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Página 20
... intersection of normals to an ellipse at the points x'y ' , x " y " . 4. Deduce the formula in spherical trigonometry cot a sin bcos C cos b cot A = sin C 5. Prove completely the formula for spherical triangles tan = √tans . tan § ( s ...
... intersection of normals to an ellipse at the points x'y ' , x " y " . 4. Deduce the formula in spherical trigonometry cot a sin bcos C cos b cot A = sin C 5. Prove completely the formula for spherical triangles tan = √tans . tan § ( s ...
Página 21
... intersection with an arbitrary circle , of any three co- axal circles ; prove the relation BC . a cos a + CA.b cos ẞ + AB . c cos y = o . MR . LESLIE . 13. Find the locus of the centre of a conic passing through four fixed points . 14 ...
... intersection with an arbitrary circle , of any three co- axal circles ; prove the relation BC . a cos a + CA.b cos ẞ + AB . c cos y = o . MR . LESLIE . 13. Find the locus of the centre of a conic passing through four fixed points . 14 ...
Página 22
... intersection of the com- mon chord with AB produced , taking origin at A , and axes of co - ordi- nates parallel and perpendicular to PQ . 4. In order to reduce the biquadratic equation x2 + px3 + qx2 + rx + s = 0 to a reciprocal ...
... intersection of the com- mon chord with AB produced , taking origin at A , and axes of co - ordi- nates parallel and perpendicular to PQ . 4. In order to reduce the biquadratic equation x2 + px3 + qx2 + rx + s = 0 to a reciprocal ...
Página 29
... intersections of corresponding sides are collinear , and conversely . 10. Show that every two triangles , one inscribed and the other circum- scribed to a circle at the same three points on its circumference , are connected as in the ...
... intersections of corresponding sides are collinear , and conversely . 10. Show that every two triangles , one inscribed and the other circum- scribed to a circle at the same three points on its circumference , are connected as in the ...
Página 30
... intersection of the lines which join the middle points of the opposite sides of a quadrilateral is the middle point of the line which joins the points of bisection of the diagonals ; and con- struct a quadrilateral , being given its ...
... intersection of the lines which join the middle points of the opposite sides of a quadrilateral is the middle point of the line which joins the points of bisection of the diagonals ; and con- struct a quadrilateral , being given its ...
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Palavras e frases frequentes
acid Æneid agus angles argument Aristotle Articles axis Beginning Book Butler calculate centre Cicero circle circumscribing circle cloth conic curve cylinder deduce Demosthenes Describe determine doctrine Edition Ending equal equation Euripides Explain expression find the value following passage force formula Give an account Give some account given heat Hebrew Herodotus horizontal Ibid Iliad inches inclined inclined plane intersection LIVY magnet meaning Mention method origin parabola passage into Greek passage into Latin passages into English perpendicular plane Plautus principle PROFESSOR prophecy prove Psalms radius respect Roman sides Sophocles spherical surface Tacitus tangents Tertullian Testament theory Thucydides tion Translate the following triangle velocity verb vertical vols weight words Write a note Write a short δὲ ἐν καὶ μὲν τὰ τὴν τῆς τὸ τὸν τοῦ τῶν
Passagens conhecidas
Página 200 - To beg the voice and utterance of my tongue, A curse shall light upon the limbs of men; Domestic fury and fierce civil strife Shall cumber all the parts of Italy ; Blood and destruction shall be so in use, And dreadful objects so familiar, That mothers shall but smile when they behold Their infants quarter'd with the hands of war ; All pity choked with custom of fell deeds : And Caesar's spirit ranging for revenge, With Ate by his side come hot from hell, Shall in these confines with a monarch's...
Página 28 - She sings the wild song of her dear native plains, Every note which he loved awaking — Ah '. little they think, who delight in her strains, How the heart of the minstrel is breaking...
Página 281 - In that day shall there be upon the bells of the horses, Holiness unto the Lord; and the pots in the Lord's house shall be like the bowls before the altar. Yea, every pot in Jerusalem and in Judah shall be holiness unto the Lord of Hosts...
Página 240 - I' the commonwealth I would by contraries Execute all things ; for no kind of traffic Would I admit ; no name of magistrate ; Letters should not be known : riches, poverty, And use of service, none ; contract, succession, Bourn, bound of land, tilth, vineyard, none : No use of metal, corn, or wine, or oil : No occupation ; all men idle, all ; And women too ; but innocent and pure : No sovereignty : — Seb.
Página 240 - Twere now to be most happy, for I fear My soul hath her content so absolute That not another comfort like to this Succeeds in unknown fate.
Página 200 - Shall cumber all the parts of Italy : Blood and destruction shall be so in use, And dreadful objects so familiar, That mothers shall but smile, when they behold Their infants quarter'd with the hands of war, All pity chok'd with custom of fell deeds ; And Caesar's spirit, ranging for revenge, With Ate by his side, come hot from hell, Shall in these confines, with a monarch's voice, Cry " Havock !" and let slip the dogs of war, That this foul deed shall smell above the earth With carrion men, groaning...
Página 233 - Thy hopeful eye Is bright as thine own sunny sky. Ay, let them rail — those haughty ones, While safe thou dwellest with thy sons. They do not know how loved thou art, How many a fond and fearless heart Would rise to throw Its life between thee and the foe.
Página 125 - When the market is very small, no person can have any encouragement to dedicate himself entirely to one employment, for want of the power to exchange all that surplus part of the produce of his own labour, which is over and above his own consumption, for such parts of the produce of other men's labour as he has occasion for.
Página 240 - how the world wags: Tis but an hour ago since it was nine, And after one hour more 'twill be eleven; And so, from hour to hour, we ripe and ripe, And then, from hour to hour, we rot and rot; And thereby hangs a tale.
Página 214 - War in each breast, and freedom on each brow. How much unlike the sons of Britain now ! Fir*d at the sound, my genius spreads her wing, And flies where Britain courts the western spring ; Where lawns extend that scorn Arcadian pride, And brighter streams than fam'd Hydaspes glide.