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It is manifeft that the difference of the fquares of AT and TG, must not be lefs than the fquare on AB, in the firft cafe; and, in the fecond cafe, the fum of those fquares muft not exceed the fquare on AD.
77. QUESTION (I. Nov.) answered by MATHEMATICUS, the propofer. The parallels AB, CD being drawn, and C the fituation O taken in AC produced, fet off AP the given ditance 50 feet and make PQ parallel to AC. Bifect AC in R; and, joining PR, QR, let the points P, Q, be fuppofed in a R horizontal plane, and O and R, in a line fixfeet above it; and OR, PR, and QR fhall be equal (Ditton's Perspect. Prop. 3.) Put m=20 feet, n-6 feet, d50 feet, sfine of the angle A POQ, and 2x=AC. Then the points O,P,Q, being in the circumference of a circle, the center of which is R, the angle PRQ is double the angle POQ (Euc, 3, 20) and the angle POQ=the angle APR, and 1 : m+x;;s: x ;.x0
Hence the verfed fine of the complement of the maximum angle is to double the diftance of the spectator from the nearest parallel as the fine of that angle is to the distance which the parallels are afunder. Again, 1:m+x:: √1—ss: the hypothenufal line from P to an elevation of fix feet above A, by substitution to m× and thence AP2 comes cut mm x dd+nn-mm --nndd, and s = 72752nat. fine of 46° 41′; and 2x=106.8 feet, the distance of the parallels
78. QUESTION (II. Nov.) not answered.
79. QUESTION (III. Nov.) anfwered by Mr. S. HAMILTON.
Suppofe the thing done, and that BCD is the triangle required. Then, by the queftion, BD+BP+BC-M, a given line, and BDxBC+BP×BC÷ BC2 (BD+BP+BCX BC) = M x BC, N, a given fquare: hence BC, being a third proportional to M and N, is given; and, therefore, BD+BP is given being M-BC, alfo BD × BP is given by Euc. VI. Cor. 8, and VI. 16; confequently, both BD and BP are themfelves given by Euc. 111. 36.
Draw the indefinite line QR, and, at any point, B, erect the perpendicular BC, equal to a third proportional to M and N. Apply half M-BC, from C to S, in the indefinite line QR, and on S, as a center, with the radius SC, defcribe the feini-circle ACR. Draw CD parallel to QR; and, from B, apply BA to D, and BCD is the triangle required.
91. QUESTION I. by NUMERICUS.
It is required to find two numbers, fuch, that the fum of their cubes, when increased by 2, may be equal to the cube of their fum.
92. QUESTION II. by Mr. WILLIAM KAY.
Given the fum of the fides of a plane triangle, the vertical angle, and the line drawn from the vertical angle to the middle of the bafe, to construct the triangle.
93. QUESTION III. by .
Granting the spheroidical figure of the earth, and the moon in the equinoctial, at the time of her perigee; how far will she rise and set from the east and weft points, at Greenwich?
94. QUESTION IV. by the fame Gentleman.
Three pofts A=5, B=4,5, C=4 feet long, are fet erect upon the horizon, at the diftances AB=9,5, BC=9, CA=8.5 feet; three rafters, AD, = BD=6,65, CD=6,15 feet long, are placed on thefe, and unite at the top D: it is required to find how far the point, perpendicularly under D, in the hori zontal plane, is from the bottom of each poft?
***The other two queftions fent by this gentleman are not expreffed with fufficient clearness to be generally understood.
The answers to these questions may be directed (poft-paid) to Mr. Baldwin, in Paternofter-row, London..
FOR THE LONDON MAGAZINE.
A DIALOGUE OF THE DEAD.
WILLIAM DE CABESTAN AND ALBERT FREDERIC OF BRANDENBURGH.
Poets were very scarce furely in your time, that they could be in fuch high efteem as to be poifoned on account of jealoufy. I am very forry that you were not born in the age in which I lived. You might then, I can affure you, have celebrated all forts of beauties, without any danger of being poifoned.
I know it. I never hear any of your beaux efprits, who come hither at this time, complain of a fimilar fate. But as to yourself now, pray how came you to be metamorphofed into a fool? BRANDENBURGH.
In a very rational way. A King once met with the fame accident, by seeing a spectre in a foreft, and that you know was no fuch great thing. But whatI beheldwas much more terrible. CABESTAN.
