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) × 10 Hence 35-25=10, and the area. 150, the area required. 4 Again, by Masters H. Atkin, Sheffield, and J. Macann, Lutton. From Bonnycastle's mensuration, prob. 3. cor. 3. we 25+35 60 have px (pa), that is × (00—25)= 150, the area required. 2 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, 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 Δ 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 x the number of oxen, then =price of one 156 x 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. Again, by Master W. Balme. 156 and by the nature of the question which equation resolved, gives r = 26, therefore 6, the number bought. 26 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. It would be needless to insert the answers by Masters Aydon, Atkin, Balme, Bramall, Harrison, (Burton), Macann, Chambers, Fisher, Pickering, Thackwell, and Har 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 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 Sidera nautis ; Otium bello furiosa Thrace, Non enim gazæ neque consularis Vivitur parvo bene, cui paternum Quid brevi fortes jaculamur ævo Scandit æratas vitiosa naves Cura; nec turmas equitum relinquit, Ocior Euro. Lætus in præsens animus, quod ultra est, Abstulit clarum cita mors Achillem; Te greges centum Siculæque circum Murice tinctæ Vestiunt lanæ mihi parva rura et Spernere vulgus. ARTICLE II. Gesner's Edition. 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 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. ARTICLE III. Cicero de Senectute. 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 |