Catalogue Entry: NATP00220

Newton's Waste Book (Part 1)

Author: Isaac Newton

Source: MS Add. 4004, ff. {cover}-15r, Cambridge University Library, Cambridge, UK

[Normalized Text] [Diplomatic Text] [Manuscript Images]

[1] {Se}{p}t 1664.

[2] Figure

[3] Figure

[4] Figure

[5] Figure

[6] Figure

[7] Figure

[8] Figure

[9] Figure

[10] Figure

[11] Figure

[12] Figure

[13] Figure

[14] Figure

[15] Figure

[16] Figure

[17] Figure

[18] Figure

[19] Figure

[20] Figure

[21] Figure

[22] Figure

[23] Figure

[24] Figure

[25] Figure

[26] Figure

[27] Figure
{illeg} 2x+13xx=gd2. xx+4x+1=ag2.

[28] 36_ 2025 1620_ 0405
Figure
29376_ 162_ 29376_ 07776_ 07290_ 00486_ a'____________b'_____c' 32076×25dd_=801900dd16038064152_ 72907290 13405370486_00518400486000324 012960648962}=104976×9_944784 09000361800 0405 1620_ 2025×25dd_=50625 10125 4050 Q:324_=104976 01296 0648 972 0216106_000 6 360216106_0127611484 9×25×36324162064_8_810018_00_ 99
Figure
36×3240194409720_11664 x+rqxx=9. r2+rxqq=2 {illeg}x=2xrx2 . rx2+2x=9.
Figure x=3. rx=6 r=2 rx+4x=18 qr2+2q=rx
Figure
2qqr2+4x=18 qr2+72r+418=0

[29] cc=52c117. c=2 6156(0 520_(0 559(2 4 1 00(0 cc=80c180

[30] 1600141420(30020 0 13. 14.192 15.225 16.5 17.289 18.324 19.361 20.400

[31] {illeg}

[32]

Figure

x3+y3axy=0 . v=3xxyayyax3yy x+3xxy2ayyz9x4yy6axxy3+aay4+aaxxyy6a3xyy+9a4y4 for x. x+3zxxazy9x46ayxx+10aayy+aaxx6a3x for x . y+3yyzazx9x46ayx2+10a2y2+aax26a3x for y
Figure
Figure ab=a=2ad ad=3aa4

[33]

Figure

{illeg}=x. ce=y. af=q. {illeg}xxx=yy. ed=z. ed=s . {illeg}c=qx. eb 2=qq. eb=q. {illeg}:2qxxx:zz: eh2. eh=2qxzzxxzzqq {illeg}= 2qxxxzq00000xx {illeg} =2qxxx+2zzqx000qq {illeg}4zx+2zxxq {illeg}=qzxzq {illeg}zxq

[34] Figure

[35] Figure

[36] dxqy+2fxyy 2pfxybyx 2ayyxdexyddyyyf

[37] {illeg} xy+ay=0 ax+yy
Figure
ed=v. cd=x. ac=y. ab=s. {illeg}=z. eg=ξ. 0=yy2xy+axx2 y= O2xxax=ac yy=2xxaxO22x4ax3. eg2=3x260xax+ao O2x4ax3 . eg2=3z2azO2z4az3 yy2xy+axxx=0 2yy+ay2xy 2y+2x +x=v x+y+ay 2x2y =v 8x44ax3+4az38z4 x3+4xxz+4xzz+4z3 2xxa2axz2az2 2xxax2z2zzaz +2z2xxax
Figure
ab=a. bdbebc. cxb=be . cϩb=eh. fe2==ccϩϩbbϩϩbb fe=cxbzb=ϩccbbb bz+ϩccbb c=x ed=xccbbb ed= ϩccϩbb+bzccbb bc eh= ϩb+zccbbca b
Figure
Figure

[38] Figure

[39] ϩecdd=ex .

[40] {illeg}00+4d3ϱ3ϩeedd+

[41] {illeg}000ϱ5+5d4ϱ4ϩeedd

[42] {illeg}00dϩ+ϱeedd=ey.

[43] ϱ2ddϱϩ+eeϱϩ0+ceϩeedd=eexy.

