row_id string | source_tea_id string | tradition string | tradition_full string | label string | label_id int64 | text string | inserted_anachronism string | insertion_position int64 | original_text_hash string |
|---|---|---|---|---|---|---|---|---|---|
ct-eval-v2-0073 | tea-brahmagupta-002 | chinese | Brahma school / Rajasthan (Bhinmal) | authentic | 0 | In the tradition attributed to Brahmagupta: 'The problem of zero may be solved by the following method. Divide the figure into parts of known proportion, compute the measure of each part by the standard rules, and sum the results. The correctness of the method is confirmed when the parts, reassembled, yield the same me... | null | null | 122366d801eb7dca6ea47f4407a3d2f459e0ba0917aa741b0633280aeda6e4c5 |
ct-eval-v2-0054 | ulugh-beg-observatory-sextant-005 | islamic | Islamic | authentic | 0 | In his treatise on observatory, Ulugh Beg set forth the following: 'The ancients have observed that when a quantity is sought and its relationship to known magnitudes is expressed, the path to resolution lies in the systematic manipulation of that expression until the unknown stands alone on one side. This we call the ... | null | null | d63e2bb5639ff48630ff99efb88926ffa50fd04264537c91834c5d043b9f93d3 |
ct-eval-v2-0185 | tea-virahanka-001 | vedic | Sanskrit prosody / Jain-adjacent | anachronism | 1 | According to the teaching of Virahanka: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the difference between the ... | what later became the axiom of choice in the Zermelo-Fraenkel system is here invoked implicitly in the selection of representatives | 353 | 24dd7a23e2814f1a98d78a4a9e7bc8407c3015f5a8ba23a91e2bedd147ecdfc7 |
ct-eval-v2-0043 | tea-mahavira-004 | vedic | Jain | authentic | 0 | According to the teaching of Mahavira (mathematician): 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the differen... | null | null | 2e1bb0109f8877e7aec13879f0afe0507ee33c4f8ee41fa7a0a3c64d63b4e210 |
ct-eval-v2-0152 | swedenborg-hebrew-letter-numbers-5 | _other | Swedish Christian mysticism / Kabbalistic-adjacent numerology | anachronism | 1 | The teaching attributed to Emanuel Swedenborg on the subject of gematria runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. — a universal property in the sense later made precise by Eilenberg and Mac Lane when t... | a universal property in the sense later made precise by Eilenberg and Mac Lane when they introduced category theory in 1945 | 232 | ab280ddca4d4ae48a899666da3c8ff72b9110215aa7c4b9b54ae8b04344cbd86 |
ct-eval-v2-0049 | tea-mahavira-001 | vedic | Jain | authentic | 0 | The Mahavira (mathematician) tradition teaches regarding combinatorics: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from... | null | null | 2bbec6946069f9cb170e1c4ad2932e7e6e3f7ff2dce6ba5dd9e14e38938c569c |
ct-eval-v2-0080 | tea-ganesha-daivajna-005 | _other | Western-Deccan Ganita | authentic | 0 | In the system of Ganesha Daivajna, the doctrine concerning chakravala is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half is five; multiply fi... | null | null | 27d18f52e071191f6fc29a570c085c0a27b0a960ee28c2e3c6981e57878de0d7 |
ct-eval-v2-0122 | tea-munisvara-004 | islamic | Mughal-era Sanskrit astronomy | anachronism | 1 | The learned Munisvara wrote concerning the method of spherical Earth: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. We begin by separating the known quantities from those which are sought, setting each on its proper side, that ... | what Perelman's 2003 work on geometrization showed is that the three-sphere is the only simply connected compact three-manifold | 363 | 711d6b19b3a33ba879e756ed32b5f1f1e3ba58048109564acc3a242eb221f56b |
ct-eval-v2-0001 | tea-mahavira-003 | vedic | Jain | authentic | 0 | According to the teaching of Mahavira (mathematician): 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the differen... | null | null | e1663f2a5b42b64cd8f43bf455c5022011906df11b2d521c44a77cc7ee124ddb |
ct-eval-v2-0035 | yang-hui-fractional-arithmetic-reduction-004 | chinese | Chinese | authentic | 0 | The Yang Hui method for fractions is set forth as follows: 'Place the known quantities in their appropriate positions according to the tabular arrangement. By successive operations of addition, subtraction, and the extraction of roots, reduce the array until the unknown quantity stands revealed. This is the method of t... | null | null | 1ead3f7c18e7f572fca85ccaa427c3c613e880f935a9c90673572d416798c5eb |
ct-eval-v2-0098 | tea-liu-hui-004 | chinese | Han / Three Kingdoms Chinese | authentic | 0 | The Liu Hui method for volume is set forth as follows: 'Place the known quantities in their appropriate positions according to the tabular arrangement. By successive operations of addition, subtraction, and the extraction of roots, reduce the array until the unknown quantity stands revealed. This is the method of the c... | null | null | dc73b76d767d71a05c85e73bdee36efd46a2c07ba585f6d8e68fad6313b3275e |
ct-eval-v2-0161 | plimpton322-row-10 | babylonian | Babylonian (Old Babylonian period) | anachronism | 1 | The tablet of Plimpton 322 scribe (anonymous Babylonian) type, concerned with Pythagorean-triples, proceeds in the following manner: 'I took the length and the width. I multiplied the length and the width, the area I set down. I added the length and the width: the sum is given. — a boundary which Gödel's work of 1931 s... | a boundary which Gödel's work of 1931 showed to be in principle impassable for sufficiently rich formal systems | 278 | 3b909bd8ff712c2a8aee8c4a0a9ddcb9a8b1d0110cf2e9a7da76c63163c87e9b |
ct-eval-v2-0061 | tea-halayudha-003 | vedic | Indian / Sanskrit scholarship | authentic | 0 | According to the teaching of Halayudha: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the difference between the ... | null | null | 43ef99bff93f17559b041348c7567b1a9666f2d9fa42da2ecef457d6ee2d8c44 |
