Lovelace-De Morgan Correspondence

AAL to ADM	ADM to AAL
Folios 48, 49, 164, 163, 165, 13 Sept 1840 Dissatisfied with progress; seeks clarification of meaning of ‘equation of a curve’ and ‘functional equation’ Transcription, 49v-48r, 48v-49r, 163r-164v, 165r Folios 146–148, 16 Nov 1840 Differential coefficients; manipulation of functions; a little trigonometry Transcription, 147v-146r, 146v-147r, 148r, 148v Folios 149–151, 27 Nov 1840 Functional equations Transcription, 150v-149r, 149v-150r, 151r, 151v Folios 62–67, 10 Nov 1840 Difficulties over the meaning of differentials; fractional expressions; proofs of the binomial theorem; comments on the necessarily slow and painstaking nature of learning mathematics, with a remark on how the ‘University’ method must be prejudicial to understanding in the long run; is puzzling over composition of ratios Transcription, 63v-62r, 62v-63r, 65v-64r, 64v-65r, 67v-66r, 66v-67r Folios 68–69, 17 Dec 1840 Remarks on how the poor weather is keeping her indoors doing mathematics; persists on a point of convergence that was apparently discussed earlier in the week (Monday evening) Transcription, 69v-68r, 68v-69r Folios 70–73, 22 Dec 1840 Now sees her mistake regarding a series previously discussed; learns from, and no longer regrets, such mistakes; seeks clarification over incommensurables and ratio Transcription, 71v-70r, 70v-71r, 73v-72r, 72v-73r Folios 74–76, 4 Jan 1841 More-or-less direct continuation of the previous: series and ratio Transcription, 75v-74r, 74v-75r, 76r, 76v Folios 77–83, 10 Jan 1841 Series; differential coefficients Transcription, 78v-77r, 77v-78r, 80v-79r, 79v-80r, 82v-81r, 81v-82r, 83r, 83v Folios 91–95, Jan 1841 Details of proof of binomial theorem; more series, inc. exponential and logarithmic; Christmas plans Transcription, 92v-91r, 91v-92r, 94v-93r, 93v-94r, 95r Folios 84–87, 17 Jan 1841 Limits of series of fractions; remaining difficulties over differential coefficients, which she feels she ought to have got to grips with by now Transcription, 85v-84r, 84v-85r, 86r, 86v-87r Folio 156, Jan 1841 Rearrangement of meeting Transcription, 156r, 156v Folio 88, 22 Jan 1841 Nothing mathematical: arrangement to call round on Monday evening, without Lord Lovelace Transcription, 88r, 88v Folios 54-57, Feb 1841 Seeks clarification of various issues: functions of two variables, logarithms (Napierian in particular) Transcription, 55v-54r, 54v-55r, 57v-56r, 56v-57r Folios 89–90, 3 Feb 1841 More on limits of fractions Transcription, 90v-89r, 89v-90r Folios 96–98, 6 Feb 1841 Was too hasty in sending letter of Weds, for now understands the matter at hand (on fractions); resolves to rein in her tendency towards metaphysical musing Transcription, 97v-96r, 96v-97r, 98r, 98v Folios 100–103, 19 Feb 1841 Differential coefficients; brief question about logarithms Transcription, 101v-100r, 100v-101r, 102r, 102v-103r Folios 104–105, 22 Feb 1841 Problems over the coefficients of a particular series Transcription, 105v-104r, 104v-105r Folios 58–60, Mar/Apr 1841 No mathematical content; hopes to see the De Morgans before going to Paris; has a bundle of papers for ADM; recounts recent social life (inc. trips to the opera) Transcription, 59v-58r, 59r, 60r, 60v Folios 50–52, May/Jun 1841 No mathematical content: bemoans the fact that she hasn’t had much time for mathematics, asks to see ADM Transcription, 51v-50r, 50v-51r, 52r Folios 159–160, Jun 1841 Annoyance that ADM was turned away by footman; arrangements for meeting Transcription, 160v-159r, 159v-160r Folios 161–162, Jun 1841 Follows on from previous; arrangements for meeting Transcription, 161r, 161v-162r Folios 106–107, 4 Jul 1841 Follows on from previous; arrangements for meeting Transcription, 107v-106r, 106v-107r