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ARTICLE XXIV.

QUESTION 1.

Answered by Master W. Balme, Attercliffe. The area of a right angled triangle, is equal to the rectangle of half the perimeter and its excess above the hypothenuse. Em. Geom. 37. 2. Hence (35+25)÷ 2=30, and 30× (30—25)=150 ch.15 acres.

Again, by Master J. Bramall, Holthead.

In every right angled triangle, the sum of the sides. less the hypothenuse, is equal to the diameter of the inscribed circle, and the perimeter multiplied by the diameter of the inscribed circle, is equal to four times (35+25) x 10 Hence 35-25=10, and

1

the area.

150, the area required. Again, by Masters H. Atkin, Sheffield, and J. Macann, Lutton.

From Bonnycastle's mensuration, prob. 3. cor. 3. we 25+35 have px (pa), that is

X

<(60—25)=

2

150, the area required.

The same, by Master S. Stead, Farnley.

From the nature of right angled triangles, it is obvious that the triangle, whose area is required, is similar to one whose sides are 3, 4, and 5 respectively and area 6; therefore, by similar figures 52 : 6 :: 252 : 150, the area required.

This question was answered also by Masters S. Aydon; W. Harrison, Burton Pidsea ; R. Chambers; W. Harrison; R. Fisher; and G. Pickering, of Broughton; also W. Thackwell.

QUESTION 2.

Answered by Masters S. Aydon, Leeds; and W. Balme. Let A B one side of the polygon,

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C the centre, and let CD radius ;
then the ACB= 5° or AC D=2°
30′ whose nat. tan. is .436609 area
of ACB to rad. 1. therefore, .436609
X72 3.1435848 the area of a 72 A

D

B

sided polygon, whose rad. is one; therefore, 3.1435848 × 9' 254.63036, the area of a 72 sided polygon, whose radius is 9.

Answers were sent by Masters Atkin; Bramall; W. Harrison, Burton; Chambers; Harrison; Fisher; Pickering; Macann, and Thackwell.

QUESTION 3.

Answered by Masters Aydon, Macann, and W. Harrison, Burton.

Let the number of oxen, then

=price of one

156

156

ox, and by the question

6=

or 6 x3

x

x+2'

13 x 312, or x2 + 2 x = 48, or x2 + 2 x + 1=49, or x+1=7, or x=6, the number of oxen bought.

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156

x

Again, by Master W. Balme.

156

x

Let x price of one ox, then

and by the nature of the question

number bought,

= + 2,

156

26

156

X -6 which equation resolved, gives x 26, therefore 6, the number bought.

Answers were sent by Masters Atkins, Bramall, Chambers, Fisher, Harrison, Pickering, and Thackwell.

QUESTION 4.

Answered by Master S. Stead, æt. 12, Farnley, Academy.

The solidity of a frustrum whose less base, slant height, and greater base, are 2, 5 and 8, is found to be 87.9648, and sim. solids being as the cubes of like dimensions; we have, 87.9648 : 23:: 703.7184: 64, and 644 is the less base of the required frustrum. By the same method we find its slant height = 10, and its greater base = 16.

156

X

It would be needless to insert the answers by Masters Aydon, Atkin, Balme, Bramall, Harrison, (Burton), Macann, Chambers, Fisher, Pickering, Thackwell, and Har

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rison, (Broughton), as they are all very similar to the

above.

Master James Macann, of Lutton, aged 134, is requested to send for the SILVER MEDAL.

PRIZE SUBJECTS

TO BE ANSWERED IN NO. VI.

ARTICLE I. VOL. II.

THE best translation of the following Ode, by gentlemen not 17 years old, will be entitled to a PRIZE.

HORATII CARM. LIB. II. ODE XVI.

AD GROSPHUM.

OTIUM divos rogat in patenti
Prensus Ægæo, simul atra nubes
Condidit Lunam, neque certa fulgent
Sidera nautis ;

Otium bello furiosa Thrace,
Otium Medi pharetra decori,
Grosphe, non gemmis neque purpura ve-
nale nec auro.

Non enim gazæ neque consularis
Summovet lictor miseros tumultus
Mentis, et curas laqueta circum
Tecta volantes.

