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Miscellaneous notebook containing Newton's accounts for 1665-9, a series of increasingly complicated mathematical problems, and a highly revealing personal confession. At Whitsun 1662, Newton compiled a list of all the 47 sins he could remember having committed in his life, from stealing cherries to "threatning my [step]father and mother ... to burne them and the house over them". The accounts section charts the beginning of his study of alchemy in 1669, with purchases of books, materials and a furnace to equip the makeshift laboratory he set up in the grounds of Trinity College.

Described and partly published in Brewster (1855), 1: 31-3. The shorthand section deciphered and discussed in Westfall, 'Short-Writing and the State of Newton's Conscience, 1662'.

Contains expense lists, a confession of Newton's sins, and miscellaneous problems in mathematics and physics

Flyleaf inscribed 'Isaac Newton/ pret. 8d'. This is followed by a sequence of letters (the key to a cipher?), reading:

'Nabed Efyhik

Wfnzo Cpmfke'.

The book proper begins with shorthand notes on 3 pp., dated 1662, and detailing Newton's sins before and after Whitsunday of that year. Then follows a list of expenses, 7 pp., dated from 23 May 1665 to April 1669 (about 140 entries), including assorted chemicals, two furnaces and a copy of the Theatrum chemicum [ed. Lazarus Zetzner, 1659-61: H1608] bought in April 1669. On f. 10v another hand has listed the names of four German noblemen.

The other end of the book begins with 'Nova Cubi Hebræi Tabella' on 1 p., followed by various problems in geometry and the conic sections (ellipsis, parabola, hyperbole, etc.), with diagrams, 24 pp. On the back flyleaf in Thomas Pellet's hand: 'Sep 25 1727/ Not fit to be printed/ T Pellet'.

in English

Bought at the Sotheby sale by Maggs Brothers for £180 on 14 July 1936. By the end of the month it had been presented to the museum by the Friends of the Fitzwilliam Museum with financial assistance from Sir Thomas Barlow.

