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Paper Citation Record · LEDGER

The unreasonable effectiveness of the cathetus rule in ancient and modern optics

As of 13 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 0 inbound Pith citation observations for arXiv:2606.28851.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.28851 v1

Coverage vector

measured 56 of 56 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-30T08:48:50.109501Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

56 of 56 outbound references displayed

  • verified exact1
  • verified fuzzy43
  • unresolved4
  • parse uncertain6
  • malformed identifier1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ae0c3b37-b577-49b0-94b9-a92b01ce0385 · outbound

This paper cites 120 & Figure.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 120 & Figure

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 21aa5478-7057-44a0-91d4-3cb10e8ddfe9 · outbound

This paper cites true ray.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics true ray

Reference 2

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation cc792cb2-b8f1-46ee-870d-75d7efc86838 · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 3

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation d78f6267-d023-499b-af02-7340963ffcfe · outbound

This paper cites exterior or apparent.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics exterior or apparent

Reference 4

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 3ce1fc75-99e3-4b34-b8c2-f2b2b8264dff · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 5

Resolution
parse uncertain
raw_fallback, observed 2026-07-10T14:07:07.178907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 68d7c387-08d5-45a8-9f47-40a25ea8abe0 · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 6

Resolution
parse uncertain
raw_fallback, observed 2026-07-10T14:07:07.188054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:982244ffa96aac09a91dc4d515714b7a0da7c7f9fcd68e8a2f78de771eefe048

Observation 759c716b-b1d0-4f6f-b5f0-933bacdff33f · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-07-10T14:07:07.171294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 9fac24df-c8dc-4d3e-8424-29d5b3234e0a · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 8

Resolution
parse uncertain
raw_fallback, observed 2026-07-10T13:47:06.778377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation c1d97641-6029-4009-8157-c88ab670b456 · outbound

This paper cites 1 (Definition 9).

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 1 (Definition 9)

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.143277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation b887e823-1a1b-491f-97b4-738363d3d6c4 · outbound

This paper cites yow shall discerne nothinge thorowe the glasse: But like a myst, or water.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics yow shall discerne nothinge thorowe the glasse: But like a myst, or water

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T13:47:06.776083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 85c13475-86d8-4143-9362-092f286df39e · outbound

This paper cites [distant].

The unreasonable effectiveness of the cathetus rule in ancient and modern optics [distant]

Reference 11

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation db98598b-c268-4e68-bbc4-66a3d80181eb · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-07-10T14:07:07.132693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 5014ca4b-c8a3-413f-a7e1-090bc3a0f531 · outbound

This paper cites 80 & 82 are used in Kepler’s subsequent explanation of the magnify- ing power of a Dutch telescope; see Malet, 2003 at p.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 80 & 82 are used in Kepler’s subsequent explanation of the magnify- ing power of a Dutch telescope; see Malet, 2003 at p

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.160839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 96234e74-a109-4673-8878-4e87c21537f4 · outbound

This paper cites 223, quoted in translation by Shapiro (1990, p.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 223, quoted in translation by Shapiro (1990, p

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.130513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 9cf86f5e-312c-4e68-ae0d-50e79bf6db17 · outbound

This paper cites destroys.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics destroys

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T13:47:06.790583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 3d53b35e-c7aa-4393-9f95-75dd82e3ab59 · outbound

This paper cites 4, quoted in translation by Shapiro, 1990, p.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 4, quoted in translation by Shapiro, 1990, p

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.127157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:1fbd75ee4617624db6a469dcd2780ca286ab7b447f1b57fb8a7d0febc550adda

Observation 4d7c4201-54cb-48cc-bbb5-268257d72a31 · outbound

This paper cites 144, 159–65.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 144, 159–65

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.175463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:ffec5e9bc01792add83b22db3bba719502d5f8fd98cd4fdecd380c7c217b6d1c

Observation 8296d2ce-951a-4af5-8a7d-7fbe82f9285d · outbound

This paper cites the object appearing extremely near begins to vanish into mere confusion.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics the object appearing extremely near begins to vanish into mere confusion

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.166137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 3754e525-ac91-43a9-9e26-948458602c62 · outbound

This paper cites 160, line.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 160, line

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.148616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation f6d3cf36-6974-4713-a9b7-6c09db3c68c5 · outbound

This paper cites 175 Berkeley (1901), p.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 175 Berkeley (1901), p

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.172809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 60a468a5-b935-4a60-a704-d935033e977d · outbound

This paper cites light. . . again collected in one place.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics light. . . again collected in one place

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.136160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:236071868ec04987a93cd214a1dc0018fd40ff9904f172598c09716614c02616

Observation 1297decf-ab1c-40d4-a0e9-b465964afd83 · outbound

This paper cites 194–5, with further commentary in Smith, 2017, pp.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 194–5, with further commentary in Smith, 2017, pp

Reference 22

Resolution
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raw_fallback, observed 2026-07-10T14:07:07.155510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 5f06a079-ae67-47da-abe0-9a652e8f73ce · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-07-10T14:07:07.164344Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 9fe8476e-369e-41e6-a739-40c0659379b3 · outbound