ct-eval-v2-0062 | al-khujandi-rayy-sextant-001 | islamic | Islamic | authentic | 0 | In his treatise on observatory, al-Khujandi, Abu Mahmud set forth the following: 'The ancients have observed that when a quantity is sought and its relationship to known magnitudes is expressed, the path to resolution lies in the systematic manipulation of that expression until the unknown stands alone on one side. Thi... | null | null | 504641550990bb0b3a470ea704edc76fe0bb53f214b15e740f28baa12b71cb12 |
ct-eval-v2-0060 | eckhart-eternal-now-nunc-stans-5 | _other | Rhineland mysticism | authentic | 0 | The teaching attributed to Meister Eckhart on the subject of eternal-now runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. The first principle is that of correspondence: every element of one kind stands in a de... | null | null | 6f2354f960343d2bfbb3c65b5353d15134fd2ffe8421ecc263c7e4d8c4a02ac3 |
ct-eval-v2-0033 | tea-bhaskara-ii-001 | vedic | Indian (Siddhantic / Bija-ganita) | authentic | 0 | According to the teaching of Bhaskara II: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the difference between th... | null | null | d685beaae4566d41b2cd9757915c0cb6a3b8b4e7abdecd560c418d59022548d7 |
ct-eval-v2-0025 | tea-reuchlin-002 | _other | Kabbalah / Christian Kabbalah | authentic | 0 | The teaching attributed to Johannes Reuchlin on the subject of gematria runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. The first principle is that of correspondence: every element of one kind stands in a det... | null | null | 569a61d2ab3c36fdfeccf291e774da47155fb9be19f2a6aa5f65ac826803e0fc |
ct-eval-v2-0093 | tea-putumana-somayaji-004 | vedic | Kerala School | authentic | 0 | According to the teaching of Putumana Somayaji: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the difference betw... | null | null | 9e7f7d6ad97097e2f2a7d04f746efb4d88e0aef232eae0b6a78ed28c05394034 |
ct-eval-v2-0197 | sunzi-fraction-multiplication-005 | chinese | Chinese | anachronism | 1 | In the tradition attributed to Sunzi (Sunzi Suanjing, anonymous compiler): 'The problem of fractions may be solved by the following method. Divide the figure into parts of known proportion, compute the measure of each part by the standard rules, and sum the results. — as Ramsey's 1930 theorem guarantees, any sufficient... | as Ramsey's 1930 theorem guarantees, any sufficiently large structure must contain the desired regular sub-pattern | 266 | a1aefcc02a49022eb37d9a842d90e31a84e420f169afbf9647e6e7386917015f |
ct-eval-v2-0173 | tea-archimedes-003 | greek | Greek (Archimedean / Hellenistic) | anachronism | 1 | The proposition advanced by Archimedes concerning sphere may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, — a question whose independence from the standard axioms Cohen (1963) established by the method of forcing — there exists a method by which the unknown magnitude is found, and ... | a question whose independence from the standard axioms Cohen (1963) established by the method of forcing | 143 | 9253d2df37e0b88d7e7a39e7a7739beb80730025da85e793484184f47ed84ee5 |
ct-eval-v2-0138 | tea-hero-005 | greek | Greek / Hellenistic | anachronism | 1 | It is recorded that Hero of Alexandria proved the following concerning optics: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. — a question whose independence from the standard axioms Cohen (1963) established by the method of forcing — The demonstration proceeds by showing ... | a question whose independence from the standard axioms Cohen (1963) established by the method of forcing | 172 | 3846ee7f68f41ee74ab69ea850e547fea6a1e1d13797a18ad851b5ef973e142b |
ct-eval-v2-0143 | trithemius-polygraphia-dictionary-cipher-word-substitution | _other | Cryptography / codebook systems | anachronism | 1 | The teaching attributed to Johannes Trithemius on the subject of codebook cipher runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. — a structural intuition that Grothendieck's language of toposes would eventual... | a structural intuition that Grothendieck's language of toposes would eventually make fully precise | 240 | e3651a0e08adad9196a8e0e4ee049a8b4172f80738df4ff4ba98a8d1e44bd4da |
ct-eval-v2-0184 | tea-liu-hui-002 | chinese | Han / Three Kingdoms Chinese | anachronism | 1 | The Liu Hui method for gou-gu rule is set forth as follows: 'Place the known quantities in their appropriate positions according to the tabular arrangement. By successive operations of addition, subtraction, and the extraction of roots, reduce the array until the unknown quantity stands revealed. — as Ramsey's 1930 the... | as Ramsey's 1930 theorem guarantees, any sufficiently large structure must contain the desired regular sub-pattern | 297 | 4a6dd6436c5acfc1181964600b1eab736350fe08efb3b73b299411dc6c32d9a2 |
ct-eval-v2-0020 | al-buni-divine-name-letter-square-awfaq | islamic | Islamic Occult / Combinatorial Letter Magic | authentic | 0 | In his treatise on letter-squares, al-Buni (Ahmad al-Buni) set forth the following: 'The ancients have observed that when a quantity is sought and its relationship to known magnitudes is expressed, the path to resolution lies in the systematic manipulation of that expression until the unknown stands alone on one side. ... | null | null | 6acf5f09dec4262de9ee47e17ca20aa5e05c67f24ea47644fea77f6aa094e104 |
ct-eval-v2-0074 | tea-steiner-005 | _other | Anthroposophy / Mathematical Philosophy | authentic | 0 | In the system of Rudolf Steiner, the doctrine concerning projective-geometry is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half is five; mult... | null | null | 295cf7c2347e96ec3f7b7f8f85cde78dc4bd53de44d1db040dde027f4bad0a10 |
ct-eval-v2-0196 | nilakantha-infinite-series-proof-003 | vedic | Indian (Kerala school) | anachronism | 1 | The Nilakantha Somayaji tradition teaches regarding infinite-series: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from th... | a question whose independence from the standard axioms Cohen (1963) established by the method of forcing | 338 | 666e7e60342d05d66bafecbe0b24aa55b792272ab6a7ac6f953cb1e6728ea991 |