Folios 108–109, 6 Jul 1841 Many very specific queries about the calculation of various integrals in the textbook, including the pointing out of possible misprints Transcription, 109v-108r, 108v-109r Folios 110–111, 6 Jul 1841 Continuation of 108–109, with brief mention also of the dynamics in 106–107 Transcription, 110r, 110v-111r Folios 152–153, Jul 1841 Derivatives: primitive and derived functions; definite vs. indefinite integrals Transcription, 152r, 152v-153r Folios 112–114, 11 Jul 1841 Continuation of the last two letters on integration; mention also of the mechanics problem; query over differentials – that dV/dx does not represent a division Transcription, 113v-112r, 112v-113r, 114r Folios 115–118, 15 Aug 1841 Queries over the solution of particular integrals; logarithms of negative quantities; differential coefficients; accelerating force as an application of the calculus Transcription, 116v-115r, 115v-116r, 117r, 117v-118r Folio 119, 16 Aug 1841 Sends proof of result which she has carried out in a opposite manner to that in the book; more on accelerating force Transcription, 119r, 119v Folio 166, 20 Aug 1841 Developments of integrals; accelerating force Transcription, 166r Folios 121–122, 21 Aug 1841 Same integral as in preceding letters; manipulation of differentials; more on logarithms of negative quantities; another integral from book Transcription, 122v-121r, 121v-122r Folios 144–145, 28 Aug 1841 Various problems involving integrals, apparently in a dynamical context Transcription, 145v-144r, 144v-145r Folios 46–47, 4 Sept 1841 Misapprehensions over meaning of differentials Transcription, 47v-46r, 46v-47r, vertical text on 46r Folios 123–125, 9 Sept 1841 Asks whether she should be able to prove a certain formula, or whether she is overreaching herself; questions the point of complicated method in the book; determination of maxima and minima; nature of logarithms and differential coefficients; accelerated force Transcription, 124v-123r, 123v-124r, 125r, 125v Folios 127–129, 19 Sept 1841 Cubic equations; complex numbers; asks whether there can be a three-dimensional analogue; asks about Monge’s descriptive geometry Transcription, 127r, 127v, 128r, 128v-129r Folios 130–131, 27 Oct 1841 Will be coming to town for a few days from next Tuesday (without her mother’s knowledge); hopes to see Mr. and Mrs. De Morgan at some point Transcription, 130r, 130v-131r Folios 132–133, 4 Nov 1841 Manipulation of differentials; calculus involving trigonometric expressions; differential equations? Transcription, 133v-132r, 132v-133r Folios 134–135, 8 Nov 1841 Continuation of the last letter; logarithms; queries notation for (and notion of) the inverse of a function Transcription, 135v-134r, 134v-135r Folio 136, 10 Nov 1841 Continuation of the last letter; logarithms; queries notation for (and notion of) the inverse of a function Transcription, 136r, 136v Folios 138–139, 11 Nov 1841 Journey to town has been unexpectedly delayed Transcription, 138r, 138v-139r Folios 140–141, Nov 1841 Revised plan for being in town; mention of an integral that has appeared in previous letters Transcription, 140r, 140v-141r Folios 142–143, 21 Nov 1841 Arrangements for meeting; assorted problems involving expressions for/operations on functions Transcription, 142r, 142v-143r Folios 154–155, 14 Jan 1842 Arrangements for meeting; has been amusing self with book named in next note Transcription, 154r, 154v-155r Folios 157-158, 1848 Promises to send ADM an unspecified paper which is about to be published Transcription, 157r, 157v-158r	Folios 1-2, 1840 Advises on readings on acoustics; clarifies the nature of zero; notes foundation of society for publication of scientific manuscripts and suggests that AAL should join Transcription, 1r, 