This paper cites seem to diverge.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics seem to diverge

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.137835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation f17ae8e8-be64-47c7-a69f-83f3733bfd37 · outbound

This paper cites relative.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics relative

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T13:47:06.775481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 7ca4c440-89e7-4589-99f6-bd28fae25dd1 · outbound

This paper cites 28, 74–5; Shapiro, 1990, pp.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 28, 74–5; Shapiro, 1990, pp

Reference 26

Resolution
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raw_fallback, observed 2026-07-10T13:47:06.773774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:d92b1d9d0202ff7494565346eb242ba73c20cbc845b5de5bbd27a6efdc51a914

Observation 71bc2984-ec41-427c-8e4c-33c52cbab10b · outbound

This paper cites That the former is the limit of the latter follows from the displayed equation on p.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics That the former is the limit of the latter follows from the displayed equation on p

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.183565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:b04a8c7ebcf23495ccb5eaf422bcd022f851bd83974c58313745c59bb517281f

Observation 848f38b0-ae83-49d9-adc0-7263d866f914 · outbound

This paper cites 195 Shapiro, 1990, pp.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 195 Shapiro, 1990, pp

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.139472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:f71747b45b355ab1d16f607a873c85470ec2cb4b4f9a2c325dbb7c8adb2b4ec7

Observation 34ebc83b-afa4-454b-aad9-18464cdd25c2 · outbound

This paper cites 128–30; Kepler /Donahue, 2000, pp.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 128–30; Kepler /Donahue, 2000, pp

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.141704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation b95a7305-f17e-4ce7-99bb-0a769c205750 · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-07-10T13:47:06.767208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:0fb0f3f907f54fb96966841c108000289d775eea4dd1e772585de4bb9a628092

Observation f308d46f-7e83-4a7a-849b-3698e378b674 · outbound

This paper cites not inelegant.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics not inelegant

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T13:47:06.788326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:dc766e827b6a32c86a08e64e77351ad2456e7ae021cf8341c5bc623a381dc331

Observation ea64e39b-7247-410c-b7f7-0a0e8ea8f2a1 · outbound

This paper cites 85–6 (Prop.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 85–6 (Prop

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T13:47:06.785335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:7affe50730688ee0563ec1e4a5f8ad423785c6d220b63aac8584a7d89971ddca

Observation 87353206-21b0-4a03-8538-07e44466f2c5 · outbound

This paper cites Axioms and their Explications.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Axioms and their Explications

Reference 33

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raw_fallback, observed 2026-07-10T13:47:06.784624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation c717da86-4977-4b60-a6d1-8db526ca1c1f · outbound

This paper cites these Rays do make the same Picture in the bottom of the Eyes as if they had come from the Object really placed ata.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics these Rays do make the same Picture in the bottom of the Eyes as if they had come from the Object really placed ata

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T13:47:06.780430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:d02cbca72409d683eeaa472166399e876caa1f645cf340eec165649dc4002279

Observation 91b1e218-d5a4-461d-a41e-3a9909e6cf9f · outbound

This paper cites 92–3 & n.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 92–3 & n

Reference 35

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verified fuzzy
raw_fallback, observed 2026-07-10T13:47:06.769552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:05a2dd409e43ef5ff54ba3957d574889795098d304bc8c6a2ba2137388114fb5

Observation 06864496-6693-411a-adc6-894aac2baa06 · outbound

This paper cites inflected.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics inflected

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T13:47:06.764740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:48368e7a8c362ca4153318f97f89291766e4b11eb77719ba051473e3988c29e5

Observation de64a19d-a723-4572-8dab-f85a4ad9052f · outbound

This paper cites 89, end of Prop.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 89, end of Prop

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.147043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:9763ebd374ab5c8573c8d514cc0fe80ec6fc81cc8585c86848f49183813371ec

Observation 9f1bf0ef-63a2-4637-ae03-f5391a9a3793 · outbound

This paper cites 131–2; the diagram is upside-down for an air-water surface.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics 131–2; the diagram is upside-down for an air-water surface

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.191182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:214448520867a2e8143e7cf3597be4c77b9b876bb6dba375a277092085905dff

Observation a8dd9981-2ca0-4787-a1ef-f73198691e6a · outbound

This paper cites optical axis.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics optical axis

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.162532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:c701341b57d8a8ea9d46bb74e44fa85cc64361beed90cd2f4de3529ae4370a45

Observation 0a04f2b4-8e1c-4d92-8448-a63e2fc531c1 · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 40

Resolution
parse uncertain
raw_fallback, observed 2026-07-10T14:07:07.128984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:b2b72640b38fcfa9b0e678b266864261e475dc907349047a7aa2b1ed90ab132e

Observation 53f9915e-ae98-4ff6-bfb4-81ee8fdf9e4a · outbound

This paper cites the axis itself is considered as the second light ray.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics the axis itself is considered as the second light ray

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.145424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:43f808b6b88a15e03c64352ed5ff598556edc4bac78bb086962e2bb5e0bd7291

Observation d4a87922-4a7f-4273-98f7-f9f02310f10c · outbound

This paper cites Gaussian formula.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Gaussian formula

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.159018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:9d2f2d0122e626f6c7b4ced738adf7ec8677f5f4a91d2045bc81d944519ac4b0

Observation 49e5a382-da4f-41b2-9be1-d7f36bf50bd2 · outbound

This paper cites Now it is clear from the symmetry that s′ is an even function of α−ϕ′.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Now it is clear from the symmetry that s′ is an even function of α−ϕ′

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.185894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:0960ae9bda05d1901270717a39fa93758ce9af14dbb4165142c0c1b0cf4bde43

Observation b895a99c-38ee-41e7-ab1b-ff1fc2e50eff · outbound

This paper cites Let the distances OP and PI be respectively σ and σ′ (as shown).