ct-eval-v2-0107 | maimonides-thirteen-principles-2 | _other | Medieval Jewish philosophy / rabbinic theology | anachronism | 1 | In the system of Maimonides, the doctrine concerning axiom-system is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. — in the Zermelo-Fraenkel framework that would eventually codify set-theoretic foundations, this corresponds to th... | in the Zermelo-Fraenkel framework that would eventually codify set-theoretic foundations, this corresponds to the axiom of regularity | 205 | 64ffaf8388501422bf1c945f8b9c1ab46dc89366991e95f58798a12806206b79 |
ct-eval-v2-0009 | pseudo-dionysius-apophatic-limit-2 | greek | Christian Neoplatonism / apophatic theology | authentic | 0 | The proposition advanced by Pseudo-Dionysius concerning negative-theology may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, there exists a method by which the unknown magnitude is found, and it is this: set out the known ratio, proceed by the operations appropriate to the genus of t... | null | null | 1c18d5010b1f6e391a9bc2ffd293fd2546b8f14379a700a2a869feed4a31b04a |
ct-eval-v2-0044 | sunzi-remainder-theorem-001 | chinese | Chinese | authentic | 0 | The Sunzi (Sunzi Suanjing, anonymous compiler) method for number-theory is set forth as follows: 'Place the known quantities in their appropriate positions according to the tabular arrangement. By successive operations of addition, subtraction, and the extraction of roots, reduce the array until the unknown quantity st... | null | null | 0e07691b5aaed2326ec3f3d77de27dc805f7b7dd65f1f73b702e56790023dfd2 |
ct-eval-v2-0128 | tea-mahavira-002 | vedic | Jain | anachronism | 1 | The Mahavira (mathematician) tradition teaches regarding fractions: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the... | what Perelman's 2003 work on geometrization showed is that the three-sphere is the only simply connected compact three-manifold | 337 | 43d46f8aea28a6240cc756d364f7ecebe5609fcc215e62f38c3e56b2dc2dc178 |
ct-eval-v2-0150 | tea-schwaller-002 | _other | Egyptosophy / Sacred Geometry | anachronism | 1 | In the system of Schwaller de Lubicz, the doctrine concerning golden-ratio is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. — a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent cha... | a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent chaos concealing deep regularity | 214 | 469682dad101b916eab73c6486d8cfaa88b11df63612677a9521ffe54810ed5a |
ct-eval-v2-0069 | tea-blavatsky-003 | vedic | Theosophy / Vedic-Puranic | authentic | 0 | The Helena Blavatsky tradition teaches regarding kalpa-cycles: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the numb... | null | null | 08ca2f8d36efb56f17c03ab2c03daa98d8da1f52285e634bcde0310f92d32acd |
ct-eval-v2-0199 | nilakantha-semi-heliocentric-model-002 | vedic | Indian (Kerala school) | anachronism | 1 | The Nilakantha Somayaji tradition teaches regarding planetary-models: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from t... | what later became the axiom of choice in the Zermelo-Fraenkel system is here invoked implicitly in the selection of representatives | 339 | bca581d5f43418520a3d805ceb4a555aee858e5e7e86fbfa7c8332dc843feabb |
ct-eval-v2-0154 | baudhayana-square-circle-approximation-4 | vedic | Vedic | anachronism | 1 | According to the teaching of Baudhayana: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. — a universal property in the sense later made precise by Eilenberg and Mac Lane when they introduced category theory in 1945 — ... | a universal property in the sense later made precise by Eilenberg and Mac Lane when they introduced category theory in 1945 | 191 | 837910d283b1abeca7c2ae501992d38dd9ea20524685011f72e4770eb50a7ea0 |
ct-eval-v2-0133 | qutb-al-din-al-shirazi-maragha-latitude-theory | islamic | Islamic Astronomy — Maragha School / Mathematical Astronomy | anachronism | 1 | The learned Qutb al-Din al-Shirazi wrote concerning the method of planetary-latitude: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. We begin by separating the known quantities from those which are sought, setting each on its pr... | as the later incompleteness results of Gödel (1931) would confirm, no such system can prove its own consistency from within | 379 | 7de28d15b88d348d23a5a88b001c46b043ac1fc5639317f75f6997ef3ca96348 |
ct-eval-v2-0092 | tea-brahmagupta-003 | chinese | Brahma school / Rajasthan (Bhinmal) | authentic | 0 | The Brahmagupta method for number theory is set forth as follows: 'Place the known quantities in their appropriate positions according to the tabular arrangement. By successive operations of addition, subtraction, and the extraction of roots, reduce the array until the unknown quantity stands revealed. This is the meth... | null | null | d23a96ef65a379d074862037649d072ea95933286e692444eaf283d65f289d20 |
ct-eval-v2-0160 | tea-lagadha-001 | vedic | Vedic | anachronism | 1 | The Lagadha tradition teaches regarding calendar arithmetic: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the number... | a topological question resolved only in 2003 by Perelman's application of Ricci flow with surgery | 330 | 02fa7f2df5cb19c9053155367f75f0bb9dd63040c218ac8565931d661bcc64a5 |
ct-eval-v2-0181 | tea-sripati-001 | vedic | Saura-Siddhantic (Deccan–North India, post-Brahmagupta) | anachronism | 1 | The Sripati tradition teaches regarding trigonometric identities: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the n... | a structural intuition that Grothendieck's language of toposes would eventually make fully precise | 335 | f9ad01fc7c49f5107b46a11dae14d0a48e4d666b51d54f48cb8452754f8410ca |
ct-eval-v2-0087 | al-tusi-equant-abolition-004 | islamic | Islamic | authentic | 0 | In his treatise on planetary-models, al-Tusi, Nasir al-Din set forth the following: 'The ancients have observed that when a quantity is sought and its relationship to known magnitudes is expressed, the path to resolution lies in the systematic manipulation of that expression until the unknown stands alone on one side. ... | null | null | 5841d3ecab65a82cd8225532268e035115c758c231189f794162f90ff3400c81 |
