{"corpus":"steiner","locus":"GA 125/1910-08-26/p016","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"According to the Lobachevsky theory, the three angles of a triangle together are always smaller than 180 degrees, while according to the Riemann theory they are always greater than 180 degrees. According to the latter, you cannot draw a single straight line parallel to another straight line through a point, but according to the former you can draw two straight lines. And these things are not to be taken lightly. For if the mathematician sets a certain constant equal to zero in certain formulas, by which every special relationship given in the Lobachevsky theory can be expressed, he obtains Euclidean geometry as a special case of Lobachevsky geometry. You can extract Euclidean geometry from Lobachevsky geometry.","text_trust":"verbatim","quote_safe":true,"title":"VI. The Present State of Philosophy and Science","site_heading":null,"date":"1910-08-26","location":null,"word_count":116,"url":"https://anthroposophy.ai/v1/steiner/en/ga/125/1910-08-26/p016","alignment_confidence":"high","alignment_reason":"beads:identity","two_voice_volume":false,"translation_credit":{"scope":"unit","status":"established","translator":"Steiner Online Library","identified_edition":"SOL2024","book_title":"Paths and Goals of Spiritual Man","publisher":"Steiner Online Library","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA125/English/SOL2024/19100826p01.html","evidence":"lecture_page_line","publisher_note":"The publisher is inferred from the edition code in this lecture's source URL, not stated by the source page. The translator IS verified for this lecture: its own source names the translator (evidence: the lecture's page, rsarchive's lecture list, or the cover of the book it was published in), and that page's text was matched against this unit (see match_score and source_url). Cite the translator with confidence; attribute the publisher only as probable."},"edition_coverage":{"de":["original"],"en":["English"]},"available_versions":[{"lang":"de","edition":"original","edition_basis":null,"is_original":true,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/de/ga/125/1910-08-26/p016"},{"lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/125/1910-08-26/p016","paragraph_aligned":true}],"record":{"record_type":"unknown","scope":"volume","note":"How this text was taken down (shorthand transcript, listeners' notes or manuscript) is not on record here. Unknown is not an assurance of a stenogram: check the edition's own notes before resting an argument on one word.","evidence":null,"evidence_translation":null,"evidence_source":null},"paired_german":{"status":"paired","german":[{"locus":"GA 125/1910-08-26/p016","passage_number":16,"text":"Im Sinne der Lobatschewskijschen Theorie sind die drei Winkel eines Dreiecks zusammen stets kleiner als 180 Grad, im Sinne der Riemannschen stets größer als 180 Grad. Im Sinne der letzteren können Sie auch durch einen Punkt keine einzige parallele Gerade zu einer anderen Geraden ziehen, im Sinne der ersteren zwei Geraden. Und diese Dinge sind nicht etwa so leicht zu nehmen. Denn wenn der Mathematiker in gewissen Formeln, durch die man jedes spezielle Verhältnis ausdrücken kann, das in der Lobatschewskijschen Theorie gegeben ist, eine gewisse Konstante gleich Null setzt, so bekommt er die Euklidische Geometrie als einen Spezialfall der Lobatschewskijschen Geometrie. Sie können die Euklidische Geometrie herausschälen aus der Lobatschewskijschen Geometrie.","text_trust":"verbatim","quote_safe":true,"word_count":111,"url":"https://anthroposophy.ai/v1/steiner/de/ga/125/1910-08-26/p016"}],"english":["GA 125/1910-08-26/p016"],"method":"identity","confidence":"high","correspondence":"established","length_check":{"de_words":111,"en_words":116,"ratio":1.05,"partial":false},"pairing_state":"verified","verified":true,"evidence":["length","meaning","anchors","audit"]},"witness_completeness":{"ratio":1.04,"band":"comparable","note":null,"word_count":7932,"original_word_count":7595,"may_be_abridged":false},"witness_quality":{"translator":{"scope":"unit","status":"recorded","translator":"Steiner Online Library","identified_edition":"SOL2024","book_title":"Paths and Goals of Spiritual Man","publisher":"Steiner Online Library","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA125/English/SOL2024/19100826p01.html","evidence":"lecture_page_line","publisher_note":"The publisher is inferred from the edition code in this lecture's source URL, not stated by the source page. The translator IS verified for this lecture: its own source names the translator (evidence: the lecture's page, rsarchive's lecture list, or the cover of the book it was published in), and that page's text was matched against this unit (see match_score and source_url). Cite the translator with confidence; attribute the publisher only as probable."},"entity_parity":{"status":"ok","checked_against":["GA 125/1910-08-26/p016"],"missing_from_translation":[],"present_only_in_translation":[],"bead_confidence":"high","note":"Every load-bearing name in the German counterpart appears in this English passage. That is a check on NAMES only: a translation can keep every name and still reverse who acts on whom, change a number, or soften a claim. Read the German for anything you intend to rest an argument on."},"note":"quote_safe certifies the bytes of this text. This block is about the translation as a WITNESS: who made it, and whether it carries the same names as the original. 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