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2. Æquationum Constructio per Conicas Sectiones. 3. Aquationum Constructio Geome trica. 4. Additamenta de Curvis. These tracts appear to have been written before his Geometrical Lectures.
2. Theorema Generale ad Lineis Curvis Tangentes, et Curvarum Figurarum Areas, per Motum Determinandas.
3. Letters to Mr. John Collins, upon various mathematical subjects ; viz. 1. Concern-, ing Parabolical Conoids ; without date. 2. Rectifying a Mistake of Mr. Collins, concerning the Parallel Sections of the Cubical Parabolical Conoid ; without date. 3. Rules to compute the Portions of a Sphere or Spheroid. Sept. 5, 1664.
. 4. A Character of Mengolus's Elementa Geometria Speciosa, with whom he is displeased for his affectation of new definitions, and uncouth terms. Nov. 12, 1664.
5. He thanks him for a catalogue of mathematical books, which he sent him; gives a character of Alsted's Admiranda Mathematica, which he thinks a work of no great importance. Nov. 29, 1664.
6. Concerning a Parabolical Conoid cut parallel to the Axis. Jan. 9, 1665.
1. About printing his Archimedes, Apollonius, and Theodosius; as also a new edition of his Euclid. March 3, 1665.
8. Concerning the Area of the Common Hyperbola, found by Logarithms. Feb. 1, 1666.
9. Containing a variety of rules relating to the Circle and Hyperbola, with 'Theorems concerning the Curve Surfaces of Conoids and Speroids. March 6, 1667.
10. A continuation of nearly the same subject. March 26, 1668. .
11. A farther continuation of the same subject. May 14, 1668.
12. Concerning the Linea Secantium ; with two papers, one of the figure of Secants and Tangents, applied to the Arch or Radius; the other concerning the Cissoidal Space. March 13, 1668.
13. Concerning the publication of his Lectiones Optica. Easter-eve, 1669.
14. Sends him some few things to be inserted in bis Lectiones Geometrica, which were then printing. March 29, 1670.
15. Concerning the publication of those Lectures. April 23, 1670.
16. Sends him bis Apollonius, and Perspective Lectures. Oct. 11, 1570.
Firsi it may be demanded what the thing we speak of is, or whal this facetiousness doth import? To which question I might reply as Deinocritus did to him that asked the definition of a man; “'Tis that which we all see and know.” Any one better apprehends what it is by acquaintance than I can inform him by description. It is indeed a thing so versatile and multiform, appearing in so many shapes, so many postures, so many garbs, so variously appréhended by several eyes and judgments, that it seeme eth no less hard to settle a clear and certain notion thereof, than to make a portrait of Proteus, or to define the figure of the fleeting air. Sometimes it lieth in pat allusion to a known story, or in seasonable application of a trivial saying, or in 'forging an apposite tale : sometimes it playeth in words and phrases, taking advantage from the ambiguity of their sense, or the affinity of their sound. Sometimes it is wrapped in a dress of humorous expression; sometimes it lurketh under an odd similitude: sometimes it is lodged in a sly question, in a smart answer, in a quirkish reason, in a shrewd intimation,
Yn cunningly diverting, or cleverly retorting an obfection: sometimes it is couched in a bold scheme of speech; in a tart irony; in a lusty hyperbole; in a startling metaphor; in a plausible reconciling of contradictions, or in acute nonsense: sometimes a scenical representation of persons or things; a counterfeit speech; a mimical look or gesture passeth for it : sometimes an affected simplicity, sometimes a presumptuous bluntness giveth it being: sometimes it riseth only from a lucky hitting upon what is strange; sometimes from a crafty wrestling obvious matter to the purpose often it consists in one knows not what, and springeth up one can hardly tell how. Its ways are unaccountable and inexplicable, being answerable to the numberless rovings of fancy and windings of language. It is, in short, a manner of speaking out of the simple and plain way (such as reason teacheth and proveth things by) which by a pretty surprizing uncouthness in conceit or expression doth affect and amuse the fancy, stirring in it some wonder, and breeding some delight thereto. It raiseth admiration, as signifying a nimble sagacity of apprehension, a special felicity of invention, a vivacity of spirit, and, reach of wit more than vulgar. It seemeth to argue a rare quickness of parts, that one can fetch in remote conceits applicable; a notable skill, that he can dexterously accommodate them to the purpose before him, together with a lively brisk
ness of humour, not apt to damp those sportful flashes of imagination. Whence in Aristotle such persons are termed do, dexterous men; and Erpool, men of facile or versatile manners, who can easily turn themselves to all things, or turn all things to themselves. It also procureth delight, by gratifying curiosity with its rareness or semblance of difficulty; as monsters, not for their beauty, but their rarity; as juggling tricks, not for their use, but their abstruseness, are beheld with pleasure; by diverting the mind from its road of serious thoughts; by instilling gaiety and airiness of spirit; by provoking to such dispositions of spirit in way of emulation or complaisance; and by seasoning matters, otherwise distasteful or insipid, with an unusual, and thence grateful tang.
The sermons of Dr. Barrow were of an unusual length, even for the time in which he lived. He seldom employed less than an hour and a half in delivering a discourse; and on one occasion in particular, he preached a charity sermon at the Spital, before the lord mayor and aldermen, which lasted three hours and a half. Being asked, on descending from the pulpit, whether he was not tired,