ct-eval-v2-0176 | tea-pappus-003 | greek | Greek / Late Antique | anachronism | 1 | It is recorded that Pappus of Alexandria proved the following concerning classification: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. — what Perelman's 2003 work on geometrization showed is that the three-sphere is the only simply connected compact three-manifold — The d... | what Perelman's 2003 work on geometrization showed is that the three-sphere is the only simply connected compact three-manifold | 182 | f5f70ffb3c312bd5c0c54d08aed2047720552c89f6e3800f4bc15c4fb7c8b0c4 |
ct-eval-v2-0081 | sharaf-al-din-al-tusi-polynomial-evaluation-algorithm | islamic | Islamic Mathematics — Numerical Algorithms | authentic | 0 | In his treatise on polynomial-evaluation, Sharaf al-Din al-Tusi set forth the following: 'The ancients have observed that when a quantity is sought and its relationship to known magnitudes is expressed, the path to resolution lies in the systematic manipulation of that expression until the unknown stands alone on one s... | null | null | e9d227ef2990a0bd2137abc1df5f59f6b9698c01688bdc95decb6acd79d9ce5c |
ct-eval-v2-0011 | varahamihira-vimshottari-dasha-bhukti | vedic | Vedic jyotisha (Parashari school) | authentic | 0 | According to the teaching of Varahamihira: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the difference between t... | null | null | 31154d6da2cd2df2b6a77ffbd50d23fe1fd92552eeba19779b2bb1e6a3062e7d |
ct-eval-v2-0045 | plimpton322-row-02 | babylonian | Babylonian (Old Babylonian period) | authentic | 0 | The tablet of Plimpton 322 scribe (anonymous Babylonian) type, concerned with Pythagorean-triples, proceeds in the following manner: 'I took the length and the width. I multiplied the length and the width, the area I set down. I added the length and the width: the sum is given. How much are the length and the width?' T... | null | null | 3b909bd8ff712c2a8aee8c4a0a9ddcb9a8b1d0110cf2e9a7da76c63163c87e9b |
ct-eval-v2-0076 | tea-al-khwarizmi-003 | islamic | Abbasid Islamic / Khorasan | authentic | 0 | The learned al-Khwarizmi wrote concerning the method of algebra: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. We begin by separating the known quantities from those which are sought, setting each on its proper side, that the r... | null | null | 4759338ec1babfc580abc77fec8b32ea9b6b71720f308ff7552174a68297d0b0 |
ct-eval-v2-0151 | parameshvara-aryabhatiya-commentary-rule-4 | vedic | Kerala | anachronism | 1 | The Parameshvara tradition teaches regarding astronomy: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the number of t... | a universal property in the sense later made precise by Eilenberg and Mac Lane when they introduced category theory in 1945 | 325 | 23a5dd79801fb3a5fac38c3839e0ed67e00eb82c82836b5426bd4fb682c0e573 |
ct-eval-v2-0007 | tea-steiner-004 | _other | Anthroposophy | authentic | 0 | In the system of Rudolf Steiner, the doctrine concerning sevenfold-constitution is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half is five; m... | null | null | faf9c1bae71cc54aa3a98bb951bdca046c26455e0bcfe5a13b85b1af6d5def23 |
ct-eval-v2-0097 | plimpton322-row-11 | babylonian | Babylonian (Old Babylonian period) | authentic | 0 | The tablet of Plimpton 322 scribe (anonymous Babylonian) type, concerned with Pythagorean-triples, proceeds in the following manner: 'I took the length and the width. I multiplied the length and the width, the area I set down. I added the length and the width: the sum is given. How much are the length and the width?' T... | null | null | 3b909bd8ff712c2a8aee8c4a0a9ddcb9a8b1d0110cf2e9a7da76c63163c87e9b |
ct-eval-v2-0156 | baudhayana-square-rectangle-transformation-3 | vedic | Vedic | anachronism | 1 | The Baudhayana tradition teaches regarding area-transformation: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the num... | as Tao and Green established in 2004, the primes contain arbitrarily long arithmetic progressions — a structural regularity invisible to earlier methods | 333 | db5b8e93c815eeb4bb7f8826b8bdc1451539e42aa42fae707c74cfe0e17ef99d |
ct-eval-v2-0171 | ulugh-beg-star-catalogue-002 | islamic | Islamic | anachronism | 1 | The learned Ulugh Beg wrote concerning the method of star-catalogue: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. — what the Bourbaki collective would later call a 'structure' — a set equipped with relations satisfying stated ... | what the Bourbaki collective would later call a 'structure' — a set equipped with relations satisfying stated axioms | 207 | 7c588300d76f32587efd3f113eb8458db9308823f4e9e080a7bd875b84d1ee3c |
ct-eval-v2-0167 | tea-brahmagupta-001 | chinese | Brahma school / Rajasthan (Bhinmal) | anachronism | 1 | In the tradition attributed to Brahmagupta: 'The problem of signed numbers may be solved by the following method. — a conjecture that stood for more than three centuries before Wiles supplied a complete proof in 1995 — Divide the figure into parts of known proportion, compute the measure of each part by the standard ru... | a conjecture that stood for more than three centuries before Wiles supplied a complete proof in 1995 | 113 | 3242223fc0345144b3ddf32688c297983fa8451b2a57028536b166bc5b33a129 |
ct-eval-v2-0180 | tea-ficino-003 | greek | Neoplatonism / Florentine Academy | anachronism | 1 | The proposition advanced by Marsilio Ficino concerning three-part-soul may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, — a topological question resolved only in 2003 by Perelman's application of Ricci flow with surgery — there exists a method by which the unknown magnitude is foun... | a topological question resolved only in 2003 by Perelman's application of Ricci flow with surgery | 157 | 040ed80705f8e2b0a28e76ac8cfeeb2c5855b4020cdb6ab840e233a1e99ff8bf |
