On Euclid

    On Euclid
    November 27, 2020 TeSplendente

    Euclid is first encountered by Anne in the Journals during early studies with Reverend Samuel Knight back in 1808. Mr. Knight, a Cambridge alum, taught the prevailing curriculum of the day of which the Elements were a staple. The first Journal mention is Saturday, 13 February, 1808, where at the age of 16 Anne notes, using the Greek alphabet, “Began Euclid” (SH:7/ML/E/26/1/0022/F.28). This was accomplished between corresponding with Eliza Raine, giving lessons to Miss Maria Alexander, and learning about the quadratic.

    “Saturday 13th [Began Euclid] – “

    Euclid is something Anne visits many times and it is unclear in the journals which edition was used, or even if the same edition was used: at the age of 18, 1809, June 8th, Thursday, “began to look Euclid over again by myself,” (SH:7/ML/E/26/1/0032/F.12):

    “Thursday 8 … began to look Euclid ^over again by myself”

    and again at the age of 25, 1816, October, 22, Tuesday (SH:7/ML/E/26/2/0008/R.52, R.83) “Began Euclides,” and in the Literary Index, “Euclid. -”

    “[October] Tuesday 22 Began Euclid -“

    “[October] 22 – Euclid. -“

    It is on 13 May, 1817, after “Mariana Left Us” (1817 February 27), where for the fourth time and at the age of 26, Anne starts at the beginning of Elements with Book 1, Propositions 1-7 (being studied against Demosthenes de corona and Aschines contra Ctesiphon). Here Anne diligently embarks on a “Scheme of a plan of study -” (SH:7/ML/E/1/0082) marking a turning point with the Post-Mariana vow (SH:7/ML/E/1/0011/V.05-13):


    “- and between 1 and 2 the first 7 propositions of the 1st book of Euclid – with which I mean to renew my acquaintance proceed diligently, in the hope that, if I live, I may sometime attain a tolerable proficiency in mathematical studies – I would rather be a philosopher than a polyglot, and mean to turn my attention eventually and principally to natural philosophy – For the present I mean to devote my mornings before breakfast to Greek, and afterwards, till dinner, to divide the time equally between Euclid and Arithmetic”

    This path is followed with adaptations to the schedule and in the Journals on Friday, 27 June, 1817, (SH:7/ML/E/1/0022/V.10-11) (SH:7/ML/E/1/0081/R.) the first six books outlining the elements of plane geometry and the theory of proportions are completed:

    “- Finished book 6 Euclid i.e. did propositions B,C,&D – and / looking on the definitions of lib. 11 and the book of Data –” / [Margin Vertical] “Got thro’ the 1st 6 / books of Euclid”

    “+ 27 Got thro’ the 1st 6 books of Euclid”

    It is unclear from the Journals whether or not Anne read through the first six books in the autumn of 1816, or during the second attempt in 1809 (perhaps there is more on this in the notebooks and indexes), but there is an annotation that the first time through this gauntlet was Friday, 19th August, 1808 to 17th September, 1808 (SH:7/ML/E/26/1/0011):

    “[August] Friday 19 Began 6th lib Euclid -“

    “[September] Saturday 17th finished 6th lib Euclid -“

    Prior to advancing to Book VII, Anne does it all again! Just to be clear. Monday, June 30th, 1817 (SH:7/ML/E/1/0081/R.16-17):

    “- Began Euclid a 2nd time and did 9 Propositions lib. 1 -“

    “Began Euclid 2nd time – begin to wean myself / from the thought of Mariana

    Nearly a month later on Friday, 25th July, after completing the days literary comparisons of Book 12 of Homer’s Iliad in Greek against two different translations in English (Cowper and Pope), and uncomfortably just prior to embarking on the crypted “The French Pox.”  Anne encounters the 13th Proposition in Book 2 (~ the Law of Cosines, used in triangulation), this the third time having noted the second recent attempt two days previous on Jul 23rd, (SH:7/ML/E/1/0027/B.28) and doubled in the index ((SH:7/ML/E/1/0081/R.40):

    “prop 6-13 liber 2 Euclid”

    “Did the 2 last propositions (13 and 14) of liber 2, and the first / 8 propositions of liber 3 Euclid – I know not how it is, but, as for the 13th proposition liber 2 I was very / stupid about it, the last time I did it over the 1st six books of Euclid and tho’ I have / comprehended it thoroughly this morning, yet it has cost me above 1/2 hour – it / is certainly my pons asinorum instead of proposition 5 liber 1 which Mr. Knight used to tell / me was always called by this name at Cambridge -“

    “Lib. 2 proposition 13 Euclid My pons asinorum”

    Proposition 5, Liber 1, (the isosceles triangle theorem) recollects the day of the vow and remains known as the pons asinorum. ‘Pons‘ translating to ‘bridge’ and ‘asinus‘ to ‘ass’ – a beast of burden. Its first known use was in 1645, or 1780, or 1494 depending on which source is consulted. (Though, there is some consensus around the diagrams of Petrus Tartarus.) In logic it is “a method for finding the middle term of a syllogism in Aristotlean analytics.” And recalls Horace’s maxim : Segnius irritant animos demissa per aurem, Quam quae sunt oculis subjecta sidelibus (A feebler impress through the ear is made, Than what is by the faithful eye conveyed.) This is not an issue for Anne, altitude is her thing. Proposition XIII Liber II includes the maxim: The whole is based on the parts and the interaction between them. The journals and indexes indicate that this, for Anne, may be an obsession.

    [This sidetrack was first posted on an early iteration of ELU, Friday, November 27th 2020, it is being re-posted with the new(ish) site, its largely a dry listing of entries that are read in the space around and between.]

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