d

March 25 1666.
Lent Wilford | ——X—— | 0 . 1 . 0. |

To yethe Poore on yethe fast | ———— | 0 . 1 . 0. |

To MrMaster Babint9 tons : Wom, 6d. Porter 6d | ———— | 0 . 1 . 0. |

Spent wthwith Rubbins 4d. | ———— | 0 . 0 . 4 |

Lent to SrSir Herring | ———— | 1 . 6 . 0. |

Lent to SrSir Drake | ———— | 1 . 0 . 0. |

Payd my Laundresse | ———— | 0 . 5 . 6. |

ffor a paire of shoos | ———— | 0 . 4 . 0. |

Caverly | ———— | 0 . 0 . 4. |

6
Payd Iohn Falkoner | ———— | 0 .11 . 6. |

A paire of shooestrings | ———— | 0 . 0 . 8. |

Payd my Bedmaker | 0 . 5 . 0. | |

Dew from Iohn Euans | ———— | 0 . 1 .10. |

Euans | | |

The summe of my expences | 1 .10 . 4. | |

+ | 8 .10 . 10 | |

In all | 10 . 1 . 2 | |

Dew to mee | ———— | 3 . 5 .10 |

More from MrMaster Guy | ———— | 0 .10 . 0 |

Lent In all | ———— | 3 .15 .10. |

1666.
RdReceived 10li March 20th | ———— | 10 . 0 . 0 |

Remaining in my hands | ———— | 8 . 8 . 4. |

In all | 18 .8 . 4 | |

Expences & wtwhat I lent deducted yethe rest is | ———— | 4 .11 . 4. |

1667 Apr 22 Received | 10 - 0 - 0 | |

In my hands besid debts | 14 -11 - 4d | |

My Iourney to Cambridg | 0 - 6 - 6. | |

Two paire of shoos | ———— | 0 - 8 - 0 |

~~A Cap~~ | ~~——X——~~ | ~~0 - ~~ |

~~Cloths & ~~ dying & mending | | 0 - |

bordering twice | ~~——X——~~ | 0 - |

~~Lynings~~ | | ~~0 - 6 - 6~~ |

Lath & Table | ———— | 0 -15 - 0 |

Iron worke for it | 0 - 9 - 0 | |

Drills, Gravers, a Hone & Hammer & a Mandrill | 0 . 5 . 0 | |

A Magnet | ———— | 0 .16 . 0 |

Compasses | ———— | 0 . 3 . 6 |

Glass bubbles | ———— | 0 . 4 . 0 |

Chappell Clarke | ———— | 0 . 2 . 6 |

My Bachelors Act | ———— | 0 .17 . 6. |

At yethe Taverne severall other times &c | ———— | ~~0~~1 . ~~1~~0 . 0 |

Spent on yethe M y Couz Ayscough | 0 .12 . 6.. | |

On other Acquaintance | ———— | 0 -10 : 0 |

Shoos | ———— | 0 . 4 . 0 |

Cloth 2 yards & buckles for a Vest. | 2 . 0 . 0 | |

ffor Woosted Prunella ~~7~~8 yds $\frac{1}{2}$ . | 1 . 5 . 6 | |

ffor yethe lining 4yds | ———— | 0 . 9 . 4 |

Philosophicall Intelligences | 0 . 9 . 6. | |

yethe Hystory of yethe Royall Ssoc: | 0 . ~~6~~7 . 0. | |

~~Shoe Strings~~ | ~~————~~ | ~~0 . 1 . 0~~ |

To Goodwife Powell | ———— | 0 . 7 . 6 |

To my Laundresse | ———— | 0 . 8 . 6 |

To Caverly | ———— | 0 . 1 . 6 |

To the Glasier | ———— | 0 . 1 . 0 |

New fire cheeks & pointing yethe chamber & windows | ———— | 0 . 1 . 6 |

Gunters book & sector &c to DsDominus ffox | 0 . 5 . 0 | |

Letters, wyer, files, boats, | ———— | 0 . 2 . 6. |

ffor a ffellows key | ———— | 0 . 1 . 0 |

~~A Cap turning~~ | ~~————~~ | ~~0 . 1 . 4.~~ |

To the Taylor Octob 29. 1667. | ———— | 2 .13 . 0 |

To the Taylor. Iune 10. 1667 | ———— | 1 . 3 .10 |

For keeping Christmas | ———— | 0 . 5 . 0 |

Lost at cards at twice | 0 .15 . 0 | |

7
At yethe Taverne twice | ———— | 0 . 3 . 6. |

6$\frac{1}{2}$ sacks of coales, carriage & sedge | ———— | 0 .11 . 0 |

Shoos & mending | ———— | 0 . 4 .10. |

Two paire of Gloves | ———— | 0 . 5 . 0 |

wthwith MrMaster Lusmore, Hautrey, Salter | 0 . 3 . 6 | |

Received of my Tutor wchwhich I lent Perkins
| 0 .10 . 0 | |

Received of my Mother | ———— | 30 . 0 . 0 |

My Iourney | ———— | 0 . 7 . 6 |

ffor my degree to yethe Colledg | 5 .10 . 0 | |

To yethe Proctor | ———— | 2 . 0 . 0 |

ffor 3 Prismes | ———— | 0 . 3 . 0 |

4 ounces of Putty | ———— | 0 . 1 . 4 |

To yethe Painter | ———— | 0 . 3 . 0 |

To yethe Ioyner | ———— | 1 . 1 . 8 |

Lent to DsDominus Wickins | ——X—— | ~~1 . 7 . 6.~~ |

To yethe shoe maker | ———— | 0 . 5 . 0 |

