## Responsions Papers in Stated Subjects (exclusive of Books), 1901-1906: With Answers to Mathematical Questions and Introduction |

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Page 12

... volume it has been systematically referred to . ( 3 ) Loci . For the study of these ,

the four or five simplest cases ( of those in which the locus is a straight line or a

... volume it has been systematically referred to . ( 3 ) Loci . For the study of these ,

the four or five simplest cases ( of those in which the locus is a straight line or a

**circle**) should be carefully learnt , and their most important applications noted . Page 22

Find the rate in miles per hour at which it is travelling , assuming that the

circumference of any

. in 32 per cent . stock at 106 , what is my income ? What advantage do I derive

by a ...

Find the rate in miles per hour at which it is travelling , assuming that the

circumference of any

**circle**is 31 times the diameter . 11 . If I invest £1779 . 08 . 8d. in 32 per cent . stock at 106 , what is my income ? What advantage do I derive

by a ...

Page 65

6 . A finite straight line AB is bisected at C , and P is any external point . Prove

that ( a ) PA ? + PB2 = 2 PC2 + 2 AC2 ; ( 6 ) PA + PB is not less than 2 PC . 7 .

Show how to draw the two tangents to a

that ...

6 . A finite straight line AB is bisected at C , and P is any external point . Prove

that ( a ) PA ? + PB2 = 2 PC2 + 2 AC2 ; ( 6 ) PA + PB is not less than 2 PC . 7 .

Show how to draw the two tangents to a

**circle**from an external point , and provethat ...

Page 66

7 ) Prove that the straight line which passes through the middle points of two

parallel chords of a

prove that the distance between the centres is equal to either the sum or the ...

7 ) Prove that the straight line which passes through the middle points of two

parallel chords of a

**circle**is a diameter of the**circle**. 8 . ( 6 ) If two**circles**touch ,prove that the distance between the centres is equal to either the sum or the ...

Page 67

( 6 ) Prove that in a

are equal respectively to the segments of the ... ( b ) Show that if two

intersect , the tangents drawn to them from any point on the common chord are

equal .

( 6 ) Prove that in a

**circle**, if two equal chords intersect , the segments of the oneare equal respectively to the segments of the ... ( b ) Show that if two

**circles**intersect , the tangents drawn to them from any point on the common chord are

equal .

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### Common terms and phrases

active ages angle base bisected Book cent centre circle contains cost decimal described difference Divide draw drawn English equal examination Express feet field Find the square Find the value fixed four fraction gain Give given Greek half HILARY TERM income indic interest invested Join king Latin locus meaning meet MICHAELMAS TERM middle point miles minutes Multiply Oratio pass perf pers person plur plural present produce propositions Prove quae quam receive Reduce respectively SEPTEMBER share shillings Show sides Simplify sing singular Solve the equations square root straight line subjunctive taken tangents Translate triangle TRINITY TERM Turn twice whole wide yards γάρ δε και μεν ου προς τε

### Popular passages

Page 89 - Quis deus hanc mundi temperet arte domum, Qua venit exoriens, qua deficit, unde coactis Cornibus in plenum menstrua luna redit...

Page 92 - Theseus aut praemia laudis. non ingrata tamen frustra munuscula divis promittens tacito succendit vota labello. 104 nam velut in summo quatientem brachia Tauro quercum, aut conigeram Sudanti cortice pinum, indomitus turbo contorquens flamine robur eruit...

Page 89 - Aut Alcmaeoniae furiae aut ieiunia Phinei, Num rota, num scopuli, num sitis inter aquas, Num tribus infernum custodit faucibus antrum Cerberus, et Tityo iugera pauca novem, 45 An ficta in miseras descendit fabula gentes, Et timor haud ultra quam rogus esse potest.

Page 73 - Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third. 144. Find the locus of a point which moves so that the sum of the squares of the distances from two given points is fixed.

Page 99 - ... invidiamque eam sua sponte gliscentem insignis unius calamitas accendit. Magno natu quidam cum omnium malorum suorum insignibus se in forum proiecit. Obsita erat squalore vestis, foedior corporis Habitus pallore ac macie perempti; ad hoc promissa barba et capilli efferaverant speciem oris.

Page 81 - Christian was hard put to it ; for he had gone but a little way before he espied a foul fiend coming over the field to meet him ; his name is Apollyon. Then did Christian begin to be afraid, and to cast in his mind whether to go back or to stand his ground. But he considered again, that he had no armour for his back, and therefore thought that to turn the back to him might give him greater advantage with ease to pierce him with his darts; therefore he resolved to venture, and stand his ground. For,...

Page 102 - Phoebe, pigebit formosae medicas applicuisse manus. 5 effice ne macies pallentes occupet artus, neu notet informis candida membra color, et quodcumque mali est et quidquid triste timemus, in pelagus rapidis evehat amnis aquis.

Page 89 - Eurus, et in nubes unde perennis aqua ; sit ventura dies mundi quae subruat arces, purpureus pluvias cur bibit arcus aquas, aut cur Perrhaebi tremuere cacumina Pindi, soils et atratis luxerit orbis equis, cur serus versare boves et plaustra Bootes, Pleiadum spisso cur coit igne chorus, curve suos fines altum non exeat aequor, plenus et in partes quattuor annus eat ; sub terris sint iura deum et tormenta...

Page 99 - ... sabino bello ait se militantem, quia propter populationes agri non fructu modo caruerit, sed villa incensa fuerit, direpta omnia, pecora abacta, tributum iniquo suo tempore imperatum, aes alienum fecisse. Id, cumulatum usuris, primo se agro paterno avitoque exuisse, deinde fortunis aliis, postremo velut tabem pervenisse ad corpus; ductum se ab creditore non in servitium, sed in ergastulum et carnificinam esse.

Page 99 - Dicite, quo portu clausa puella mea est?" Et dicam : " licet Arķaciis considat in oris, 25 Et licet HyZleis : illa futura mea est." Hic erat ! hic iurata manet ! rumpantur iniqui ! Vicimus ! assiduas non tulit illa preces ! Falsa licet cupidus deponat gaudia livor : Destitit ire novas Cynthia nostra vias.