And what did you fee?
BRANDENBURGH. Preparations made for my wedding. 1 efpoufed Mary-Eleanor of Cleves, and I made fuch wife reflections on matrimony, during that magnificent feftival, that I loft my fenfes.
Frantic people are only fools of a different fort. The follies of the whole race of mankind being of the fame fpecies, are fo eafily reconcileable to each other, that they form the ftrongeft bonds of human fociety. Witness that thirt of immortalizing their names - that falfe glory, and many other principles, on which the actions of the world in general turn, and on account of it none are accounted fools but a particular fort of people, who are few in number, and if we may fo term it, are out of employment. Their folly differs from that of the reft of the world, only as far as it does not enter into the general economy of life.
Frantic perfons are fo foolish, that they treat each other as fuch. The ret of mankind, however, behave to one another like people of senfe.
Ah! what are you talking about? All mankind understand each other very well, and Nature has moft judiciously eftablished this order of things. The folitary derides the courtier, but in recompence he never approaches the court to give it any difturbance. The courtier laughs at the folitary, but he leaves him to enjoy his retirement in
A SOLILOQUY, WRITTEN AMONG THE TOMBS.
The beauties of rate our daily
Solitary Walks. of knowing the night of death cometh
Every tombstone round me, in this place of skulls, feems to addrefs me in the language of infpiration, be ye also ready, for ye know not the day nor the hour when the fon of man cometh.-Yes, methinks I hear it reverberated from fepulchre to fepulchre, while I read the numerous infcriptions prefented to my view, and obferve the dates of many who are gone before me much younger than myself, I am naturally led to the enquiry, Am I prepared for my laft great change? Am I fit to die? for ere another morn and I may be numbered with the mouldering dead.
Time is haftening and eternity approaching: I cannot tell what a day or an hour may bring forth. Oh then let it be my folicitous concern, as well as my earneft prayer, to believe on jefus Chrift, who is the refurrection and the life, in whom whofoever believeth fhall live though he die, and whofoever liveth and believeth in him shall not die eternally.
THE RURAL CHRISTIAN. John-street, Tottenham-Court-road, March 5, 1785.
HERE is no inftance, but in re
to approve the profeffion, and abufe ANECDOTES
Tligion, where it is a compliment the practice.
LOND. MAG. Mar. 1785.
FOR THE LONDON MAGAZINE.
A curious EDICT of CONSTANTINE
"TO all our fubjects throughout
Anecdote of the late GENERAL OTWAY.
This officer had been many years in the fervice with the rank of colonel, during which time feveral junior colonels had got regiments over his head. His friends frequently intreated him to ftate his fervices, and petition the King: he refifted their importunities for a confiderable time; but being at length prevailed upon, he defired the chaplain of the regiment he ferved in to draw him a petition, which being done and fent to the colonel, he took notice that it concluded with the words, and your petitioner shall
ever pray." He fent for the chaplain,
and told him that he had made a mif
take, and imagined he was prefenting a petition for himself by the manner he had concluded it. He defired the petition to be altered from the ufual conclufion: he infifted that the word pray was unfit to come from an officer. It was to no purpofe that he was informed of the ufual mode of drawing the prayer of all petitions; he would not give up his opinion upon the mate ter; it should run thus, and your petitioner fhall ever fight. He took the petition to court, and prefented it to the late King, who was pleafed with the novelty of the conclufion, and the honeft bluntnefs of the officer: and in the course of a few weeks a regiment became vacant, which he gave to Otway, in oppofition to his minifters, who had promifed to provide for a friend that had some interest in parliament.
Anecdote of VOLTAIRE.
This extraordinary genius, in his younger life, wrote a very biting fatire against a man of quality in France. The nobleman, on meeting the poet one day in a narrow lane where it was impoffible to efcape, gave him a fevere drubbing. Voltaire made his complaint to the regent, who very fhrewdly replied "What would you have me do? juftice has been done already."
Anecdote of the prefent EMPEROUR of
When Prince Piccolomini, who poffeffes great estates in Bohemia and Naples, was at Venice, he was very fond of driving a phaeton and four furiously about the city; and coming near the guard, the latter turned out his men to falute the Prince. A puddle of water happened to be just before the officer, who was at the head of his guard, and had on a new fuit of white regimentals. The Prince drove, however, with fuch rapidity, that the of