1v-2r Folios 3–4, 1 Aug 1840 Comments that AAL has understood the problem of the stone (?); explains the notion of a variable and its passing to a limit; defines coordinates; again promotes manuscript publishing society Transcription, 3r, 3v-4r Folios 5–6, Aug 1840 Going to see Frend as his health is not good, so may not be able to see AAL; reminds AAL that she is not supposed to know about differentiation for the material at hand (CH: she has been skipping ahead?); defines, and suggests reading in connection with, logarithms Transcription, 5r, 5v-6r Folios 7–8, 17 Aug 1840 Clarifies theorem involving inequalities and fractions; discusses right-angled triangles and defines tangent; discusses nature of differential and integral calculus, with historical comments; recommends further reading in differential calculus, but warns that it will also require extra reading in algebra and trigonometry (which he recommends) – “mechanical expertness in the differential calculus is of the utmost consequence”; W. Frend is better; Lord Lovelace’s name added to list of members (presumably of historical manuscript society) Transcription, 7r-7v, 8r-8v Folios 9–10, Aug/Sept 1840 Responds to enquiry about book (?): directs AAL to ‘Algebra’ or ‘Trigonometry’, rather than ‘Study of Mathematics’; advises that continuity must be studied well Transcription, 9r, 9v-10r Folios 12-13, Aug/Sept 1840 Discussion of equations and curves; gives example of finding the equation of a curve passing through given points; thanks AAL for partridge Transcription, 12r, 12v Folios 14–15, 15 Sept 1840 Comments on Nicolas Occam and similarity to AAL’s son’s title – asks whether Lord Lovelace has any Occam manuscripts; general advice on making progress in mathematical study; distinction between quantity and form; explains the equation of a curve; W. Frend neither better nor worse Transcription, 14r, 14v-15r, 15v Folios 16-17, 27 Sept 1840 Recommends continuing with incommensurables, and notes that progress in differential calculus may have to be paused from time to time to fil in gaps in algebra and trigonometry; notes on limits and meaning of differentials; AAL should try some examples of differentiation from Peacock’s book; should also read Proportion in Penny Cyclopaedia when it comes out Transcription, 16r, 16v Folios 18–19, 15 Oct 1840 Muses on differing national notions of of guilt and innocence; explanations on convergence of functions; algebraic truth vs. arithmetical truth of expressions Transcription, 18r, 18v-19r, 19v Folios 20–22, 14 Nov 1840 Points out sign error; handling differentials; combinations; validity of integer formulae for fractions also; value vs. form Transcription, 20r, 20v-21r, 21v, 22r Folios 24–26, Nov 1840 Comments on writing of d; formulae true for whole numbers and for fractions Transcription, 24r, 24v, 25v, 26r Folios 27-28, Nov/Dec 1840 Clarifies problem concerning solution of equation; believes that AAL has got everything out of the chapter on functions that she ought to have done Transcription, 27r, 27v Folios 29-30, Nov/Dec 1840 On the meaning of the ratio θ/sin θ Transcription, 29r, 29v Folios 31–32, Dec 1840 Correct form of terms in series; convergence of series Transcription, 31r, 31v-32r Folios 33–34, Jan 1841 Returns papers on series; responds to some comments on limits and continuity – AAL must wait until she has studied discontinuous functions; notes AAL’s circular reasoning in a derivation of a binomial coefficient (assumes binomial theorem); thanks for pheasants and hare Transcription, 33r, 33v-34r Folios 35–36, Jan 1841 Points out that if it is necessary for x to diminish without limit in order to prove a conclusion, it is not necessarily the case that that conclusion holds only for small x or x=0; illustrates