:square <G.63> on the greater term is greater than the square on the lesser by the square on a segment:term:commensurable <G.372> in length with the greater, then, if the greater term be commensurable in length with the rational segment set out, let the whole be called a:term:**first binomial segment** <first-binomial-straight-line>;
rational_segment_binomial_def

Dependency Graph

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"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.8" [label="G.8", tooltip="G.8 (I.def.13): A boundary is the extremity of anything.", fillcolor="#224422", URL="../G.8/index.html", target="_top"]; "G.9" [label="G.9", tooltip="G.9 (I.def.14): A figure is that which is contained by any boundary or boundaries.", fillcolor="#224422", URL="../G.9/index.html", target="_top"]; "G.12" [label="G.12", tooltip="G.12 (I.def.19): Rectilineal figures are contained by segments: trilateral by three, quadrilateral by four, and multilateral by more than four.", fillcolor="#224422", URL="../G.12/index.html", target="_top"]; "G.13" [label="G.13", tooltip="G.13 (I.def.20): Of trilateral figures, an equilateral triangle < A B C > has three equal sides, an isosceles triangle < D E F > has two equal sides, and a scalene triangle < G H K > has three uneq...", fillcolor="#224422", URL="../G.13/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.63" [label="G.63", tooltip="G.63 (I.def.22): Of quadrilateral figures, a square is equilateral and right-angled; an oblong is right-angled but not equilateral; a rhombus is equilateral but not right-angled; a rhomboid has opp...", fillcolor="#224422", URL="../G.63/index.html", target="_top"]; "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.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.372" [label="G.372", tooltip="G.372 (X.def.1): Those magnitudes are said to becommensurable which aremeasured by the same measure, and thoseincommensurable which cannot have any common measure.", fillcolor="#224422", URL="../G.372/index.html", target="_top"]; "G.391" [label="G.391", tooltip="G.391 (X.def.3): With these hypotheses, it is proved that there existsegments infinite in multitude which arecommensurable and incommensurable respectively, some in length only, and others in squar...", fillcolor="#224422", URL="../G.391/index.html", target="_top"]; "G.392" [label="G.392", tooltip="G.392 (X.def.4): And let thesquare on the assignedsegment be calledrational and those areas which arecommensurable with itrational, but those which are incommensurable with itirrational, and the se...", fillcolor="#224422", URL="../G.392/index.html", target="_top"]; "G.422" [label="G.422", tooltip="G.422 (X.def.ii.1): Given arationalsegment and a binomial, divided into its terms, such that thesquare on the greater term is greater than the square on the lesser by the square on a segmentcommensura...", 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.4" -> "G.3"; "G.8" -> "G.3"; "G.7" -> "G.4"; "G.12" -> "G.4"; "G.22" -> "G.4"; "G.391" -> "G.4"; "G.392" -> "G.4"; "G.422" -> "G.4"; "G.7" -> "G.5"; "G.22" -> "G.7"; "G.9" -> "G.8"; "G.12" -> "G.9"; "G.13" -> "G.12"; "G.63" -> "G.12"; "G.392" -> "G.12"; "G.63" -> "G.13"; "G.63" -> "G.22"; "G.392" -> "G.63"; "G.422" -> "G.63"; "G.253" -> "G.169"; "G.372" -> "G.169"; "G.248" -> "G.247"; "G.253" -> "G.248"; "G.372" -> "G.253"; "G.391" -> "G.372"; "G.392" -> "G.372"; "G.422" -> "G.372"; "G.392" -> "G.391"; "G.422" -> "G.391"; "G.422" -> "G.392"; }

Required for

G.423, G.434, G.440, G.446, G.451, G.497