Letter from Thomas Horne to Newton, with notes by Newton on Middle Eastern cities

Author: Thomas Horne

Source: Keynes Ms. 97a, King's College, Cambridge, UK

Published online: January 2008

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<1r>

S^r

I have lately tryed to looke into Cartes 3^d booke of y^e nature of æquations, thinking to understand what goes before by y^e helpe of his rules delivered there: & I begin to hope I may by my owne strength, & j judge it is better to find one conclusion out than have 20 shewed me, w^ch made me defer moving questions to you so long, & partly because j cannot move my many doubts in proper termes. But I know you are to good & wise to deride me. Some things \Rules/ I think j understand in y^t discourse of æquation {sic}, but I stick at y^e first hypothesis pag 69^th. for first though I may suppose y^t x is æquall to 2 or x − 2 æquall to nothing \&c: –/; yet methinks this does not reach y^e y^e universall nature of æquations, though some may be imagined so to be made & then all things follow according \to/ y^e subsequent rules. let x − 2 be 0 y^e & x − 3 = 0 \x − 4 = 0/ y^e first magnitude y^t rises is xx − ex + 6 & y^e cube (if j may so call it) x³ − 9^xx + 2bx − 29. But set you thus x 2 x 3 x 4 then y^e first æquation on each hand is xx = 6 y^e 2^d æquation x³ = 29 Now heare all y^e midle species are lost, such as −9^xx + 26x. In y^e next place why must I alter y^e value of x & make it some times æquall to 2 & some times to 3 methinks this is more like a square x − 2 = 0 x − 2 = 0 & xx − 4x + 4 0. &c:

In pag. 74. I cannot understand y^e note H.

pag. 78.{illeg} I cannot find out y^e order of dividing y^e noted æquation by yy − aa − cc. neither am j able to find y^e meaning of those words in y^e bottome of y^e page. Id quod monstrat radiem quæsitā esse aa + cc quemadmodū per multiplicationem probari potest

pag. {illeg} \79/ y^e rule of making 2 æquations + x4*.pxx.qx.r &c. I have practised \upon/ some of his æquations but have not y^e reason of it nor {Basins} demonstration. p. 137. Nor y^e rule p. 81 of making 2 æqua\tions/ out of one.

I remember Cartes says if one try methodically to examine his rules, one shall find y^e demonstration of y^m, be pleased to shew me y^e methodicall examination in y^t aponation pag. 78 or some other.

pray sir if you can spare time to ease a doubter, deliver a note to M^r Michell or M^r Yard of Kings & they will send it to y^or

humble & thankfull pupill

T. Horne

Hadly Suffolk. Aug. 22^d.

<1v>

	Long	Lat
Amasia Cappadociæ	65.52	43.20
Amida Mesopotamiæ	78.15	39.30
Amisus Cappadociæ	65.50	44.15
Anararbus Ciliciæ	64.20	38.50
Anemurium Ciliciæ	65.10	36.50
Antiochia Syriæ	68.10	36.20
Antiochia ad Taurum	68.40	39.20
Antiochia Ciliciæ	62.30	38.30
{Arania} Mesopotamiæ	79.50	34.20
Arbela Assyriæ	89.0	35.52
Arbua Persidis	92.15	30.0
Aria Ariæ	106.40	36.45
Arsatia Mediæ	91.00	31.30
Armusa Persiæ sinûe	95.30	23.30
Arserate Armeniæ maj.	79.30	43 30
Artaxata Armeniæ major	78.0	42.40
Artemita Armen maj	78 40	40 30
Aziris Armeniæ major	72.00	42 30
Babylon Babyloniæ	79.00.	35.00
Berrhæa Syriæ	71.{3}0.	36.00
Cæsaria Cappadociæ \seu Mazaca/	64.40.	41 40
C{h}arrhæ Mesopotamiæ	73.20.	36.10
Chaboras Mesopotamiæ	78 0	55 30
Chorsa Armeniæ maj	74 40	42 30
Chotena Armen min	67 30	40 40
Cyropolis Mediæ	83 12.	44 00
Cyrrhum Syriæ	70 10	36 0
Damascus Syriæ	69 0	33 0
Ecbatana Mediæ	88 0	41 10
Edessa Mesopotamiæ	72 30	37 30
Emesa Syriæ	69 40	34 0
Gabala Syriæ	68 20	34 56
Hecatompilos Parthiæ	96 0	37 50
Heliopolis Syriæ	68 40	33 40
Heraclea Syriæ	68 20	35 10
Hierapolis Syriæ	70 30	38 0
Iban Armeniæ majoris	87 00	40 5
Iconium Cappadociæ	63 45	39 49
Marde Mespopotamiæ	76 0.	38 15
Melita Melitane Arm. min	71 0.	40 32
Nicephorium Mesopotamiæ	73 6.	35 20
Nicopolis Armeniæ	69 0.	42 25
Nisibis Ariæ	111.0.	35.3
Nisibis Mesopotamiæ	75.10.	37.30
Nyssa & Nysa Arm. min	66 30.	40 20
Orchoe Babyloniæ	78 30.	32 40.
Palmyra Syriæ	71 30.	34 0
Persepolis Persidis	91 0	33 20
Samosata Syriæ	71 30	37 36
Samunis Mediæ	79 0	46 40
Sebaste Cappadociæ
{Seleucia} magna Mesopotamiæ	79 20.	{illeg}
Seleucia Syriæ	{68 36}	{illeg}
S{illeg}bra Armen. major	{illeg}	{illeg}
Susa Susianæ	{illeg}	{illeg}
Tabresium Mediæ	89.{illeg}	{illeg}
Teredon Babyloniæ	84.10	31 37
Thospia Armen maj	76 40	41 17
Trapezus Cappadociæ	{illeg}6	44 {illeg}

For his worthy freind Mr Is: Newton

Math: Prof.

Cambridge.