this with an example; politely declines invitation to Ockham, as he is too busy with lectures Transcription, 35r, 35v, 36v Folio 37, 6 Feb 1841 Comments on bounds that may be placed on a particular fraction using those on ithe various terms making it up; comments on proof of Taylor’s Theorem; it is not necessary for a beginner to know what use differential coefficients are Transcription, 37r, 37v Folios 38–39, 11 Feb 1841 Just because a theorem is true for continuous functions, this does not mean that it is false for discontinuous ones; discontinuous functions are excluded for the time being because they have no language to describe them – AAL will have enough of them when she comes to study the theory of heat; acknowledges a letter from AAL to Mrs DM Transcription, 38r, 38v-39r Folios 42–43, 22 Feb 1841 Discussion of logarithms; more functions – justification of the fact that a particular function depends on certain variables; (finite?) differences; advises AAL to leave discontinuous functions alone for the time being Transcription, 42r, 42v-43r Folios 40–41, 24 Feb 1841 Notes misprint in book; asks AAL to call one night other than Sunday, as Mrs DM will be at her mother’s then (the day after Frend’s funeral) Transcription, 40r, 40v-41r, 42v

AAL to ADM

ADM to AAL

Folios 48, 49, 164, 163, 165, 13 Sept 1840
Dissatisfied with progress; seeks clarification of meaning of ‘equation of a curve’ and ‘functional equation’
Transcription, 49v-48r, 48v-49r, 163r-164v, 165r
Folios 146–148, 16 Nov 1840
Differential coefficients; manipulation of functions; a little trigonometry
Transcription, 147v-146r, 146v-147r, 148r, 148v
Folios 149–151, 27 Nov 1840
Functional equations
Transcription, 150v-149r, 149v-150r, 151r, 151v
Folios 62–67, 10 Nov 1840
Difficulties over the meaning of differentials; fractional expressions; proofs of the binomial theorem; comments on the necessarily slow and painstaking nature of learning mathematics, with a remark on how the ‘University’ method must be prejudicial to understanding in the long run; is puzzling over composition of ratios
Transcription, 63v-62r, 62v-63r, 65v-64r, 64v-65r, 67v-66r, 66v-67r
Folios 68–69, 17 Dec 1840
Remarks on how the poor weather is keeping her indoors doing mathematics; persists on a point of convergence that was apparently discussed earlier in the week (Monday evening)
Transcription, 69v-68r, 68v-69r
Folios 70–73, 22 Dec 1840
Now sees her mistake regarding a series previously discussed; learns from, and no longer regrets, such mistakes; seeks clarification over incommensurables and ratio
Transcription, 71v-70r, 70v-71r, 73v-72r, 72v-73r
Folios 74–76, 4 Jan 1841
More-or-less direct continuation of the previous: series and ratio
Transcription, 75v-74r, 74v-75r, 76r, 76v
Folios 77–83, 10 Jan 1841
Series; differential coefficients
Transcription, 78v-77r, 77v-78r, 80v-79r, 79v-80r, 82v-81r, 81v-82r, 83r, 83v
Folios 91–95, Jan 1841
Details of proof of binomial theorem; more series, inc. exponential and logarithmic; Christmas plans
Transcription, 92v-91r, 91v-92r, 94v-93r, 93v-94r, 95r
Folios 84–87, 17 Jan 1841
Limits of series of fractions; remaining difficulties over differential coefficients, which she feels she ought to have got to grips with by now
Transcription, 85v-84r, 84v-85r, 86r, 86v-87r
Folio 156, Jan 1841
Rearrangement of meeting
Transcription, 156r, 156v
Folio 88, 22 Jan 1841
Nothing mathematical: arrangement to call round on Monday evening, without Lord Lovelace
Transcription, 88r, 88v
Folios 54-57, Feb 1841
Seeks clarification of various issues: functions of two variables, logarithms (Napierian in particular)
Transcription, 55v-54r, 54v-55r, 57v-56r, 56v-57r
Folios 89–90, 3 Feb 1841
More on limits of fractions
Transcription, 90v-89r, 89v-90r
