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Page 22
... passes through and supports a smooth ring whose weight is W ; find the greatest distance between P and Q con- sistent with equilibrium . 15. Find the law of force by which a particle may describe the lem- niscate , the centre of force ...
... passes through and supports a smooth ring whose weight is W ; find the greatest distance between P and Q con- sistent with equilibrium . 15. Find the law of force by which a particle may describe the lem- niscate , the centre of force ...
Page 53
... pass through three fixed points , and whose area is a maximum . 5. Prove that the triangle formed by joining the centres of equilateral triangles described on the sides of any triangle is equilateral . MR . BURNSIDE . 6. Through a given ...
... pass through three fixed points , and whose area is a maximum . 5. Prove that the triangle formed by joining the centres of equilateral triangles described on the sides of any triangle is equilateral . MR . BURNSIDE . 6. Through a given ...
Page 54
... pass through three fixed points . 9. Prove that the centre of the circle passing through the centres of the exscribed circles of a triangle lies on the right line joining the centres of the inscribed and circumscribed circles . 10. If ...
... pass through three fixed points . 9. Prove that the centre of the circle passing through the centres of the exscribed circles of a triangle lies on the right line joining the centres of the inscribed and circumscribed circles . 10. If ...
Page 59
... pass , between the order and the execution ; and the want of a speedy explanation of a single point is enough to defeat a whole system . You have , indeed , winged ministers of vengeance , who carry your bolts to the remotest verge of ...
... pass , between the order and the execution ; and the want of a speedy explanation of a single point is enough to defeat a whole system . You have , indeed , winged ministers of vengeance , who carry your bolts to the remotest verge of ...
Page 92
... passes through the external centre of similitude of the latter pair when the contacts are of the same kind , and through the internal centre of similitude when the contacts are of different kinds . ( a ) . Hence , or otherwise , prove ...
... passes through the external centre of similitude of the latter pair when the contacts are of the same kind , and through the internal centre of similitude when the contacts are of different kinds . ( a ) . Hence , or otherwise , prove ...
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Common terms and phrases
acid agus angle Aristotle axis Beginning BURNSIDE calculate CATHCART centre Cicero circle circumscribed circle cubic curve Deduce Describe determine DOWDEN ellipse Ending English equation equilibrium Euripides Explain expression following passages forces formula French Give an account Give some account given Greek Herodotus horizontal Ibid inscribed intersection Julius Cæsar Latin length literature Lucretius MAHAFFY meaning Mention method Mill Mill's nature OVID perpendicular Pindar plane Plautus position principle PROFESSOR prose prove quadric Quote radius relation respectively right line Roman sides sketch Sophocles square supposed surface syllogism tangents Theocritus theory thou Thucydides tion Translate the following triangle velocity verb vertical weight words Write a note γὰρ δὲ ἐν καὶ μὲν μὴ οἱ οὐκ τὰ τε τὴν τῆς τὸ τοῖς τὸν τοῦ τῷ τῶν ὡς
Popular passages
Page 325 - QUEEN and huntress, chaste and fair, Now the sun is laid to sleep, Seated in thy silver chair, State in wonted manner keep: Hesperus entreats thy light, Goddess, excellently bright! Earth, let not thy envious shade Dare itself to interpose: Cynthia's shining orb was made Heaven to clear when day did close: Bless us then with wished sight, Goddess, excellently bright!
Page 129 - J'aime mieux un ruisseau qui, sur la molle arène, Dans un pré plein de fleurs lentement se promène, Qu'un torrent débordé qui, d'un cours orageux, Roule, plein de gravier, sur un terrain fangeux. Hâtez-vous lentement ; et, sans perdre courage, Vingt fois sur le métier remettez votre ouvrage : Polissez-le sans cesse et le repolissez ; Ajomtez quelquefois, et souvent effacez.
Page 414 - And when I feel, fair creature of an hour! , That I shall never look upon thee more, Never have relish in the faery power Of unreflecting love: — then on the shore Of the wide world I stand alone, and think Till love and fame to nothingness do sink.
Page 356 - They say miracles are past ; and we have our philosophical persons, to make modern and familiar, things supernatural and causeless. Hence is it that we make trifles of terrors ; ensconcing ourselves into seeming knowledge, when we should submit ourselves to an unknown fear.
Page 313 - tis done, then 'twere well It were done quickly: If the assassination Could trammel up the consequence, and catch, 'With his surcease, success ; that but this blow Might be the be-all and the end-all here. But here, upon this bank and shoal of time, — We'd jump the life to come...
Page 282 - That fires the length of Ophiuchus huge In the arctic sky, and from his horrid hair Shakes pestilence and war.
Page 282 - Hell-doomed, and breath'st defiance here and scorn Where I reign king, and to enrage thee more, Thy king and lord?
Page 141 - T do confess thou'rt smooth and fair, And I might have gone near to love thee. Had I not found the slightest prayer That lips could speak, had power to move thee; But I can let thee now alone, As worthy to be loved by none.
Page 440 - Reason thus with life : If I do lose thee, I do lose a thing That none but fools would keep.
Page 349 - Phoebus lifts his golden fire: The birds in vain their amorous descant join, Or cheerful fields resume their green attire. These ears, alas ! for other notes repine; A different object do these eyes require...