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Let the distances OP and PI be respectively σ and σ′ (as shown)

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.190238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:a45d8a76d0f0b7a9ad357e572c08e8f4e73abbf0f5d63222a8bbf476b76cce22

Observation 2211f84f-fc9a-4781-9b1a-d420c61e1165 · outbound

This paper cites VII. Axioma.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics VII. Axioma

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.167862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:5c0aa02fa3a9072270b3c7ee05a938779fa6b5f3d813eb04e045cb28e25c0774

Observation a9460c07-881a-4055-aabf-f44461218db1 · outbound

This paper cites A cathetus by any other name.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics A cathetus by any other name

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.181304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:8a31031b877c0b5358892dae8abdaaf4c04f4d26ef16f0d8715ca473a9420b4f

Observation 94fc3279-c8df-4ee1-a132-81da020e76ac · outbound

This paper cites two candidates.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics two candidates

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.134152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:6c8a1705ddc774aab756e6645e8a57a462286a7ddf1b3d8bf434d831abc755c4

Observation fae751c5-33c5-4342-89a2-929751c01744 · outbound

This paper cites If in place of ray 4 another ray were drawn throughC and parallel to ray 3,.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics If in place of ray 4 another ray were drawn throughC and parallel to ray 3,

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.153961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:fc08b154b72d4111d74d9e54944b523c6af017d3bf9c0be21105e989dec9a915

Observation 3d10beee-ff89-41ce-90e0-148b0c0d9f32 · outbound

This paper cites auxiliary axis.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics auxiliary axis

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.125257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:6c795172bf6cc30055679f36133791d59d4110e5b83a4d21beb22cdd954bfa06

Observation 8ba3881b-613c-490a-98fe-4334774ca948 · outbound

This paper cites as is often incorrectly asserted in the literature.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics as is often incorrectly asserted in the literature

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.123187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:1389159d9ba6c4985b49abcc506c6bb921a624b592a9fc9b62e48134cb0c9872

Observation 844fb559-c52a-467e-8a77-3d122fc8ba4f · outbound

This paper cites In our Figure 6, thesagittal plane after refraction is the plane perpendicular to the plane of the diagram and containing the ray PI.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics In our Figure 6, thesagittal plane after refraction is the plane perpendicular to the plane of the diagram and containing the ray PI

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.169579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:bda81f654cd22a4de1a0de15cd04863fbf4d51f294e6b68ef522f26cd86c5a75

Observation 76ea3903-8f80-4a5f-8f11-bcbf05871437 · outbound

This paper cites an unresolved cited work.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work

Reference 52

Resolution
parse uncertain
raw_fallback, observed 2026-07-10T13:47:06.773431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:4f1097db4b1fc1e1e03639be86242adac40ba43b9877a581a7d54ff279855d84

Observation 4188ee77-b511-43be-a8e5-7d123f465aa2 · outbound

This paper cites To the first order.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics To the first order

Reference 53

Resolution
malformed identifier
doi_truncated, observed 2026-06-30T08:54:28.977958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:5aa8c882b12b4544f8d22e2a7c512b1f6f57b32655110f8f1a9d4e064f5be48f

Observation 1ed9871a-769c-446f-af31-aeef2f231529 · outbound

This paper cites Bacon, tr.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Bacon, tr

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-07-10T14:07:07.157451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:8c8d56ee76668c27c63627fd241cfdd45708896e94afef628a28aadfe00941dd

Observation a7157868-e4c6-4106-b13c-3657183e5dd6 · outbound

This paper cites An essay towards a new theory of vision.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics An essay towards a new theory of vision

Reference 55

Resolution
verified exact
arxiv_id, observed 2026-06-30T08:54:28.982805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:4e4a008aef016e7a99c61948b872d62bf2cbbaa9edc30ebb428feb2e22379a98

Observation 90c16143-ef0b-4a34-a6ca-72d22cb81c04 · outbound

This paper cites Once Snell breaks down: From geometrical to physical optics in the seventeenth century.

The unreasonable effectiveness of the cathetus rule in ancient and modern optics Once Snell breaks down: From geometrical to physical optics in the seventeenth century

Reference 56

Resolution
metadata mismatch
arxiv_id, observed 2026-06-30T08:54:28.988442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-06-30T08:48:50.109501Z digest=sha256:4e6cbdd7f5d5c48a605f4cb9d943bb3f8120ca0a93134946b0d753da9d16fd24

Pith citing papers

No inbound Pith citation observations are available.