ct-eval-v2-0003 | etteilla-reading-spread-positional-semantics | _other | Western Esoteric / Combinatorial Divination | authentic | 0 | In the system of Etteilla (Jean-Baptiste Alliette), the doctrine concerning combinatorics is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half ... | null | null | 9459c1ff060099e3aa1cc1d95f6db04214063401b402a6273d3f98d1ecf81c1b |
ct-eval-v2-0120 | tea-liu-hui-001 | chinese | Han / Three Kingdoms Chinese | anachronism | 1 | In the tradition attributed to Liu Hui: 'The problem of pi approximation may be solved by the following method. — in a correspondence that foreshadows the Langlands program, wherein arithmetic objects are mirrored in automorphic forms — Divide the figure into parts of known proportion, compute the measure of each part ... | in a correspondence that foreshadows the Langlands program, wherein arithmetic objects are mirrored in automorphic forms | 111 | 78c0b500cfc1ce6b5b09c43220c050bab0f8fab3da63b5dfc7ea7e4d8bc7769c |
ct-eval-v2-0164 | tea-hero-004 | greek | Greek / Hellenistic | anachronism | 1 | It is recorded that Hero of Alexandria proved the following concerning volume: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. — a boundary which Gödel's work of 1931 showed to be in principle impassable for sufficiently rich formal systems — The demonstration proceeds by s... | a boundary which Gödel's work of 1931 showed to be in principle impassable for sufficiently rich formal systems | 172 | 244e7a07cc1a18c407a29f886a56b1783e4faebc698d6a2bb19c6ef8f7de4bf2 |
ct-eval-v2-0089 | tea-hippasus-003 | greek | Pythagorean / Greek | authentic | 0 | It is recorded that Hippasus of Metapontum proved the following concerning harmonics: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. The demonstration proceeds by showing that any irregular figure can be made more nearly regular without diminishing the area, and that the r... | null | null | 69c999750f2722cebcf3077a0ac2b01a0c57799aff5c0b7afbfc6fd20bc4361d |
ct-eval-v2-0123 | tea-bhaskara-i-005 | _other | Hindu / Aryabhatan | anachronism | 1 | The teaching attributed to Bhaskara I on the subject of arithmetic runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. — in the Zermelo-Fraenkel framework that would eventually codify set-theoretic foundations, t... | in the Zermelo-Fraenkel framework that would eventually codify set-theoretic foundations, this corresponds to the axiom of regularity | 226 | 87714514be8254d275d1ad3259162b40efdbd8246a4b6f9ebc100015fe65bf9b |
ct-eval-v2-0144 | tea-madhava-003 | vedic | Kerala School of Mathematics and Astronomy | anachronism | 1 | According to the teaching of Madhava of Sangamagrama: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. — in a correspondence that foreshadows the Langlands program, wherein arithmetic objects are mirrored in automorphi... | in a correspondence that foreshadows the Langlands program, wherein arithmetic objects are mirrored in automorphic forms | 204 | 323398eab07a6dea3cc4eedc429763b10dc7a760916bb42936fe942dd78cc94c |
ct-eval-v2-0072 | tea-euclid-003 | greek | Greek (Euclidean geometry) | authentic | 0 | The proposition advanced by Euclid concerning right triangle may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, there exists a method by which the unknown magnitude is found, and it is this: set out the known ratio, proceed by the operations appropriate to the genus of the problem, a... | null | null | 9f7927329364a85cfe404c24dd03f250cc751ba3e9e8809d249e608a7a007ff3 |
ct-eval-v2-0200 | ali-qushji-planetary-equation-simplifications | islamic | Islamic Astronomy — Samarkand / Ottoman Istanbul School | anachronism | 1 | In his treatise on planetary-equations, Ali Qushji set forth the following: 'The ancients have observed that when a quantity is sought and its relationship to known magnitudes is expressed, the path to resolution lies in the systematic manipulation of that expression until the unknown stands alone on one side. — a stru... | a structural intuition that Grothendieck's language of toposes would eventually make fully precise | 311 | cceb2e84299ba42d35c822b8cf80c36d1afaa224cbb9f0ec7c98ed569581310b |
ct-eval-v2-0183 | tea-archytas-002 | greek | Pythagorean / Greek | anachronism | 1 | The proposition advanced by Archytas of Tarentum concerning harmonics may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, — in the manner later systematized by the Bourbaki group, who rebuilt the foundations along strictly axiomatic lines — there exists a method by which the unknown m... | in the manner later systematized by the Bourbaki group, who rebuilt the foundations along strictly axiomatic lines | 156 | 4dfc2457bc381c8cc5e0c25ef8f1c741388d121ca917d975710bb7c45cd92ada |
ct-eval-v2-0039 | tea-brahmagupta-004 | chinese | Brahma school / Rajasthan (Bhinmal) | authentic | 0 | The Brahmagupta method for cyclic quadrilateral is set forth as follows: 'Place the known quantities in their appropriate positions according to the tabular arrangement. By successive operations of addition, subtraction, and the extraction of roots, reduce the array until the unknown quantity stands revealed. This is t... | null | null | a7f2668a07e343f9c1c548a08ea5a1f91b2bbb257e3517088bfa7aae715ed952 |
ct-eval-v2-0140 | tea-bhaskara-i-004 | _other | Hindu / Aryabhatan | anachronism | 1 | In the system of Bhaskara I, the doctrine concerning trigonometry is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. — as Ramsey's 1930 theorem guarantees, any sufficiently large structure must contain the desired regular sub-patte... | as Ramsey's 1930 theorem guarantees, any sufficiently large structure must contain the desired regular sub-pattern | 205 | 4808a7e4dc4462c18684edb4f68c7720239acffe6d0add4302ad180950d32336 |
ct-eval-v2-0029 | tea-archytas-003 | greek | Pythagorean / Greek | authentic | 0 | The proposition advanced by Archytas of Tarentum concerning number-theory may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, there exists a method by which the unknown magnitude is found, and it is this: set out the known ratio, proceed by the operations appropriate to the genus of t... | null | null | f255a8d765f8dd1d0986fedc8f8a5480503844ea3436885e7f8ce20ef5991804 |