Folios 96–98, 6 Feb 1841
Was too hasty in sending letter of Weds, for now understands the matter at hand (on fractions); resolves to rein in her tendency towards metaphysical musing
Transcription, 97v-96r, 96v-97r, 98r, 98v
Folios 100–103, 19 Feb 1841
Differential coefficients; brief question about logarithms
Transcription, 101v-100r, 100v-101r, 102r, 102v-103r
Folios 104–105, 22 Feb 1841
Problems over the coefficients of a particular series
Transcription, 105v-104r, 104v-105r
Folios 58–60, Mar/Apr 1841
No mathematical content; hopes to see the De Morgans before going to Paris; has a bundle of papers for ADM; recounts recent social life (inc. trips to the opera)
Transcription, 59v-58r, 59r, 60r, 60v
Folios 50–52, May/Jun 1841
No mathematical content: bemoans the fact that she hasn’t had much time for mathematics, asks to see ADM
Transcription, 51v-50r, 50v-51r, 52r
Folios 159–160, Jun 1841
Annoyance that ADM was turned away by footman; arrangements for meeting
Transcription, 160v-159r, 159v-160r
Folios 161–162, Jun 1841
Follows on from previous; arrangements for meeting
Transcription, 161r, 161v-162r
Folios 106–107, 4 Jul 1841
Follows on from previous; arrangements for meeting
Transcription, 107v-106r, 106v-107r
Folios 108–109, 6 Jul 1841
Many very specific queries about the calculation of various integrals in the textbook, including the pointing out of possible misprints
Transcription, 109v-108r, 108v-109r
Folios 110–111, 6 Jul 1841
Continuation of 108–109, with brief mention also of the dynamics in 106–107
Transcription, 110r, 110v-111r
Folios 152–153, Jul 1841
Derivatives: primitive and derived functions; definite vs. indefinite integrals
Transcription, 152r, 152v-153r
Folios 112–114, 11 Jul 1841
Continuation of the last two letters on integration; mention also of the mechanics problem; query over differentials – that dV/dx does not represent a division
Transcription, 113v-112r, 112v-113r, 114r
Folios 115–118, 15 Aug 1841
Queries over the solution of particular integrals; logarithms of negative quantities; differential coefficients; accelerating force as an application of the calculus
Transcription, 116v-115r, 115v-116r, 117r, 117v-118r
Folio 119, 16 Aug 1841
Sends proof of result which she has carried out in a opposite manner to that in the book; more on accelerating force
Transcription, 119r, 119v
Folio 166, 20 Aug 1841
Developments of integrals; accelerating force
Transcription, 166r
Folios 121–122, 21 Aug 1841
Same integral as in preceding letters; manipulation of differentials; more on logarithms of negative quantities; another integral from book
Transcription, 122v-121r, 121v-122r
Folios 144–145, 28 Aug 1841
Various problems involving integrals, apparently in a dynamical context
Transcription, 145v-144r, 144v-145r
Folios 46–47, 4 Sept 1841
Misapprehensions over meaning of differentials
Transcription, 47v-46r, 46v-47r, vertical text on 46r
Folios 123–125, 9 Sept 1841
Asks whether she should be able to prove a certain formula, or whether she is overreaching herself; questions the point of complicated method in the book; determination of maxima and minima; nature of logarithms and differential coefficients; accelerated force
Transcription, 124v-123r, 123v-124r, 125r, 125v
Folios 127–129, 19 Sept 1841
Cubic equations; complex numbers; asks whether there can be a three-dimensional analogue; asks about Monge’s descriptive geometry
Transcription, 127r, 127v, 128r, 128v-129r
Folios 130–131, 27 Oct 1841
Will be coming to town for a few days from next Tuesday (without her mother’s knowledge); hopes to see Mr. and Mrs. De Morgan at some point
Transcription, 130r, 130v-131r
Folios 132–133, 4 Nov 1841
Manipulation of differentials; calculus involving trigonometric expressions; differential equations?
