"Logometria Auctore Rogero Cotes" pp. 5-45 (Cotes); WITH "The Art of Living under Water: Or, a Discourse concerning the Means of Furnishing Air at the Bottom of the Sea in Any Ordinary Depths" (pp. 492-499); "An Account of Several Extraordinary Meteors or Lights in the Sky" (pp. 159-164); "An Account of Several Nebulae or Lucid Spots Like Clouds, Lately Discovered among the Fixt Stars by Help of the Telescope" (pp. 390-392);"Methodus Singularis Qua Solis Parallaxis Sive Distantia a Terra" pp. 454-464; (Halley) WITH "An Account of Some Experiments of Light and Colours Formerly Made by Sir Isaac Newton, and Mention'd in His Opticks" pp. 433-447 (Newton and Desaguliers); "A Plain and Easy Experiment to Confirm Sir Isaac Newton's Doctrine of the Different Refrangibility of the Rays of Light" pp. 448-452; WITH "An Account of an Experiment made by Dr. Brook Taylor assisted by Mr. Hauksbee, in order to discover the Law of Magnetical Attraction" pp. 294-295 (Taylor) In: Philosophical Transactions. Giving Some Account of the Present Undertakings, Studies and Labours of the Ingenious, In many Considerable Parts of the World, Volume XXIX [29], For the Years 1714, 1715, 1716. London: Printed for W. Innys, at the Princes-Arms in St. Paul's Church-Yard. 1717. Roger WITH Halley Cotes, Edmund, Roger WITH Newton Halleio WITH Cotes, Isaac, J. T. WITH Taylor Desaguliers, Brook.

"Logometria Auctore Rogero Cotes" pp. 5-45 (Cotes); WITH "The Art of Living under Water: Or, a Discourse concerning the Means of Furnishing Air at the Bottom of the Sea in Any Ordinary Depths" (pp. 492-499); "An Account of Several Extraordinary Meteors or Lights in the Sky" (pp. 159-164); "An Account of Several Nebulae or Lucid Spots Like Clouds, Lately Discovered among the Fixt Stars by Help of the Telescope" (pp. 390-392);"Methodus Singularis Qua Solis Parallaxis Sive Distantia a Terra" pp. 454-464; (Halley) WITH "An Account of Some Experiments of Light and Colours Formerly Made by Sir Isaac Newton, and Mention'd in His Opticks" pp. 433-447 (Newton and Desaguliers); "A Plain and Easy Experiment to Confirm Sir Isaac Newton's Doctrine of the Different Refrangibility of the Rays of Light" pp. 448-452; WITH "An Account of an Experiment made by Dr. Brook Taylor assisted by Mr. Hauksbee, in order to discover the Law of Magnetical Attraction" pp. 294-295 (Taylor) In: Philosophical Transactions. Giving Some Account of the Present Undertakings, Studies and Labours of the Ingenious, In many Considerable Parts of the World, Volume XXIX [29], For the Years 1714, 1715, 1716. London: Printed for W. Innys, at the Princes-Arms in St. Paul's Church-Yard. 1717.

