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Hic definit MS. Ang plan., cui Da- quaintance with the Greek language, is vides Hascheins, U. C. sua manu in very clearly evinced by this collafine adjrip/ft:-λειπει μια σεις, περας tion of the manuscript Scholia on Eu. sampe uvin nio plowa d. 29. Dec, 1714. ripides, and more particularly by the EY: E. COS. TAVETE; C 4222002. judgement with which he had adopted Valckenaer then proceeds thus: “I

I and approved the best lections.” have been informed by the celebrated We must not, however, omit inRciíke, that under the capital letters forming our readers that the name of is concealed the name of George Fre. Thryliitius occurs very frequently in deric Thryllitius, who was born near the Miscellaneæ obferuationes, which Leipsic, in the year 1688. After he were begun by Jortin, in England, had published feveral specimens of his and continued for several years after learning, and was preparing for the he had given up the scheme, by the press the 17:00u.minis, Oumping, and learned Philip D’Orville, and 'Peter Mebouw funz, of Tzetzes, he died at Burman, the elder*, in Holland, and Wittenberg, in 1915. The wonderful that wherever it is mentioned, he is depth of erudition which Thryllitius mentioned with the praise which he had acquired, and his intimate ac merited.

O. E. * How far Burman was concerned in the management or expence of this work, we know not; but it is certain, that many of the notes in the earlier voluines, besides several of the original pieces, are his.

EDITOR.

MATHEMATICS. ANSWERS TO MATHEMATICAL QUESTIONS, 62. QUESTION (111. June) antwered by Mr. G. SANDERSON,

CONSTRUCTION.
D
RAW any line DB at pleasure, which

cut into extreme and mean proportion at A, such that BAXBD-DA?, make AE perpendicular to and equal AB; through

E
E draw DEC, to meet BC drawn parallel
to E A in C, and the triangle ACB shall be
Similar to the required one.

DEMONSTRATION.
By similar triangles DA : AE (AB) :: D

A

B DB : BC, and, hy construction, DA: AB :: DB : DA, where ex equo, DB : DB :: DA: BC. Therefore, BC=DA, but AB=AE by conitruction; therefore the tiangle AED-triangle AC3. 65. QUESTION (11. July) answered by Mr. G. SANDERSON.

CONSTRUCTION. Make AD equal to the given sum of the sides

K and perpendicujar, on which take A B equal to I the given bate, and bifeet it in O; erect the indetinile perpendicular Bk, and on O, as a center, at the distance AD delcribe the circle DIII, cut

H ting BK in H: tien by Proh. 19, Simplon's Geometry, make KH such that FIK X HK +2HBA02,=B02; from K to the circle DHL apply KG=AO, draw AG cutting BH in E; Jaitly draw CO perpendicular to AB, and meeting AG in C, join CB, and ACB is the triangle required. DEMONSTRATION,

Α,

B Describe the circle about the triangle ACB;

0 also conceive the circle DHI to be completed, and HB produced to meet it in b. Then, because KB is perpendicular to AD, therefore Bb = HB, Euc.

=AG2 (AO?) by construction, KGE is a right angle, Euc. 37, and 18, UJI. Whence the triangles KGE, ABE, AOC, and BOC are equiangular, but KG= AO=OB. : EG=CO, and KE=AC=BC=AE, therefore AC + CB+-CO =AE+EG=AD, the given sum.

Now, because the arc ACB is bifected in C, it is well known that the perpendicular CO and the sum of the fides AC+CB (=AE) is the greatelt that can be drawn in the segment ACB ; confequenily, if either be greater, the ve:tex C iust * fall without the circle, but two lines drawn from A and B to meet without the circle contain an angle less than ACB, the angle in the segment; therefore, ACB is a maximum.

Q. E. D.

67. QUESTION (1. Aug.) answered by Tasso, the proposer, by Mr. Emerson's

metliod of Increments. Lets = the fum of n terms. Then the n + 1 or s term is evidently equal to

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3.1+1.n+2 +3nts being corrected, and ntı restored, we obtain s=

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3.n+1.n+2.n+ 3 the fum required. Cor. The sum of the given series, infinitely continued is

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68. QUESTION (II. Aug.) answered by the proposer, Mr. J. WALSON, when

the vertical angle is a right angle.