Vivitur parvo bene, cui paternum
Splendet in mensa tenui salinum;
Nec leves somnos timor aut cupido
Sordidus aufert.

Quid brevi fortes jaculamur ævo
Multa? quid terras alio calentes
Sole mutamus? patriæ quis exul
Se quoque fugit?

Scandit æratas vitiosa naves
Cura; nec turmas equitum relinquit,
Ocior cervis, et agente nimbos
Ocior Euro

Lætus in præsens animus, quod ultra est,
Oderit curare, et amara lento
Temperet risu. Nihil est ab omni
Parte beatum.

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Vestiunt lanæ mihi parva rura et
Spiritum Graiæ tenuem Camœnæ
Parca non mendax dedit, et malignum
Spernere vulgus.

Gesner's Edition.

ARTICLE II.

THE best translation of the following piece, by young gentlemen not 14 years of age, will be entitled to a

SILVER MEDAL.

EQUIDEM efferor studio patres vestros quos colui et dilexi, videndi, neque vero eos solos convenire aveo quos ipse cognovi; sed illos etiam de quibus audivi, et legi, et ipse conscripsi: Quo quidem me proficiscentem haud sane quis facile retraxerit ; neque tamquam Peliam recoxerit; et si quis deus mihi largiatur, ut ex hac ætate repueriscam, et in cunis vagiam, valde recusem: nec vero velim, quasi decurso spatio, ad carceres à calce revocari: quid enim habet vita commodi? quid non potius laboris ? sed habeat sane; habet certe tamen aut satietatem, aut modum; non lubet enim mihi deplorare vitam, quod multi et ii docti sæpe fecerunt; neque me vixisse pœnitet, quoniam ita vixi, ut non frustra me natum existimem et ex vita ita discedo, tamquam ex hospitio, non tamquam ex domo; commorandi enim natura diversorium nobis, non habitandi dedit. O præclarum diem, cum ad illud divinum animorum concilium cætumque proficiscar! cumque ex hac turba et colluvione discedam! proficiscar enim non ad eos solum viros, de quibus

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ante dixi: sed etiam ad Catonem meum, quo nemo vir melior natus est, nemo pietate præstantior cujus à me corpus crematum est: quod contra decuit ab illo meum; animus vero non me deserens, sed respectans, in ea profecto loca discessit, quo mihi ipsi cernebat esse veniendum: quem ego meum casum fortiter ferre visus sum: non quod æquo animo ferrem: sed me ipse consolabar, existimans non longinquum inter nos digressum et discessum fore. His mihi rebus, Scipio, id enim te cum Lælio admirari solere dixisti, levis est senectus, nec solum non molesta, sed etiam jucunda; quod si in hoc erro, quod animos hominum immortales esse credam, lubenter erro: nec mihi hunc errorem, quo delector, dum vivo, extorqueri volo; sin mortuus, ut quidam minuti philosophi censent, nihil sentiam, non vereor, ne hunc errorem meum mortui philosophi irrideant; quod si non sumus immortales futuri, tamen exstingui homini suo tempere optabile est. Nam habet natura, ut aliarum omnium rerum, sic vivendi modum. Senectus autem peractio ætatis est tamquam fabulæ cujus defatigationem fugere debemus, præsertim adjuncta satietate.

Cicero de Senectute.

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ARTICLE III.

THE best translation of the following passage, from the sermons of Saurin, by any young lady or gentleman not 16 years old, will be entitled to a SILVER

MEDAL.

ENVISAGEZ-la cette mort, par raport aux types qui l'ont figurée; par raport aux ombres qui l'ont tracée; par raport aux cérémonies qui l'ont représentée; par raport aux oracles qui l'ont prédite.

Envisagez-la cette mort, par raport aux fondres et aux carreaux qui ont été lancez sur la tête de J. C. Voyez cette ame accablée de tristesse ; ce sang decoulant en terre; cette coupe d'amertume dont votre Sauveur est abreuvé; ecoutez ces insultes, ces calomnies, ces accusations, ces sentences d'iniquité: regardez ses pieds et ses mains clouez, ce corps qui n'est bien tôt qu'une playe, cette populace efrenée acharnée a sa croix et augmentant l'horreur de son supplice; allez

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