London: Royal Society. 1st Edition. FIRST EDITION of Roger Cotes' "Logometria Auctore Rogero Cotes," his only paper and the one in which he provides the first proof of the relation between exponential function to trigonometric functions -- the identity now known as Euler's formula. The Phil Trans is the oldest continuously published journal of an academy of science. As such, the Phil Trans established the important principles of scientific priority and peer review that have become the central foundations of scientific journals ever since. Works in every field of science are present; in addition to those of Hauksbee, there are papers by Halley, Newton, Desaguliers, and Taylor. ALSO INCLUDED: First edition of Edmund Halley's description of his diving bell. Though Halley lodged a patent for his diving bell in 1691, this 1716 Phil Trans paper was his first public description of his improved device. "Halley's paper, 'The Art of Living Underwater,' sets out the problems as he saw them of the bells constructed at the time. Bells were in use in shallow water throughout Europe, and there had been several notable cases of salvage... [but] Halley was keen to improve on the system, which involvwed hauling the diver and his bell all the way to the surface in order to replenish the air inside the container. He proposed a method whereby barrels of fresh air could be lowered to the bell, and emptied into it by means of a hose. Stale air would be let out from the top end of the bell through a stopcock. He tells us that air in an enclosed space loses its 'vivifying spirit,' and wisely states that he will not go into the precise physiological reasons for this, leaving that to the 'curious anatomist, to whom the structure of the lungs is better understood.' But Halley does understand that current models of diving bells contained only a small amount of air, and while it had been proposed to pump fresh air into them from the surface, the strength of the pumps available at the time was not sufficient to overcome the pressure at depths of more than fifteen feet or so. The deeper a bell descended, the smaller the air space that would be left in which to breathe, as the water pressure would compress the air inside the bell. Edmund Halley's bell was bigger and more stable than those of his contemporaries, and he further proposed that a diver might make excursions from the bell wearing a miniature bell on his head. What he suggested was a primitive diving helmet, which would be attached by a leather pipe to the large bell, although even at publication he does not reveal the precise details of this device. Unlike other scientific brains of the age, Halley tested his improved diving bell himself, descending into the waters of Pagham harbor in Sussex in the summer of 1691. According to his own account, Halley sat on a bench suspended across the lower reaches of the bell and remained dry except for his showes. Noting the effects of increased air pressure as the bell descends, he describes the physical sensations produced on the Eustachian tubes during the dive: 'The only inconvenience that attends [the descent] is found in the ears, within which there are cavities opening only outwards, and that by pores so small as not to give admission even to the air itself, unless they be dilated and distended by considerable force. Hence, a pressure begins to be felt on each ear, which by degrees grows painful, like as if a quill were forcibly thrust into the hole of the ear; till at length, the force overcoming the obstacle, that which constrains these pores yields to the pressure, and letting some condensed air slip in, present ease ensues'" (Ecott, Neutral Buoyancy, 19-20). ALSO INCLUDED are two other Halley papers, both on the astronomical phenomena of objects in the sky that produce light but do not contain a sun 'nebulae'. ALSO INCLUDED are two papers in which Desaguliers and Newton write about Newton's theory of light and colours. Desaguliers' optical experiments here were for the most paper retetitions of those described by Newton, made in order to vindicate Newton's accuracy -- which had been challenged -- and the theoretical conclusions Newton had drawn. Some of them were improved in detail -- for example, by the use of a camera obscura. Part of the success of Newtonian optics was due to those who spoke in defense of Newton's ideas, those who popularized them; Desaguliers was prominent in this role. ALSO INCLUDED is Taylor's important deduction that "at the distance of nine feet, the power alters faster, than as the cubes of the distances, whereas at the distances of one and two feet, the power alters nearly as their square." "Several important early diciples of Newton, particularly his assistants Francis Hauksbee and Brook Taylor... accordingly undertook to obtain by experiment a magnetic analog to the law of gravitation. Newton speaks of 'magnetic attraction,' which might imply the force of attraction between two magnets, but Taylor and Hauksbee measured the field of the magnet at different distances from the lodestone. Desaguliers' and Newton's papers about Newton's theory of light and colours. Item #335

CONDITION & DETAILS: In: Philosophical Transactions. Giving Some Account of the Present Undertakings, Studies and Labours of the Ingenious, In many Considerable Parts of the World, Volume XXIX [29], For the Years 1714, 1715, 1716. London: Printed for W. Innys, at the Princes-Arms in St. Paul's Church-Yard. 1717. Quarto (9 x 6.5; 225 x 163mm). [6], 544, [4]. Includes 3 page index. 13 copperplate engravings. Full volume, complete. Handsomely rebound in aged calf. 5 raised bands at the spine, each gilt-ruled; gilt-tooled fleur de lis at the spine. Red and black, gilt-lettered morocco spine labels. Tightly and solidly bound. New endpaopers. Occasional light toning and foxing. By any measure, near fine condition.

Price: $2,750.00