Bacons Miscelanys | ———— | 0 . 1 . 6 |

Expences caused by my Degre | 0 .15 . 0 | |

Subscribing 6d, Reading Græke. | 0 . 5 .10. | |

A bible binding | ———— | 0 . 3 . 0. |

Humphrey 1668 | ———— | 0 . 1 . 0. |

18 yards of Tammy for my MrMaster of Arts Goune | 1 .13 . 0 | |

Lining —— 3, 6 | ———— | 0 . ~~2~~3 . 6. |

Making ytthat & turning my Bachelors Goune | ———— | 1 . 0 . 6. |

Received of MrMaster Io: Herring | 0 .10 . 0 | |

Payd my Laundresse | ———— | 0 . 5 . 6. |

Payd to Caverly | ———— | 0 . 5 . 6. |

Payd Go~~d~~o dwif Ta~~b~~l bot from Feb 12 to Mar 25 1668 | 0 . 2 . 6 | |

Payd to my Laundresse | 0 . 2 . 6. | |

To yethe Porter | ———— | 0 . 5 . 6. |

ffor oranges 1667 for my sister | ———— | 0 . 4 . 2. |

Bedmaker & Laundresse | 0 .10 . 0. | |

Shoemaker | ———— | 0 . 5 . 8. |

A Hatt | ———— | 0 .19 . 0. |

Taverne | 0 .10 . 0. | |

Carpets of Neats Leather | 0 .18 . 0 | |

~~A~~M y part of A Couch. | 0 .14 . 0. 1 | |

Bowling Greene | ———— | 0 .10 . 0 |

To MrMaster Ieffreys for a Suit | 3 . 6 . 0 | |

A Tickin for a ffeatherbed. | 1 .10 . 0 | |

New ffeathers | ———— | 0 . 8 . 0 |

A Hood | ———— | 1 . 3 . 6. |

Making &c of my last suit | ———— | 1 .11 . 9 |

8
Dew to Iohn Hauxy | ——X—— | 1 .10 . 0. |

Spent in my Iourney to Londoon | ~~6~~5 .10 . 0 | |

As also 4li 5s m~~y~~o re wchwhich my Mother gave mee in yethe Country | 4 . 5 . 0 | |

Received for Chamberrent | 1 .11 . 0. | |

Received from my Mother | 11 . 0 . 0. | |

Bedmaker & Laundresse | 0 . 4 . 0 | |

Lent DsDominus Wickins | ——X—— | 0 .11 . 0 |

Lent MrMaster Boucheret | ——X—— | 0 . 5 . 0 |

I went into e

rth 1667.

I returned ~~Ian~~ to Cambridg

I went to London on Wednesday Aug 5t & returned to Cambridge on Munday

Aprill 1669.
Lent to MrMaster Wadsley | ———— | 0 .14 . 0 |

16 yards of Stuffe for a suit | 2 . 8 . 0 | |

ffor making &c | ———— | 1 .13 . 0 |

For turning a Cloth suit | 1 . 3 . ~~0~~3 | |

For shoe strings &c | ———— | 0 . 2 . 0 |

For Glasses in Cambridge | 0 .14 . 0 | |

For Glasses at London | ———— | 0 .15 . 0 |

For Aqua ffortis, sublimate, oyle y erbe, fine silver, Antimony, vinegar Spirit of Wine, White lead, Allome Niter, Tartar, Salt of Tartar, ![]()
| 2 . 0 . 0. | |

A ffurnace | ———— | 0 . 8 . 0 |

A tin ffurnace | ———— | 0 . 7 . 0 |

Ioyner | ———— | 0 . 6 . 0 |

41
Theatrum Chemicum | ———— | 1 . 8 . 0 |

Lent Wardwel 3s & to his wife 2 s | ———— | 0 . 5 . 0 |

Carrriage of yethe oyle | ———— | 0. .2 . 0 |

Payd I Stagg | ———— | 0 .18 . 6 |

Payd yethe Chandler | ———— | 0 . 8 . 0 |

A Table cloth | ———— | 0 .10 . 0 |

Six Napkins | ———— | 0 . 6 . 0 |

Carolus ~~g~~

Georgius Bernhardus de Theler Equites

Iohannes Christophorus Ritter Wurcenâ-Misni

Sep. 25 1727 Not fit to be printed

T Pellet

h = hypotenusa. b = basis.

c = Cathetus.

p = perpendicular.

hdc = diff: hypot & Cath

bdc = diff: basis & cathet:

bdh = difference basis & hyp

dsh = diff: seg: hypoten:

sh = segment: hypoten:

bh = greater seg

I. Any two leggs given to find e

1. bq + cq = hq.

2 r: ~~k~~

3 r: ~~k~~

~~Ought. ~~ Eucl. lib 1. pr: 47.

~~4 ~~

II e

1.

III c. h.

1.

IIII. b. p. h given to find dsh.

1. 2r: bq - pq: h = dsh.

V. b. c. h given to find dsh.

1. H - 2r: cq - Q:

2 2r: bq - Q:

VI b.c ~~b~~

1

2

3

VII b. h. or c. h. or b. c given to find dsh.

Theorem 1

As ee(in rectang: triang:) is to

eside:: so is

eegmof

eente

Theorem 2.

As eecathetus to

eeof

etseesegment of

e

Theoreem 3d.

base – Cathetus: hypotenusa:: :: greater

eg

Theor. 4.