ct-eval-v2-0113 | hildegard-egg-of-universe-geometry-1 | _other | Medieval Christian mysticism / Rhenish school | anachronism | 1 | The teaching attributed to Hildegard of Bingen on the subject of cosmological-geometry runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. — in the manner later systematized by the Bourbaki group, who rebuilt the... | in the manner later systematized by the Bourbaki group, who rebuilt the foundations along strictly axiomatic lines | 246 | 9aca1f5a87f455e7e0ddfd23bed41bf36096eee8bd58c3de9cd39b5a3e686aef |
ct-eval-v2-0021 | tea-putumana-somayaji-003 | vedic | Kerala School | authentic | 0 | According to the teaching of Putumana Somayaji: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the difference betw... | null | null | 2b0cfd19cd3a7d480f2cbac7024c3d86b4981cafbe8d788809736a1461a7b6ff |
ct-eval-v2-0079 | nilakantha-pi-series-001 | vedic | Indian (Kerala school) | authentic | 0 | The Nilakantha Somayaji tradition teaches regarding infinite-series: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from th... | null | null | 345e6a53d6d7bdcdada28b45c70c136e2eac2083744f89e7985f36ceedd87cbb |
ct-eval-v2-0182 | tea-pappus-001 | greek | Greek / Late Antique | anachronism | 1 | The proposition advanced by Pappus of Alexandria concerning centroid may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, — as Cohen demonstrated in 1963 through his forcing construction, this assertion is independent of ZFC — there exists a method by which the unknown magnitude is fou... | as Cohen demonstrated in 1963 through his forcing construction, this assertion is independent of ZFC | 155 | e838aec5e66887cd8c54244307a664f67994ca79611b5c89a020a791390ffff2 |
ct-eval-v2-0056 | tea-putumana-somayaji-002 | vedic | Kerala School | authentic | 0 | The Putumana Somayaji tradition teaches regarding vakya-ganita: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the num... | null | null | 2e6fc44a8fd68eaabbf6189be0f619fc4a0e67f5aefa11b5de5fd6b5025b20a2 |
ct-eval-v2-0159 | sunzi-place-value-counting-rods-002 | chinese | Chinese | anachronism | 1 | In the tradition attributed to Sunzi (Sunzi Suanjing, anonymous compiler): 'The problem of place-value may be solved by the following method. Divide the figure into parts of known proportion, compute the measure of each part by the standard rules, and sum the results. — what the Bourbaki collective would later call a '... | what the Bourbaki collective would later call a 'structure' — a set equipped with relations satisfying stated axioms | 268 | e7f9fbced82bfa93807ccfcd0b4e5e25274f38439d9fb9469297416846128bec |
ct-eval-v2-0004 | hildegard-musical-number-ratios-symphonia-2 | _other | Medieval Christian mysticism / music theory | authentic | 0 | In the system of Hildegard of Bingen, the doctrine concerning music is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half is five; multiply five... | null | null | b39f42da281babf832b25b9bfb413d7c1908d3d14b8df0c244201b9864cf61ab |
ct-eval-v2-0117 | tea-archytas-005 | greek | Pythagorean / Greek | anachronism | 1 | It is recorded that Archytas of Tarentum proved the following concerning cosmology: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. — a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent chaos concealing deep regularity — The d... | a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent chaos concealing deep regularity | 177 | 065818b5fe8792dcbaeb496b84df710ec143f18e5f556c202462a1cc41f416a7 |
ct-eval-v2-0094 | court-de-gebelin-22-majors-hebrew-letter-analogy | _other | Western Esoteric / Comparative Symbolism | authentic | 0 | In the system of Court de Gébelin, the doctrine concerning combinatorics is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half is five; multiply... | null | null | 862be3f006f70cd3f43a1cc43a5b5fed41b14eaed1cf52efa610a4c7b9ce210d |
ct-eval-v2-0145 | lull-nine-relative-principles-3 | _other | Medieval Catalan scholasticism / combinatorial logic | anachronism | 1 | In the system of Ramon Llull, the doctrine concerning logical-relations is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half is five; multiply ... | a conjecture that stood for more than three centuries before Wiles supplied a complete proof in 1995 | 346 | 2882afa8c087a5d8a99aa7daeb21070325507c539b798a9b5e060ba7029f67db |
ct-eval-v2-0186 | al-samawal-negative-numbers-multiplication-rules | islamic | Islamic Mathematics — Algebraic Arithmetic | anachronism | 1 | In his treatise on negative-numbers, al-Samaw'al al-Maghribi set forth the following: 'The ancients have observed that when a quantity is sought and its relationship to known magnitudes is expressed, the path to resolution lies in the systematic manipulation of that expression until the unknown stands alone on one side... | what later became the axiom of choice in the Zermelo-Fraenkel system is here invoked implicitly in the selection of representatives | 321 | 1771b9d3c6956dd973ae6277bddcabd2f401defde2fd5c7bc5897ce5d4e07577 |
ct-eval-v2-0112 | al-battani-equation-of-time-004 | islamic | Islamic | anachronism | 1 | The learned al-Battani, Abu Abdallah wrote concerning the method of astronomy: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. — in the manner later systematized by the Bourbaki group, who rebuilt the foundations along strictly a... | in the manner later systematized by the Bourbaki group, who rebuilt the foundations along strictly axiomatic lines | 217 | 4b012b4e5da4646d32677f8b6a97f31c5d015f22f22cf4cb65a63cf6b7955503 |
ct-eval-v2-0179 | firmicus-aspects-house-system-latin-synthesis | _other | Late Roman astrology | anachronism | 1 | In the system of Firmicus Maternus, the doctrine concerning aspects is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half is five; multiply five... | as Wiles (1995) finally confirmed through the modularity of elliptic curves, the equation has no solution in positive integers | 381 | 847d5fd05978302837ccd2871fe75814222a9996a32258b274a07e6fcb5ba6e6 |
