Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-06-30T08:48:50.109501Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-06-30T08:48:50.109501Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
56 of 56 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation ae0c3b37-b577-49b0-94b9-a92b01ce0385 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 120 & Figure
Reference 1
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.
Observation 21aa5478-7057-44a0-91d4-3cb10e8ddfe9 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics true ray
Reference 2
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.
Observation cc792cb2-b8f1-46ee-870d-75d7efc86838 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 3
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.
Observation d78f6267-d023-499b-af02-7340963ffcfe · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics exterior or apparent
Reference 4
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.
Observation 3ce1fc75-99e3-4b34-b8c2-f2b2b8264dff · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 5
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.
Observation 68d7c387-08d5-45a8-9f47-40a25ea8abe0 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 6
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.
Observation 759c716b-b1d0-4f6f-b5f0-933bacdff33f · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 7
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.
Observation 9fac24df-c8dc-4d3e-8424-29d5b3234e0a · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 8
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.
Observation c1d97641-6029-4009-8157-c88ab670b456 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 1 (Definition 9)
Reference 9
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.
Observation b887e823-1a1b-491f-97b4-738363d3d6c4 · outbound
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
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.
Observation 85c13475-86d8-4143-9362-092f286df39e · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics [distant]
Reference 11
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.
Observation db98598b-c268-4e68-bbc4-66a3d80181eb · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 12
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.
Observation 5014ca4b-c8a3-413f-a7e1-090bc3a0f531 · outbound
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
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.
Observation 96234e74-a109-4673-8878-4e87c21537f4 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 223, quoted in translation by Shapiro (1990, p
Reference 14
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.
Observation 9cf86f5e-312c-4e68-ae0d-50e79bf6db17 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics destroys
Reference 15
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.
Observation 3d53b35e-c7aa-4393-9f95-75dd82e3ab59 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 4, quoted in translation by Shapiro, 1990, p
Reference 16
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.
Observation 4d7c4201-54cb-48cc-bbb5-268257d72a31 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 144, 159–65
Reference 17
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.
Observation 8296d2ce-951a-4af5-8a7d-7fbe82f9285d · outbound
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
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.
Observation 3754e525-ac91-43a9-9e26-948458602c62 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 160, line
Reference 19
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.
Observation f6d3cf36-6974-4713-a9b7-6c09db3c68c5 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 175 Berkeley (1901), p
Reference 20
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.
Observation 60a468a5-b935-4a60-a704-d935033e977d · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics light. . . again collected in one place
Reference 21
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.
Observation 1297decf-ab1c-40d4-a0e9-b465964afd83 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 194–5, with further commentary in Smith, 2017, pp
Reference 22
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.
Observation 5f06a079-ae67-47da-abe0-9a652e8f73ce · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 23
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.
Observation 9fe8476e-369e-41e6-a739-40c0659379b3 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics seem to diverge
Reference 24
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.
Observation f17ae8e8-be64-47c7-a69f-83f3733bfd37 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics relative
Reference 25
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.
Observation 7ca4c440-89e7-4589-99f6-bd28fae25dd1 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 28, 74–5; Shapiro, 1990, pp
Reference 26
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.
Observation 71bc2984-ec41-427c-8e4c-33c52cbab10b · outbound
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
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.
Observation 848f38b0-ae83-49d9-adc0-7263d866f914 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 195 Shapiro, 1990, pp
Reference 28
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.
Observation 34ebc83b-afa4-454b-aad9-18464cdd25c2 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 128–30; Kepler /Donahue, 2000, pp
Reference 29
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.
Observation b95a7305-f17e-4ce7-99bb-0a769c205750 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 30
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.
Observation f308d46f-7e83-4a7a-849b-3698e378b674 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics not inelegant
Reference 31
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.
Observation ea64e39b-7247-410c-b7f7-0a0e8ea8f2a1 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 85–6 (Prop
Reference 32
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.
Observation 87353206-21b0-4a03-8538-07e44466f2c5 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Axioms and their Explications
Reference 33
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.
Observation c717da86-4977-4b60-a6d1-8db526ca1c1f · outbound
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
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.
Observation 91b1e218-d5a4-461d-a41e-3a9909e6cf9f · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 92–3 & n
Reference 35
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.
Observation 06864496-6693-411a-adc6-894aac2baa06 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics inflected
Reference 36
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.
Observation de64a19d-a723-4572-8dab-f85a4ad9052f · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics 89, end of Prop
Reference 37
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.
Observation 9f1bf0ef-63a2-4637-ae03-f5391a9a3793 · outbound
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
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.
Observation a8dd9981-2ca0-4787-a1ef-f73198691e6a · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics optical axis
Reference 39
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.
Observation 0a04f2b4-8e1c-4d92-8448-a63e2fc531c1 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 40
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.
Observation 53f9915e-ae98-4ff6-bfb4-81ee8fdf9e4a · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics the axis itself is considered as the second light ray
Reference 41
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.
Observation d4a87922-4a7f-4273-98f7-f9f02310f10c · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Gaussian formula
Reference 42
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.
Observation 49e5a382-da4f-41b2-9be1-d7f36bf50bd2 · outbound
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
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.
Observation b895a99c-38ee-41e7-ab1b-ff1fc2e50eff · outbound
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
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.
Observation 2211f84f-fc9a-4781-9b1a-d420c61e1165 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics VII. Axioma
Reference 45
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.
Observation a9460c07-881a-4055-aabf-f44461218db1 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics A cathetus by any other name
Reference 46
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.
Observation 94fc3279-c8df-4ee1-a132-81da020e76ac · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics two candidates
Reference 47
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.
Observation fae751c5-33c5-4342-89a2-929751c01744 · outbound
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
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.
Observation 3d10beee-ff89-41ce-90e0-148b0c0d9f32 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics auxiliary axis
Reference 49
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.
Observation 8ba3881b-613c-490a-98fe-4334774ca948 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics as is often incorrectly asserted in the literature
Reference 50
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.
Observation 844fb559-c52a-467e-8a77-3d122fc8ba4f · outbound
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
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.
Observation 76ea3903-8f80-4a5f-8f11-bcbf05871437 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Unresolved cited work
Reference 52
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.
Observation 4188ee77-b511-43be-a8e5-7d123f465aa2 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics To the first order
Reference 53
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.
Observation 1ed9871a-769c-446f-af31-aeef2f231529 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics Bacon, tr
Reference 54
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.
Observation a7157868-e4c6-4106-b13c-3657183e5dd6 · outbound
The unreasonable effectiveness of the cathetus rule in ancient and modern optics An essay towards a new theory of vision
Reference 55
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.
Observation 90c16143-ef0b-4a34-a6ca-72d22cb81c04 · outbound
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
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.
No inbound Pith citation observations are available.