CONSTRUCTION. Let AB = the given seg. ment, and BC=the given sum: on AC describe a semi-circle, and erect the perpendicular

1 BE: bisect AB in D, and with DE radius describe a semicircle cutting AC in G and F: on GC describe a semi-circle and apply therein GK = GB, F

ADB

G H and GKC will be the triangle required,

DEMONSTRATION. ABC=BE2-FBG, by Euc. VI. 8 cor. Hence, BC: BG :: FB : AB, by VI. 17. and GC: BG::FA or BG:AB, by divifon. Now, GC: GK or BG::GK : GH, by VI. 8. cor, therefore, GH=AB,

Q. E. D.

SCHOLI U M. AB must be less than BC. For when AB = {BC, BG becoines equal to GC and the triangle vanishes. GKC is isosceles when BC is equal to twice AB together with the diagonal of the square, whose fide is AB. When BC is greater, GK and GH will be the lesser side and segment, and vice versa.

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MATHEMATICAL QUESTIONS.

80. QUESTION I. by A. M. It is required to explain and demonstrate the principle on which a top, whilf it is whirling and baving its axis inclined to the horizon, recovers its perpendicular position.

*** Emerson, in his Treatise on Centripetai Forces, has endeavoured to explain this principle, but has failed.

81. QUESTION II. by ASTRONOMICUS. To determine the situation of the planet Mercury in respect to the earth, when the intensity of its light to a spectator on the earth is the greatest.

82. QUESTION III. by Mr. J. WALSON. Let there be two circles given in position and magnitude, and let two right lines be drawn, each of which touches both circles; if the points of contact in one of the circles be joined, and the line joining them be produced until it meets the line which joins the two points of contact in the other circle, the segments of these two lines, intercepted between the point where they meet each other and the points of contact, will be proportional: a demonstration of this is required.

The answers to these quellions may be direeted (poit-paid) to Mr. Baldwin, in Paternoster-row, London.

THE

A S T R O N O M Y. FOR THE LONDON MAGAZINE. HE following remarks on the numerous observations of Hevelius,

planet Mercury, as they have never though perhaps some of them might appeared in any of our publications, will be acceptable, if reduced with fuffiprobably be acceptable to many per- cient exactness. Halley and La Hire fons, at least certainly they will be observed with more precision, as did very inuch so to those who make aftro- also our great astronomer Flamstead; nomical observations, as their object but this lait hardly ever noticed Meris to point out in what part of that cury, which is very unaccountable, as planet's orbit it appears the inoft bright, it is the only object in the heavens he and particularly when it can be feen has neglected. with meridian instruments.

Of all the above-mentioned astrono. Ancient observations of Mercury are mers, I believe none of them, except very scarce; Ptolemy, in his Almageft, La Hire, ever saw Mercury on the has only fixteen, two of which are meridian; they observed the planet erroneous: after these, until Tycho's when near the horizon, which obsertime, I find none that have been of vations are well known to be far less any use, except a few made by Gual. accurate; and even La Hire succeeded tere, towards the end of the fifteenth but very feldom, for in the Memoires century. Copernicus complains that de l'Academie Royale des Sciences, of he never could get a good observation. 1764, the Abbé Charpe d'Auteroche Tycho-Prahe, Longomontanus, Mar- says that only eight or nine meridian graff, and Riccioli were more successo observations are to be met with in the ful, and made several, but most of preceding Memcires; but since that them are of little use for correcting year many have been made, as may be the tables, as the planet then was not seen in the different publications of in the requisite part of its orbit; this M. M. Le Gentil, de Thury, de la objection is also made to many of the Lande, Maikelyne, Messier, &c. though

at the same time most of them men- Mercury, when brightest, is about the tion the extreme weakness of the pla- same as that of Sirius when in connet's light, and how frequently they junction with the fun. were disappointed, which was owing 4thly. As an additional proof of its to their looking for it when fartheit brightness, I find eight observations, from the sun, in which situation Mer- made with an eighteen-inch quadrant, cury àlways appears very faint. the telescope of which is two feet focal