Transcription, 133v-132r, 132v-133r
Folios 134–135, 8 Nov 1841
Continuation of the last letter; logarithms; queries notation for (and notion of) the inverse of a function
Transcription, 135v-134r, 134v-135r
Folio 136, 10 Nov 1841
Continuation of the last letter; logarithms; queries notation for (and notion of) the inverse of a function
Transcription, 136r, 136v
Folios 138–139, 11 Nov 1841
Journey to town has been unexpectedly delayed
Transcription, 138r, 138v-139r
Folios 140–141, Nov 1841
Revised plan for being in town; mention of an integral that has appeared in previous letters
Transcription, 140r, 140v-141r
Folios 142–143, 21 Nov 1841
Arrangements for meeting; assorted problems involving expressions for/operations on functions
Transcription, 142r, 142v-143r
Folios 154–155, 14 Jan 1842
Arrangements for meeting; has been amusing self with book named in next note
Transcription, 154r, 154v-155r
Folios 157-158, 1848
Promises to send ADM an unspecified paper which is
about to be published
Transcription, 157r, 157v-158r

Folios 1-2, 1840
Advises on readings on acoustics; clarifies the nature of zero; notes foundation of society for publication of scientific manuscripts and suggests that AAL should join
Transcription, 1r, 1v-2r
Folios 3–4, 1 Aug 1840
Comments that AAL has understood the problem of the stone (?); explains the notion of a variable and its passing to a limit; defines coordinates; again promotes manuscript publishing society
Transcription, 3r, 3v-4r
Folios 5–6, Aug 1840
Going to see Frend as his health is not good, so may not be able to see AAL; reminds AAL that she is not supposed to know about differentiation for the material at hand (CH: she has been skipping ahead?); defines, and suggests reading in connection with, logarithms
Transcription, 5r, 5v-6r
Folios 7–8, 17 Aug 1840
Clarifies theorem involving inequalities and fractions; discusses right-angled triangles and defines tangent; discusses nature of differential and integral calculus, with historical comments; recommends further reading in differential calculus, but warns that it will also require extra reading in algebra and trigonometry (which he recommends) – “mechanical expertness in the differential calculus is of the utmost consequence”; W. Frend is better; Lord Lovelace’s name added to list of members (presumably of historical manuscript society)
Transcription, 7r-7v, 8r-8v

Folios 9–10, Aug/Sept 1840
Responds to enquiry about book (?): directs AAL to ‘Algebra’ or ‘Trigonometry’, rather than ‘Study of Mathematics’; advises that continuity must be studied well
Transcription, 9r, 9v-10r
Folios 12-13, Aug/Sept 1840
Discussion of equations and curves; gives example of finding the equation of a curve passing through given points; thanks AAL for partridge
Transcription, 12r, 12v
Folios 14–15, 15 Sept 1840
Comments on Nicolas Occam and similarity to AAL’s son’s title – asks whether Lord Lovelace has any Occam manuscripts; general advice on making progress in mathematical study; distinction between quantity and form; explains the equation of a curve; W. Frend neither better nor worse
Transcription, 14r, 14v-15r, 15v
Folios 16-17, 27 Sept 1840
Recommends continuing with incommensurables, and notes that progress in differential calculus may have to be paused from time to time to fil in gaps in algebra and trigonometry; notes on limits and meaning of differentials; AAL should try some examples of differentiation from Peacock’s book; should also read Proportion in Penny Cyclopaedia when it comes out
Transcription, 16r, 16v
Folios 18–19, 15 Oct 1840
Muses on differing national notions of of guilt and innocence; explanations on convergence of functions; algebraic truth vs. arithmetical truth of expressions
Transcription, 18r, 18v-19r, 19v
Folios 20–22, 14 Nov 1840
Points out sign error; handling differentials; combinations; validity of integer formulae for fractions also; value vs. form
Transcription, 20r, 20v-21r, 21v, 22r
Folios 24–26, Nov 1840
Comments on writing of d; formulae true for whole numbers and for fractions
Transcription, 24r, 24v, 25v, 26r
Folios 27-28, Nov/Dec 1840
Clarifies problem concerning solution of equation; believes that AAL has got everything out of the chapter on functions that she ought to have done
Transcription, 27r, 27v
Folios 29-30, Nov/Dec 1840
On the meaning of the ratio θ/sin θ
Transcription, 29r, 29v
Folios 31–32, Dec 1840
Correct form of terms in series; convergence of series
Transcription, 31r, 31v-32r
Folios 33–34, Jan 1841
