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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 X (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 the area. Hence 35--25=10, and 150, the area required. Again, by Masters H. Atkin, Sheffield, and J. Macann,

Lutton. From Bonnycastle's mensuration, prob. 3. cor. 3. we. have į px (i p-a), that is *T

we shot 2.5+35760oth150, the area required. . The same, by Master S. Stead, Farnley.

From the nature of right angled triangles, it is ob- . vious 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, C the centre, and let CD = radius; then the LACB=5° or ACD=2° 30 whose nat. tan. is .436609 = area of ACB to rad. 1. therefore, .1.36609 *72=3.1435848 = the area of a 72 A D B

2

156

sided polygon, whose rad. is one; therefore, 3.1435848 x9=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 ; Picker. ing; Macann, and Thackwell.

QUESTION 3. Answered by Masters Aydon, Macann, and W. Har. rison, Burton. Let x = the number of oxen, then =price of one

156 ox, and by the question -61 = =

2+2 or 61 x + 13x = 312, or x + 2 x = 48, or x + 2x+1=49, or x+1=7, or x=6, the number of oxen bought.

Again, by Master W. Balne. Let r=price of one ox, then 156 = number bought,

150 156 . and by the nature of the question

X-61 7 +2, 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, Aca. demy.

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 :: 703.7 184 : 64, and » 04 = 4 is the less base of the required frustrum. By the same method we find its slant height = 10, and its greater base = 16.

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 13%, 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 gentle.

men 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 ealentes
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.
Abstulit clarum cita mors Achillem ;
Longa Tithonum minuit senectus;
Et mibi forsan tibi quod negarit,

Porriget Hora.
Te greges centum Siculæque circum
Mugiunt vaccæ; tibi tollit hinnitum
Apta quadrigis equa; te bis Afro .

Murice tinctæ
Vestiunt lanæ : mihi parva rura et
Spiritum Graiæ tenuem Camænæ
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 repueriscani, 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 penitet, quoniam ita vixi, ut non frustra me natum existi. mem : 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

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 niolesta, 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 vi. vendi modum. Senectus autem peractio ætatis est tamquam fabulæ : cujus defatigationem fugere debemus, præsertim adjuncta satietate.

Cicero de Senectute.

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 têie de J.C. Voyez cette ame accablée de tristesse ; ce sang decoulant en terre; cette coupe d'amertume dont votre Sauveur ést abreuvé; ecoutez ces insultes, ces calomnies, ces accusations, ces sentences d'iniquiié: regardez sey 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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