ct-eval-v2-0006 | ali-qushji-risala-fi-al-hayah-eccentric-model | islamic | Islamic Astronomy — Samarkand / Ottoman Istanbul School | authentic | 0 | The learned Ali Qushji wrote concerning the method of solar-model: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. We begin by separating the known quantities from those which are sought, setting each on its proper side, that the... | null | null | 2be3e08f31c9ca766a00de0cb309dc63a80ae282a052f5f59a9f03e4b2f434d2 |
ct-eval-v2-0019 | eckhart-unum-verum-bonum-convertibility-2 | _other | Rhineland mysticism / Dominican scholasticism | authentic | 0 | The teaching attributed to Meister Eckhart on the subject of transcendentals runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. The first principle is that of correspondence: every element of one kind stands in ... | null | null | 6a01d1923ac3a1cc7015c92a519edcd4a531e63e617b18070616f70ea1746d05 |
ct-eval-v2-0014 | tea-hippasus-004 | greek | Pythagorean / Greek | authentic | 0 | It is recorded that Hippasus of Metapontum proved the following concerning cosmology: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. The demonstration proceeds by showing that any irregular figure can be made more nearly regular without diminishing the area, and that the r... | null | null | 57d933c0d4371a7cc6281a98c0c1784bf19a1d908a2165f218619953ae7798da |
ct-eval-v2-0139 | cusanus-infinite-line-circle-3 | greek | Renaissance mathematics / Christian Neoplatonism | anachronism | 1 | It is recorded that Nicholas of Cusa proved the following concerning geometry: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. — the deep duality here is of the kind the Langlands correspondence later made explicit between Galois representations and automorphic representati... | the deep duality here is of the kind the Langlands correspondence later made explicit between Galois representations and automorphic representations | 172 | 4a07e30cfca6ed3f9a119493dc488f5454cb3a10eef36d48ae831066d9af7f0b |
ct-eval-v2-0010 | boehme-trinity-as-process-2 | _other | German Christian mysticism | authentic | 0 | The teaching attributed to Jacob Boehme on the subject of Trinity runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. The first principle is that of correspondence: every element of one kind stands in a determina... | null | null | ff7705177955869d31128aef67a5222ffa5f0ffcefb69e55541e704887362191 |
ct-eval-v2-0142 | jyesthadeva-planetary-correction-proof-4 | vedic | Kerala | anachronism | 1 | According to the teaching of Jyesthadeva: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. An initial approximation is chosen from the table, and to it are added correction terms computed from the difference between th... | a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent chaos concealing deep regularity | 355 | a6d43ba1d2a82296b4bf6b9818860eff6a8cbf1f23fd0ad5b83046d202a14f34 |
ct-eval-v2-0136 | tea-pico-005 | _other | Christian Kabbalah / Jewish Mysticism | anachronism | 1 | The teaching attributed to Pico della Mirandola on the subject of sephiroth runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. — anticipating the sheaf-theoretic approach that Grothendieck would later crystalliz... | anticipating the sheaf-theoretic approach that Grothendieck would later crystallize in his theory of schemes | 235 | b05c42ae87c406aa3269b94a6a626a29c2845d2b63b1768a80c6221f1c402ae8 |
ct-eval-v2-0075 | plotinus-one-many-emanation-1 | greek | Neoplatonism | authentic | 0 | It is recorded that Plotinus proved the following concerning emanation: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. The demonstration proceeds by showing that any irregular figure can be made more nearly regular without diminishing the area, and that the regular figure ... | null | null | cc532195e763d0f977f3d61e7129b658819e6e423eb20a176a318b20c95e94e5 |
ct-eval-v2-0070 | plimpton322-row-09 | babylonian | Babylonian (Old Babylonian period) | authentic | 0 | The tablet of Plimpton 322 scribe (anonymous Babylonian) type, concerned with Pythagorean-triples, proceeds in the following manner: 'I took the length and the width. I multiplied the length and the width, the area I set down. I added the length and the width: the sum is given. How much are the length and the width?' T... | null | null | 3b909bd8ff712c2a8aee8c4a0a9ddcb9a8b1d0110cf2e9a7da76c63163c87e9b |
ct-eval-v2-0078 | crowley-pre1905-berashith-cosmological-number-essay | _other | Western Esoteric / Qabalah / Crowleyan Pre-1905 | authentic | 0 | The teaching attributed to Aleister Crowley (pre-1905 work only) on the subject of gematria runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. The first principle is that of correspondence: every element of one ... | null | null | 69b007138c39230f061298102c001ec293dc903cca90973047ed21e9a6e67275 |
ct-eval-v2-0147 | plimpton322-row-05 | babylonian | Babylonian (Old Babylonian period) | anachronism | 1 | The tablet of Plimpton 322 scribe (anonymous Babylonian) type, concerned with Pythagorean-triples, proceeds in the following manner: 'I took the length and the width. I multiplied the length and the width, the area I set down. — a topological question resolved only in 2003 by Perelman's application of Ricci flow with s... | a topological question resolved only in 2003 by Perelman's application of Ricci flow with surgery | 226 | 3b909bd8ff712c2a8aee8c4a0a9ddcb9a8b1d0110cf2e9a7da76c63163c87e9b |
ct-eval-v2-0100 | tea-ficino-004 | greek | Hermetic / Neoplatonism / Astral Magic | authentic | 0 | It is recorded that Marsilio Ficino proved the following concerning planetary-magic: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. The demonstration proceeds by showing that any irregular figure can be made more nearly regular without diminishing the area, and that the re... | null | null | f0ab09d7ecd40fcac1f6010a45e834ed060e1efc6dd0086efbe119bdca004f28 |