We are new cone to the principal length, the aperture of the glasses one object of this paper, which is to point inch, magnifying eighteen times; with out in what part of his orbit Mercury which inftrument it is very difficult to is invisible, when apparently the most see stars of the seventh magnitude when bright, and also when he begins to the wires are in the least illuminated. lose and recover his light. Monsieur 5thly. The quick alteration of the D'Arquier, in the preface to his Ob- planet's brightness is particularly reJerections Aftronomiques, mentions that markable, being fometimes very confiMercury is invisible towards his infe- derable in less than twenty-four hours. rior conjunction, and visible near the 6thly. On the 11th of July, 1779, superior; and this I have been inform- Mr. Edward Pigott observed the plaed is nearly all he says on the subject; net, which was then less than three I shall, therefore, refer to a memoir I degrees distant from the fun; we may, heard read at th... French Academy of therefore, conclude, that sometimes it Science, containing observations made can be seen even

can be seen even in conjunction with in 1778 and 1779, by Mr. Edward the fun. Pigot, and which they ordered to be 7thly. It is fingular that Mercury printed in their Savans Etrangé: from and Venus appear brightest in the opthat paper most of the following arti- posite parts of their orbits; the first cles are selected, but are given here between his elongations and superior with alterations; as since that was conjunction, the other between her written I have also made fome addi- elongations and inferior conjunction; tional observations and remarks, which, therefore, Venus is seen as a crescent to avoid repetition, I take the liberty in great perfection, particularly in her to blend with those made by Mr. Ed inferior conjunction, while Mercury ward Pigott.

is feldom seen on the meridian in such ift. Mercury is brightest between perfect phases. his elongations and fuperior conjunc 8thly. In consequence of the rule tion, very near to which last he ge- settled by the first article, it is easily nerally can be seen: he becomes invi- known how often Mercury may be sible foon after he has passed his elon- seen in a year. I find that during the gation going towards his inferior con next it can be observed on the merijunction, and becomes visible again a dian about 200 times. few days before his next elongation. I hope, by thus having shewn with This is the result of above fixty ob- what facility and how frequently Merservations made with a transit inftru cury can be seen on the meridian, even ment, the telescope of which is a three with the most common instruments, feet achromatic, magnifying fifty times. that the practical astronomer may be

It must be always understood, that induced to pay more attention to this all these remarks allude to the appear- much-neglected planet. Nothing more ance the planet aliumes when on the remains, but to add that the historical meridian.

part of this paper is chiefly extracted 2dly. When Mercury has a great from the Memoires de l'Academie dos southern declination, or when the at- Sciences, and that we are indebted to mosphere is in the least thick, he fel- the distinguished Monf. de la Lande dom can be seen in those parts of his for the greatest part, as also for the orbic where he begins to recover his correctness of the present tables of light, or is much diminished in bright- Mercury, which seldom err more than nefs.

a few seconds. 3dly. The apparent brightness of

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M E DI CI N E. TO THE EDITOR OF THE LONDON MAGAZINE. SIR, I , of the

bloos, together with a few reflections upon this subject; which I have b.en led to draw observing that a proposal has been made for the revival of this practice, in a pamphlet lateix puslithed, entided, Some new Hints relative to the recovery of Perlons drowned, aird app enig duad.” As the histories of the experiments which have been made upon this subject are cifutisey Icattered throuch the different volumes of the transactions of our own and toreign furieties, I have persuaded mytelf that it would not be diipleating to your readers to lee uiem thus brought to their view in an abridged and collected itate. I am, Sir, your's, &c.

