I have also a lecture or more behind, which shall be sent in due time; also somewhat of preface. In the mean time, being entered, I could wish expedition.

I have nothing yet to answer concerning the matters of your last; indeed, for the reason, touched upon formerly, I shall presume upon you so as to forbear thinking of them until the term comes, and I set my thoughts upon such things; when perhaps I shall be better disposed thereto, although I do not hope much to hit upon any thing satisfactory to those purposes.

I did forget to answer concerning somewhat you formerly proposed, about M. Slusius his books. If any store of them lie upon your hands, you may please to deliver half a score (or so many as you shall think convenient for you) to this bearer John Stiles, a carrier of this place, receiving of him the price: however, pray, spare me one or two, which I would dispose of to friends.

I

Please to present my service to Mr. More. So with my best wishes, I rest

Your most affectionate and obliged servant,

Trin. Coll. Feb. 23, 1668-9.

ISAAC BARROW.

Dear Sir,

CLII.

BARROW TO COLLINS.

I write now only to save you the trouble of calling upon the carrier; for it will about be the end of the next week before I can send my book; and I shall take care that it come safely to your hands, without your further trouble. I leave the agreeing with Mr.

Pulleyn" wholly to you; only rather desiring you not to ask more of him than he is very willing to allow. For I would have no other benefit to myself than some copies for you to dispose of, and a few to present to my friends. I am not only willing that Mr. More peruse the book, but shall be very thankful to him for any care he shall bestow upon it, leaving it wholly to you and him to alter what you shall think fit. The Greek letters, I suppose, may be easily changed into the small letters of the Latin alphabet corresponding; but then the text must be also suitably changed. If it could be, I should think it best that the schemes were placed with the text in the book. I leave all to your ordering and pleasure.

What you ask concerning my papers is easily resolved; viz. If the ordinates KZ be equal to the secants CF, the line ZZZ will be an hyperbola, whose asymptotes [are] CK, °CY; because CK: CA :: CM: CF wherefore every where CK x KZ = CA2; CA: KZJ which is the most notorious property of an hyperbola.

}

n Barrow's Lectiones Opticæ were published in 1669, and it is said in their titlepage that præstant venales apud Johannem Dunmore et Octavianum Pulleyn Juniorem. The writers in the Gen. Dict. and the Biographie Universelle, are clearly ignorant of this edition of 1669, as also of that of the Lectiones Geome

trica of 1670 (see note 4, p. 72). From the different accounts, which they give of the titlepages, there must have been three editions, namely, those alluded to in these notes, that of 1672, (Gen. Dict. vol. II. p. 702.) and that of 1674.

o CZ in MS.

The alteration of ZZ into VV came not, I dare say, from my hand, but from somebody that misapprehended the business; and the space AZZZK is equal to the sum of (or space made by) the tangents AF applied perpendicularly to a straight line equal to the arch AM, &c. as, to my seeming, in that paper was very clearly demonstrated.

For the other questions I must desire some respite; they requiring more consideration than I can at present afford, my mind being indeed unhooked from these things and employed upon other meditations. So I rest

Your most affectionate friend

and obliged servant,

Trin. Coll. March 13, 1668-9.

IS. BARROW.

I desire you would make this agreement with Mr. Pulleyn, that the printing may be speedily dispatched, within as small a time as may be.

I have received all yours. The first, if it had been delivered to me in time, might have prevented you some trouble, for had I known M. Huygens had been printing his Optics, I should hardly have sent my book. He is one that hath had considerations a long time upon that subject, and is used to be very exact in what he does, and hath joined much experience with his speculations. What I have done is only what, in a small time, my thoughts did suggest, and I never had opportunity of any experience. So that I have

great reason to believe what he hath done, with so much advantage in all respects, will be much more perfect; yet seeing perhaps there may be in mine some things which have not occurred to him, or which he did not intend to consider, you may, if you think good, proceed in ordering the impression, the manner of which I wholly refer to your discretion. The stationer's offer is more than I expected, and doth abundantly satisfy me. Expedition will be to his advantage. The schemes being altered in quantity (retaining due proportion) will not be any prejudice. The three last lectures, if, when the book is broken up for the printers, they should be sent me, I should transcribe them more fairly; and I have not, indeed, yet read them in the schools, so that they would ease me of making new ones. I have several new (I suppose) geometrical theorems of a general importance, which perhaps I may put together and add as an appendix, having digested them into lectures, &c.. I intended to send you some of them, but my business hath hindered me, which (besides pupils and other ordinary employments) hath been imposed upon me by the college; 'tis to make Theological Discourses P (as our statutes order) upon the chief points of [the] Catechism, (the Creed, Decalogue, Lord's Prayer, Sacraments, &c.) which out of term so takes up my thoughts that I cannot easily apply them to any other matter. For I have that imperfection, as not to be able to draw my thoughts easily from one thing to another. This hath made me so backward in correspondence upon what you propounded, together with presumption in your forbearance and readiness to excuse me. I thank

These were printed after his death, and will be found in the sixth volume of the collec

tion of his Theological Works, published at Oxford in 1830.

you for M. Slusius his books, but wish you had received the price for them. I am so deep in your debt upon all accounts, that I am even ashamed to think of it, and in no hope to get out of it. With my best wishes I rest

Your most affectionate and obliged

friend and servant,

Easter Eve, 1669.

I. BARROW.

Mr. Jonas Moore was the other day here with me, and will (he said) be here again.

Part of this letter is printed in the Gen. Dict. vol. II.

թ. 702.

I was aware of your objection about your spiral. What you say is true, but not inconsistent with what I say; for I do not refer to the vulgar logarithms, but to such as are accommodated to the construction I there propound, which increase as their correspondent proportionals decrease (such as my Lord Napier first pitched upon), but you respect the common logarithms. However, to avoid mistake, you may insert these words:

Vel retro, (prout vulgares logarithmi procedunt,) si DI sit numerus in serie geometrica exorsa a DO, et desinente in D[B] ac 0 sit logarithmus ipsius DO, et arcus LK ipsius DB, erit arcus LZ logarithmus ipsius DI 9.

What you speak concerning Dr. Wallis his remarks

See Barrow's Lectiones Geometrica (1670), p. 124.