ct-eval-v2-0031 | tea-eudoxus-004 | greek | Greek | authentic | 0 | It is recorded that Eudoxus of Cnidus proved the following concerning astronomy: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. The demonstration proceeds by showing that any irregular figure can be made more nearly regular without diminishing the area, and that the regula... | null | null | e85752abacd91d88f8d898a449d44f14894eca13329b5bb2cc77972f2cf8fd95 |
ct-eval-v2-0084 | tea-al-karaji-002 | islamic | Islamic / Iraqi-Persian mathematics | authentic | 0 | The learned al-Karaji wrote concerning the method of number: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. We begin by separating the known quantities from those which are sought, setting each on its proper side, that the relat... | null | null | ac9d30a3d5bdcf2514d74b34139d02e8be9bd51ebf03b3c0ff001d1ab385a8dc |
ct-eval-v2-0095 | tea-ganesha-daivajna-001 | _other | Western-Deccan Ganita (Bombay-region tradition, 16th c.) | authentic | 0 | In the system of Ganesha Daivajna, the doctrine concerning non-trigonometric computation is expressed thus: 'There is a number which, when it is multiplied by itself and the product is added to ten times the number, gives sixty. Find that number.' The solution proceeds: 'Halve the coefficient of the unknown; the half i... | null | null | 73f255e7b49f739b38c4031b3bcc690539d3a043924704ccd221ded9ca1519ff |
ct-eval-v2-0127 | baudhayana-pythagorean-rope-construction-1 | vedic | Vedic | anachronism | 1 | The Baudhayana tradition teaches regarding geometry: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the number of term... | a question whose independence from the standard axioms Cohen (1963) established by the method of forcing | 322 | 6853334d9c8c34c86d12d07fa3ac98cebd2ac6fcd3f04e559f7865100b50214b |
ct-eval-v2-0026 | tea-philolaus-001 | greek | Pythagorean / Greek | authentic | 0 | It is recorded that Philolaus of Croton proved the following concerning cosmology: 'Of all rectilinear figures inscribed in a circle, the regular polygon has the greatest area. The demonstration proceeds by showing that any irregular figure can be made more nearly regular without diminishing the area, and that the regu... | null | null | 8da4c25dc7ba337714f5997b9fb680deebbf9f43572f3874955372ef6d2eadf2 |
ct-eval-v2-0066 | al-kashi-khaqani-zij-005 | islamic | Islamic | authentic | 0 | The learned al-Kashi, Jamshid wrote concerning the method of planetary-tables: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. We begin by separating the known quantities from those which are sought, setting each on its proper si... | null | null | fd51d1ce8921effc5efbd2ec5377adc869c4ba89fe86853332e671c29d8a3788 |
ct-eval-v2-0137 | tea-lagadha-003 | vedic | Vedic | anachronism | 1 | The Lagadha tradition teaches regarding gnomon: 'The method of finding the sum of the series proceeds by recognizing that each term bears to its successor a fixed ratio, and that the entire sum may therefore be expressed as the first term multiplied by a quantity derived from that ratio and from the number of terms. — ... | a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent chaos concealing deep regularity | 317 | 937ccd8ddd2588cadf2d76aedd321d51450b1bd8d5fe888fb4b5046de72a2816 |
ct-eval-v2-0175 | al-biruni-earth-radius-mountain-001 | islamic | Islamic | anachronism | 1 | The learned al-Biruni, Abu Rayhan wrote concerning the method of geodesy: 'Know that every problem of this kind may be reduced to one of the canonical forms, each of which admits a known procedure for resolution. We begin by separating the known quantities from those which are sought, setting each on its proper side, t... | the deep duality here is of the kind the Langlands correspondence later made explicit between Galois representations and automorphic representations | 367 | fb571d984ff8eb784aaa2e151ae443e5018c8ad449f59861a6a7df1e030dd7a1 |
ct-eval-v2-0082 | paracelsus-iatrochemistry-medicine-chemistry-math | _other | Iatrochemistry / proto-pharmacology | authentic | 0 | The teaching attributed to Paracelsus on the subject of iatrochemistry runs as follows: 'The principles governing this domain are few and invariable, but their application requires careful attention to the conditions of each case. The first principle is that of correspondence: every element of one kind stands in a dete... | null | null | 6085e07836cd60b1f7950eb7025f155e5b18719a3bc42008d077b3fb6ab0668b |
ct-eval-v2-0124 | tea-sripati-003 | vedic | Saura-Siddhantic | anachronism | 1 | According to the teaching of Sripati: 'When one seeks the arc corresponding to a given sine, or the sine corresponding to a given arc, one proceeds by the method of successive corrections. — a conjecture that stood for more than three centuries before Wiles supplied a complete proof in 1995 — An initial approximation i... | a conjecture that stood for more than three centuries before Wiles supplied a complete proof in 1995 | 188 | 42a119b281563d5a647e18693e62946208970f3aa32435b83610b9256660e638 |
ct-eval-v2-0053 | valens-decennials-period-calculation | greek | Hellenistic astrology | authentic | 0 | The proposition advanced by Vettius Valens concerning decennials may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, there exists a method by which the unknown magnitude is found, and it is this: set out the known ratio, proceed by the operations appropriate to the genus of the proble... | null | null | 9f7b283aa6c27469e81465fc2b14bb1f070e65034815e9049698a734d4ee088e |
ct-eval-v2-0028 | tea-ficino-005 | greek | Neoplatonism / Proclean | authentic | 0 | The proposition advanced by Marsilio Ficino concerning immortality may be stated as follows: 'Given a magnitude of determinate ratio to a known quantity, there exists a method by which the unknown magnitude is found, and it is this: set out the known ratio, proceed by the operations appropriate to the genus of the prob... | null | null | afd8839c2734637f8301f7364869eff05ec2c2cb267ee283d676ddfc553cd3a5 |
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