[44] dϩ3ϩ3+2ceϱϩeedd+2deeϱϱϩ3d3ϱϱϩ}=e3xxy

[45] {illeg} x+ax+bb=0 . {illeg} +aa0+bb

[46] ac=d. {illeg}=a. ad=b. ed=c. aab=ab. ae=e {aeb=eb.} bc=dbaab {illeg} c2= cc . ddbb2aabd+a4+aaccbb=ee.
Figure

[47] Figure
{illeg}d=a. pg=b. pd=g ead=dh . fad=gh . h=bdfad . {illeg} bdd2bdfa+aaff+eeaa=bbgg {illeg} aeeaadd=2bdaeedd+bbggbbdd . {illeg} a=bdeedd 2eeddO bbddee +2bbggeebbggdd 4e44eedd+d4

[48] Figure

[49] Figure

[50] Figure

[51] Figure

[52] Figure

[53] Figure

[54] Figure

[55] September 1664
Figure

[56] Figure

[57] Figure

[58] Figure

[59] dϱ+sϩe=x . tϱvϩ+cee= y

[60] Figure

[61]

dgegeddgg+dddgg=0. g=ddgg. dd=2gg or d=e ag2cg2cddgg=0 ag 2g+2ddgg=c. g3=dd+ggddgg. 2gg=dd . 3ccddddgg=0=c . 3ddg=3eeddgg d=e. aegd 6cdeddgg= adeg=0 +add 3ddccddggaddcg=0 9ccdd9ccgg=aagg . d4gg= {t4}gge4 36ccddee36ccggee=aaggee +aad4aaddgg 2cead3 rrx6xrx 3rx+8xx+16x3r+rr4 +4xx

[62] Figure

[63] Figure

[64]

Ian 20th 1664.

[65] Figure

[66] Figure

[67] Noe motion is lost in reflection. For the circular motion being made by continuall reflection would decay.

[68] Figure

[69] Def 3d

[70] {illeg}s Axiome 4th.

[71] Figure

[72] p Axiom 4th.

[73] Figure
Of the seperation of body{s} after reflection

[74] r axiome 3d

[75] Figure

[76] Figure

[77] Figure

[78] The center of motions determinacon & velocity

[79] x axiom 14

[80] Figure

[81] Figure
Of endeavor from the center
Figure

[82] Figure

[83] Figure

[84] Figure

[85] Figure

[86] Figure

[87] let this follow the 5t axiom

[88] Figure

[89] What force is required to beget or destroy equall velocity in unequall bodys

[90] Figure
What resistance in bodys

[91] What force Indeavor & Pression is

[92] What force or Motion is in equivelox bodys

[93] Figure
What velocity acquired or lost in equall bodys by unequall forces

[94] What motion in bodys

[95] Figure
A generall Theorem of the proportion of velocity & motion of given body moving ☞ through given spaces in given times.

[96] What force required to beget or destroy unequall celerity in equall bodys

[97] Of hindering and helping motion

[98] What celerity acquired or lost by equall forces in unequall bodys

[99] Figure
What velocity & motion gotten or lost by unequall forces in unequall bodys ☞ A Generall Theorem.

[100] Of the {illeg} force in reflected bodys
Figure

[101] Figure

[102] Figure
Two bodys being uniformely moved in the same plaine their center of motion which describe a streight line

[103] Figure
Figure
{illeg} the {illeg} {as divers plaines}

[104] Figure
of the velocity of the center of motion 14

[105] The 28th & 30th proposition done otherwise
Figure

[106] Or thus
Figure

[107] Figure
The {illeg} of motion is {illeg} before after {illeg}

[108] Figure
Figure
The center of motion in finite bodys hath the same velocity before & after reflection

[109] Figure
This ought to be proved by the 34th & 35t, & the 36t by this concerning the impresse of g on qdp

[110] Figure
Figure
Of the Advantage of force in divers positions to some center.

[111] Figure

[112] Figure

[113] Figure

[114] Figure

© 2020 The Newton Project

Professor Rob Iliffe
Director, AHRC Newton Papers Project

Scott Mandelbrote,
Fellow & Perne librarian, Peterhouse, Cambridge

Faculty of History, George Street, Oxford, OX1 2RL - newtonproject@history.ox.ac.uk

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