If th~~in~~touching

eif

eany points except

en a line drawn fm either touch point

perpendicular to

ewill bisect it & being produced will

cut

ee

eettded

e

ee

ethey being divided by

e

To describe an ellipsis

Let fe & gc be two lines ef make

thtaken in bd as at a &

let

t

eeend of

eon

eedescribe

e

Let c & a about

chput haveing both ends tyed to

gether. as is signified by

e3 lines cb. ba. ac. Strech it out

thstreched out draw

eit shall describe

e

Let ebe infinitely ex

tended in it take

e

eelet

ee~~y~~ let a neend of

eeoc turning round, each point of

eab betwixt ac will describe an Ellipsis

whose transvers axis is equall to oc & paral

lell to ae but each point on

e

Extend de both ways take

e

~~ab & ~~ ab equall to one another fasten

together at one

end as at a. set

eother end of ca at

elet

en take a point in ab as o & turne ac

about & it shall describe

eShooten in lib. 2

d Cartesij Geometria:

Cut eeeof

e

ee

themakes right angles

thgh

eeo

If eg be moved twixt elines ed & gd. a point in it as

(θ) shall describe an ellipsis

whose semi-axis ad is equall

If dc revolve abute

eeother end b be fastend

a triangle bca &

db = ba = bc &

ea moves on

ead

edescribe

e

epoint in

eEllipsis ehg whose diam 2dh =

2dg = 2ec &

e

& if in eas s, it shall describe an ellipsis

ediam: being

2ab + 2bs, e

If o & a be e& ca = op = it theire section in

If ab = bc = ci = ai = if or greater y

n (if) & bh = fp & ac bisects

ebai. bci. y

n if bh turne round

eof bh & ac shall describ

an Ellipsis. & hi & i

are

e

To describe a Parabola

Let bc fall perpendicular on ad & let c

eend there of move

~~per~~ uppon ad a pendicular

given line & if bc x k

a given line be equall

to ac x cd y

n shall b ebc describe

e

Draw ah perpendicuto ap. & ab from ah

parallell to ap divid

bh into equall

bcdefgh. & divide ap

into parts equall to

eformer as iklmnop.

draw lines cros to each

part of

elines ah & ap

as cb. kc. ld.

me. nf. &c

thof each

line descri

a circle as

brc

thbu in

ecut by

ediameters

of

e circle draw lines

perpendicular

to

eediameter they are drawne

epw, qx, ry, sz, t&, u+. Erect those

lines perpendicular to

eas p

eend of those lines draw a line & it

If abc be a cone: de (ediameter of

efgd) parallell to ac: & fg

(

ebc at right angles y

n is

e

Make db perpendicular to ef

on

elet

eangled figure

pbgh turne.

Let gh move per

pendicularly on ef

ever intersecting

ef & bh in one

point y

n pbgh moveing rownd

egh describe

e

If ab = bd = do = ao is greater then ac & ac = cs

eto

ee

eo

~~n~~eecorners b & o. y

n etheire intersections shall describe a Parab

&

ee

If (d) be eeruler fc = to

ethred fastened to

eat f & to

eeruler move perpen

dicparallell to de. y

n e~~e~~ing of

ee

To describe an Hyperbole

Let fa fall on ag suppose at right angles let one en

eup

e

eeg. let mp keepe par

~~r~~allel to df haveing one end p moveing in

eyet keeping an equall distance fr

ol

e~~i~~tenpl be immutable. let y

n emp & gl thus move to & fro & theire

intersections shall describe an

~~parabola~~ Hyperbola. &

e~~mad~~ de x e

ffasten a pegg as at a & another as at b upon

chede be turned at

eone end of a cord &

ee

een streching

eth

eeslip towards e & describe

e

ad & db is equall to

erectangle twixt ae &

ec

tin

eby makeing ec =

Cut eteter

ecuteth one side of

ebc produced as at d.

ethereof gh cutteth ac

eof

e

If (of) touch e& (as) be it

diam: & (gb) keepe parallel

to (eo) & (cag) aways pass

through (a).

e

e~~parab~~ Hyperb. & (bc) be always in

e(fh) fastend to (gb) & equall

to fd = de =

n elines (agc) & (gb) moveing

by theire intersection

shall describe an Hyperbola whose

asymtotes are oea, fe; eb, eb, & wx is a

right line conjugate to

eeter (as.) viz: it is

e

If dk = er be (latus transversum) & de = kr,

be latus rectum y

n ~~shall~~ is sd = sr = se = sk = sa = sx.

