From John Conwill   May 29th 18401

‘My dear Tyndall’2

‘With the man thou lovest ne’er contend

But bear a thousand frailties from thy friend.’3

I feel confident that I have no reason to offer an apology for not furnishing you with a solution to my triangle question;4 as your personal knowledge of my principles precludes further ceremony on my part.

I had the consummate pleasure of reading your soul-thrilling epistle for your dearly beloved mother,5 on whom your language had the effect of an electric shock; so powerful were its effects that in an ecstacy of joy she exclaimed, Oh! my darling son, I knew he had those innate qualifications born with him, though they are aptly denied by logicians. Nor were your sentiments heard with less enthusiasm by your father and sister and my mother. I almost forgot, your mother expects that you will not pamper your whiskers too much, because she has been informed that Munster6 men are not fond of hairy faces.

I now stand far above the reach of my most inveterate opponents.7 I am a first class teacher under the auspicies of the Board,8 receiving twenty pounds per annum. Next August there will be an examination of teachers in Graigue Carlow National School,9 at which I hope to make an able display, and hold up to public gaze many empirics who are impeding the progress of literature and debilitating the march of intellect through the base power of lordly influence.10

I fear you are greatly annoyed by those satellites or wandering stars by which you are encompassed: that you may hurl them from their orbits and make them run lawless through the sky, I shall now commence with the questions.11

To bisect an isosceles triangle by a line parallel to the base, by the first book of Euclid.

Let ABC be the [isosceles] triangle [Figure 112]. Make the [quadrilateral] HGOT = [in area to the] ∆ABC, having the ∠GOT = ∠BAC: if HGOT be a rhombus, make AF = GO; draw FE parallel to BC, and you have ABC bisected as required.

If HTOG be not a rhombus, produce GO if necessary, to P, bisect GP in N, erect NO perpendicular to GP, making LNG2=LACD, CD being perpendicular to AB; from Q as centre and inter- QG describe the ONMGKLP; produce 2N and TO to K and L; join GL and describe a rhombus on GL having ∠GLT = ∠BAC or ∠GOT; make AF=KT, and draw FE parallel to BC and the thing is done.13

Demonstration. Join GH, KP, LP, 2P, SP and LH. Produce K2 to N and draw L2N. ∠NG2 and GN2 - ∠ACD and ADC,.. ∠G2K-BAC, whence it is easy to show that the circle passes through P, that ∠GK2X ∠PK2 - ∠ABCX ∠ACB; that ∠G2NX ∠P2N-2 ∠GBP, that ∠G2MX ∠P2M-2 ∠GLP; and that ∠G2NX ∠P2N - ∠G2MX ∠P2M... ∠GKP-GLP: wherefore PLT is a straight line, and it may be shown that SGP- LGH, and of course [quadrilateral] GSTK=[quadrilateral]HGOT=∆ABC. Consequently ∆GST = ∆AFE = half ∆ABC.14

Q. E. D.15

To bisect any triangle by a line parallel to the base without passing the first book of Euclid.16

Let ABC be the given triangle [but not isosceles]. It is easy to make the isosceles ∆ABD [where D is on BC, such that AD = AB]; bisect the ∆ABD by means of the parallel line TH according to the preceding method and produce FH to I; GI bisects ∆ABC.

Demonstration. It is plain ∆AOD - ∆BOC, hence EO-OF, EF being parallel to AB. If not one is greater than the other; let EO be the greater then ∆EODX ∆EOA would be greater than ∆FOCX ∆FOB, that is AOD would be greater than BOC, an absurdity; wherefore ∆EODX _EOG- ∆FOCX ∆FOH, and whence the ∆AGE ∆BHF; from this FG-HI; if not, let FG be greater than HI; then ∆FGEX _FGA will be greater than HIFX ∆JHB, that is AGE is greater than ∆BHF, an absurdity; ergo FH-IG, and ∆FHD - ∆IHC- _CAB.17

Q. E. D.

Given the hypothenuse of a right angled triangle to construct it, so that the rectangle under the difference of the legs18 and hypothenuse will be equal the area of the triangle.

Given the sum of the base and perpendicular and the perpendicular from the right angle on the hypothenuse, to construct the triangle by the first book of Euclid.

I cannot send you any more problems in this letter, when I write again, I will send you ten more, which will constitute the twelve apostles, in a geometrical point of view. With all due respect I remain your ever affectionate teacher

J. Conwill

RI MS JT/1/11/3510

LT Transcript Only

30 May 1840: In letter 0006 Conwill referred to Sarah Tyndall’s receipt of ‘your soul-thrilling epistle’. It is not clear whether he was referring to this letter (if so, one of the two is wrongly dated) or to a letter that is missing.

‘My dear Tyndall’: In LT’s typescript of this and other letters from John Conwill, the opening greeting ‘My dear Tyndall’ appears in quotation marks. These quotation marks, which occur only in letters from Conwill, have been retained since they may possess some meaning which the editors have not been able to ascertain.

With the man … thy friend: ‘Oh, never with the man thou lov’st contend! | But bear a thousand frailties from thy friend’, Thomas Fitzgerald, ‘Golden Verses of Pythagoras’.

a solution to my triangle question: not identified as Tyndall’s preceding letter to Conwill is missing.

soul-thrilling epistle for you dearly beloved mother: Tyndall appears to claim that letter 0006 – next letter – was the first sent to his mother. If that is the case then this letter and letter 0006 are in the wrong order.

Munster: The province in the south west of Ireland comprising counties Clare, Cork (where Tyndall was stationed), Kerry, Limerick, Tipperary and Waterford.

my most inveterate opponents: Probably the school inspectors whom Conwill despised.

the Board: The National Board of Education had been initiated by Parliament in 1831 with two members drawn from each of the three main religious communities – Roman Catholic, Church of Ireland and Presbyterian. National schools were required to demarcate between secular and religious subjects; thus, Conwill confined his religious teaching to Saturdays and 9–10 a.m. on weekdays, but parents could withdraw their children from those lessons.

Graigue Carlow National School: Slater’s (p. 21) lists Michael Henessy as the master of the National School at Graigue, the suburb of Carlow on the west side of the River Barrow.

many empirics who are impeding the progress of literature and debilitating the march of intellect through the base power of lordly influence: Presumably a reference to those aristocrats and landowners who wished to limit school education to pragmatic subjects.

the questions: A number of errors occur in LT’s transcription of the following paragraphs. The editors have tried to reconstruct the geometrical arguments to the best of their ability and have added a diagram; LT’s typescript does not include the diagrams that would have appeared in the original letters.

Figure 1:

diagram

If HTOG … thing is done: In this paragraph Conwill addresses the general case of a quadrilateral that is not a rhombus, by transposing it to the case of a rhombus and then using the result established in the previous paragraph. Working from the text of the typescript a reconstruction has been attempted.

Join GH … half ∆ABC: Based on typescript transcription; no original available. Reconstruction not attempted.

Q. E. D.: abbreviation of ‘quod erat demonstrandum’, Latin for ‘which was demonstrated’.

To bisect … first book of Euclid: Cf. method used by Miles Bland, Geometrical Problems Deducible from the First Six Books of Euclid (Cambridge: A. Smith, 1819), p. 172.

It is plain … CAB: Based on typescript transcription; no original available. Reconstruction not attempted.

legs: A leg is ‘one of the sides of a triangle, viewed as standing upon a base’ (OED).

Please cite as “Tyndall0005,” in Ɛpsilon: The John Tyndall Collection accessed on 28 March 2024, https://epsilon.ac.uk/view/tyndall/letters/Tyndall0005