P. ON TRANSFUSION OF BLOOD. [T was about the year 1666 that transfusion The relation of this experiment was follosed

For by a paper, written by the fame hand, containthe priority of the discovery both nations for a ing tull and particular directions relative to the long time contended: now, however, it is pretty manner in which transfution thould be pertorired. apparent that the English were the first who It is therein advised that the blood of the recipient practed transtution upon brute, and that the animal be fuffect to Huw out in propre French were the tirit who made trial of it upon tive as that of the emitent animal runs ia: thit men. Bui, according to an Italian philosopher, thus, at the end of the operation, all, or at lea:t wtio pubashed a book a: Rome, about this time, the grea'er yırt of the blood which remains in eolitica “ Relati ne di?! 'Eyfrienze fuire in t'e vetle's of the former, may cot be its ou 2 Inghilterra, Francia, ed Italia iniurno ia Tranf- birod, but the blood of the latter. It is also fu,i one del sangue," it thould feem that trant- directed, that one of the quil's (tor it did not at fution is not of io modern a date as that of 1666, that time occur to Dr. Lower that metalline tubes but that it was known at lea!t, if not practiled, would antwer better) be inserted into an artery fifty years farther back. In proof of this, the of the emittent animal, and another into one of Italian author quotes the following pallage from the veins of the recipiunt animal. These diLibavius's Definfi byrugmutis lidmar um chic rections, it will be feet, differ from those which micorum, printeri al fianttort, in 1615: “ Ads had been given before by Libavius. This laft fit juvenis robinjtu, fanus, farza.in fpiritaso author does not make any mention of letting the pirrus. Nulsti pidetzjtus airinus, tenuis, ma blood of the animal that is to receive flow out, criminsi, l'itarimam irabens, 117.8 ir arzuha- either previously to or during the performance of Diset tué tous crgerlti, ini perlu ke?,!1'), perial the transtujion; and he ailo lays that the blai arteriam ibti, Grububum is geral Manniqut ; is to pass troin the ariery or the animal that is in in rei agroti arteri.zm pintut, 3 rubulum fami emit into the artery, not the vein, ot that which neum infigat; zum aus tubul'us foi mutuo ap is to reccive. Miui, o ex junnfanguis uzileridis, caicus In the following year, 1667, many successful ipisi?uc jus faliet in a givium, vrap vitæ fintum transtutions were made. Amongst others, that

Tei mimque languorem plee; ic. Let which was made upon a bitch seems to be a very there be a Itjut healthy your fellow, tull of remarkable one. She lot, during the operation, blood and spirits; and a weakent, thin, meagre nearly thirty ounces of blood, and received, as perton, that has hardly any lile within him. Let it was lupposed, about the same quantity from one skilled in the butinels de provided with fome the other animal. The bitch not only survived silver tubes, property adapted to enh other; let this operation, but, what is hardly credible, under. him make an inci'ion into th’artery of the robutt went very loon afterwards even a more dangerous perfon, and having introduced a cube into it, let one; for her spleen was taken out, the persons him tecure it therein; next, le: liim open one of who did it not obrerving the precaution of tying up the fick man's arteries, and tix in it aiuke inteed the veilels froin which this ziscus was separatca. for being introduced into the other tube; let him Since that time the bitch became with aut falten the two tubes torn-th." and the warm puppy, and littered, and continued afterward, 10 and firituous arterial blood will when be pro be well. This experiment, it is observed, thews pulled from the healthy into the sick puson; and thai large transtutions are not dangerous. i sviter with this blued the icuuius of lite will The iame year Sir Edm. King published an bu curricu, ul.d all livuor will be in an inttant account of an experiment of tansfution from a Jemwed."

calf into a theep, by the veins only. Previous Dr. Luer, it fvull prear, was the first who to the operation, 49 ounces of blood were taken published an account nihelbisüf hical Traila from the sheep. The transfusion was then made, actions for jóúo, of the el, erinni of transfu and when it was thought that as much blooi hau fon from one dog in to another. Ile cock a mastiff in this manner been given to, as haú been taken and a cur, and into the later introduced the away from the sheep, the operation was stoppe', blood of the former. The consequence was, that When the shcep was untied, it feemed to be as use intind died, audriat Vie cur, when he was vigorous as it had been before the loss of its own untied, ran and thook himmelig as it he had been biond. This animal was afterwards purposely Ons huwn into Watcr.

bied to dcath.

Abuut

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