at (a) & (x)

on

cherevolve, & if ac = ox = zi

= dk = er, & co = ax y

n

ee(when they move) shall describe a

~~Parabola~~ whose focus is a, & esite Hyperbola (whose focus is x is described

e

If de = dc = ex = cx is not lesse y

n ix = az & 2 of theire ends loose pind

together at (e) & 2 at (c) on

che(coe) two of

theire ends are eloosely pinnd on

e

ee(adp) at (d) soe

te~~e~~to

en eof

eeoiq. & after they are parallell they shall

describe

e

The Asymptotes aq, an, & (m) point

~~y~~emq || an. & mn || aq. Then draw

en at a venture & make er =

& r shall bee a point in

e

If eof

e(ab) bee given & any point

as (c) in

edraw

ucbf || ad. ud || ab || fg making bf = bu = 4bc. Then

at a venter draw bewh, through

eOr dw = bk & from

edraw ke,

che

The foci point in one Hyerbo

given to describe

Draw ac, cd, frothe given point c to

the foci, y

n upothe center c

thradius ce describe

etec = ef. y

n theecenters a & d describe

efhp their points of intersection p, h, shall bee

in

edistance twixt divers points thus found may

bee completed

by thent

The properties of yethe Parabola

ab = a. bc = b. ac = c. eb = d. ei = x. fi = y. b : c :: x : (ik)

yy =

tmultipling ei = if square. Or breifly

a : c :: d : (es or il)

~~b : c ::~~ Ne is called latus rectum of Apollon & Parameter by Mydorgius. gh is its base

ang pbh = phg. kg parallell to ac tangent no parallell to

en

kg x kg : nm x nm :: db x bk : db x bm :: bk : bm

ac = oc. ah = do. sit (sh) Paral

lela ad. (dr)

~~.~~ & (rh) contingat Parab: in h. & (dh) perpend: ad (dr)

If cs = sb & su parallell to ab yn ecea : cab :: l : 4. & so it may

If ab & cd, are ordinately applyed

eis to

e as Eight to

~~five~~

If rs, is parallell to gx yn are

egproxa

= gcsqxa) equall & po = cq. & if ga = ax then

ediameters ar as cut

ers in its tou

ch points.

The properties of yethe Hyperbola

rx +

☞ rx +

fi = y. b : c :: q + x : (il)

b : a :: x : (ik)

bb : ac :: q : (en)

:: x : (qpcron)

or

More breifly thus.

b : c :: q :: (es)

de is called latus tranrectum by Appolonius. but Parameter

mn = pd = bq = q. fg = db = pq = p nu = x. au = y. ha = ck = b. st = r

(1) q :

r :: qx + xx : yy. & yy = rx + (2) 2b

pd = mn = qb = axi primo, transverso &

st = r = Lateri recto.

If xt = p. sr = q : r = Param& iry = a. eno = b. in = y

~~then if pq = r as in iry~~ Then if p = q = r as in (a) : (a) is

eof all

~~Para~~n, yy = xx + qx. & if (q) is

eis propper to (b) then yy : zz :: qq : pp.

& therefore

Hyperbolas are to one another as theire rigt axis are

~~to~~ supposeing theire transverse axes equall. viz iryeon : eron :: in : en :: p : p.

therefore if (rs) is parallell

to ao, & ae = co.

n

tr & xs (cutting rs in

etouch points) are ordinately

applyed to ee~~Pa~~

If (o & a) are e& (u) a point in one of

eHyperb: s. then au + ei = ou

& if as = ei = or.

~~& rs~~ y

n us = uo. & rs = oa & (iu) bisecting

e(ria.) it shall touch

e

The Properties of yethe Ellipsis

rx -

rx -

am = a. bm = b. cm = c. ed = q. ei = x. id = q - x

b : c :: q - x : (ib)

bb : ac :: q : en =

Af = q lateri recto. ad = x

(1) q : p :: p : r. (2) yy : xq - xx :: r : q. therefo3

~~q : q~~ yy = rx -

af is e

ch is e

fg is e

se

gm

If e& co

een are eequall to one another, for ax =

ee

If ab tou~~g~~& (o) & (x) be

en

eif (ocx) be bisected by (cr)

y

n acr = bcr = right angle

If xu = ot = ys. & uo bisected in a then

If also ut = ox & ut & xo be produced till they meete in h.

ebe bisected by

e