Returns papers on series; responds to some comments on limits and continuity – AAL must wait until she has studied discontinuous functions; notes AAL’s circular reasoning in a derivation of a binomial coefficient (assumes binomial theorem); thanks for pheasants and hare
Transcription, 33r, 33v-34r
Folios 35–36, Jan 1841
Points out that if it is necessary for x to diminish without limit in order to prove a conclusion, it is not necessarily the case that that conclusion holds only for small x or x=0; illustrates this with an example; politely declines invitation to Ockham, as he is too busy with lectures
Transcription, 35r, 35v, 36v
Folio 37, 6 Feb 1841
Comments on bounds that may be placed on a particular fraction using those on ithe various terms making it up; comments on proof of Taylor’s Theorem; it is not necessary for a beginner to know what use differential coefficients are
Transcription, 37r, 37v
Folios 38–39, 11 Feb 1841
Just because a theorem is true for continuous functions, this does not mean that it is false for discontinuous ones; discontinuous functions are excluded for the time being because they have no language to describe them – AAL will have enough of them when she comes to study the theory of heat; acknowledges a letter from AAL to Mrs DM
Transcription, 38r, 38v-39r
Folios 42–43, 22 Feb 1841
Discussion of logarithms; more functions – justification of the fact that a particular function depends on certain variables; (finite?) differences; advises AAL to leave discontinuous functions alone for the time being
Transcription, 42r, 42v-43r
Folios 40–41, 24 Feb 1841
Notes misprint in book; asks AAL to call one night other than Sunday, as Mrs DM will be at her mother’s then (the day after Frend’s funeral)
Transcription, 40r, 40v-41r, 42v

Notes and Exercises	About this document
Folio 168-170 Explanations relating to differential equations 168r, 168v, 169r, 169v, 170r, 170v, Transcription Folios 171-172 Scrap featuring trigonometric calculations involving surds; handwriting uncertain; 172v: manipulation of trig identities (possibly connected with trig identities in letters to/from Mary Somerville: Box 174 fols. 29–34) Folio 174, Sept 1841 Chain rule 174, Transcription Folio 175 Definition of complete derivative and instructions for reading 175, Transcription Folios 176-177 176r: scribbling; 176v–177r: Königsberg bridges; 177v: more trig, much like 172v (both hands) 176, 177, Transcription Folio 178 Calculus- and exponential function-related jottings 178, Transcription Folio 179 Appears to be applying L’Hôpital’s rule to the generating function for the Bernoulli numbers 179, Transcription	Copyright. All Ada Lovelace manuscript images on the Clay Mathematics Institute website are © 2015 The Lovelace Byron Papers, reproduced by permission of Pollinger Limited. To re-use them in any form, please apply to katyloffman@pollingerltd.com. The LaTeX transcripts of the letters were made by Christopher Hollings (christopher.hollings@maths.ox.ac.uk). All notes and transcriptions of material from The Lovelace Byron Papers are © 2015 Christopher Hollings. Their re-use in any form requires his permission, and is subject to the rights reserved to the owner of The Lovelace Byron Papers.

Notes and Exercises

About this document

Folio 168-170
Explanations relating to differential equations
168r, 168v, 169r, 169v, 170r, 170v, Transcription
Folios 171-172
Scrap featuring trigonometric calculations involving surds; handwriting uncertain; 172v: manipulation of trig identities (possibly connected with trig identities in letters to/from Mary Somerville: Box 174 fols. 29–34)
Folio 174, Sept 1841
Chain rule
174, Transcription
Folio 175
Definition of complete derivative and instructions for reading
175, Transcription
Folios 176-177
176r: scribbling; 176v–177r: Königsberg bridges; 177v: more trig, much like 172v (both hands)
176, 177, Transcription
Folio 178
Calculus- and exponential function-related jottings
178, Transcription
Folio 179
Appears to be applying L’Hôpital’s rule to the generating function for the Bernoulli numbers
179, Transcription

Copyright. All Ada Lovelace manuscript images on the
Clay Mathematics Institute website are © 2015 The Lovelace Byron Papers, reproduced by permission of Pollinger Limited. To re-use them in any form, please apply to katyloffman@pollingerltd.com.

The LaTeX transcripts of the letters were made by Christopher Hollings (christopher.hollings@maths.ox.ac.uk).
All notes and transcriptions of material from The Lovelace Byron Papers are © 2015 Christopher Hollings. Their re-use in any form requires his permission, and is subject to the rights reserved to the owner of The Lovelace Byron Papers.