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Página 41
... surface of a sphere , and derive from it the corresponding relation in the plane . 2. If a , ß , y , d , and a ' , B ' , y ' , d ' ′ be the roots of the two biquadratic equations αox + 4α1x3 + 6α2x2 + 4α3x + a1 = 0 , a′ox2 + 4a′1x3 + 6a ...
... surface of a sphere , and derive from it the corresponding relation in the plane . 2. If a , ß , y , d , and a ' , B ' , y ' , d ' ′ be the roots of the two biquadratic equations αox + 4α1x3 + 6α2x2 + 4α3x + a1 = 0 , a′ox2 + 4a′1x3 + 6a ...
Página 53
... surface is 76 square inches , its solid contents 40 cubic inches , and the perimeter of one of its faces 18 inches . 12. Solve the equation 13. If y = - ( x2 − 1 ) ( x2 + 2x − 1 ) = 6x + 9 . I - -VI I - x2 - I - VI - y2 2 = x2 I + VI ...
... surface is 76 square inches , its solid contents 40 cubic inches , and the perimeter of one of its faces 18 inches . 12. Solve the equation 13. If y = - ( x2 − 1 ) ( x2 + 2x − 1 ) = 6x + 9 . I - -VI I - x2 - I - VI - y2 2 = x2 I + VI ...
Página 61
... surface being expressed in terms of two variables u , v in the form ds2 = P ( du2 + dv2 ) , prove the following formula for measure of curvature I = - RR1 2P ( 82 ) d2 log P + d2 log P dv2 2 ) . du2 7. Prove that confocal cyclides of ...
... surface being expressed in terms of two variables u , v in the form ds2 = P ( du2 + dv2 ) , prove the following formula for measure of curvature I = - RR1 2P ( 82 ) d2 log P + d2 log P dv2 2 ) . du2 7. Prove that confocal cyclides of ...
Página 62
... surface meets the tangent at that point in the line which joins the three points of inflection of the section of the cubic surface by the tangent plane . 9. Construct geometrically the perpendiculars on the tangent planes at the points ...
... surface meets the tangent at that point in the line which joins the three points of inflection of the section of the cubic surface by the tangent plane . 9. Construct geometrically the perpendiculars on the tangent planes at the points ...
Página 63
... surface ax2 + By2 + yz2 + dw2 = 0 . 2. If any point on the quadric a y2 с be determined as the intersection with it of the confocal surfaces x2 + a + p y2 b + p z2 I = 0 , c + p x2 y2 z2 + I = 0 ; a + q b + q c + q determine , in terms ...
... surface ax2 + By2 + yz2 + dw2 = 0 . 2. If any point on the quadric a y2 с be determined as the intersection with it of the confocal surfaces x2 + a + p y2 b + p z2 I = 0 , c + p x2 y2 z2 + I = 0 ; a + q b + q c + q determine , in terms ...
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Términos y frases comunes
angle axis Beginning Butler calculate centre character circle coefficient conic cubic curve Describe determine DOWDEN Dublin ellipse Ending English EURIPIDES Explain expression feet find the locus Find the value fixed point following passages force French German Give an account Give some account given Greek horizontal Ibid intersection Kant L. C. PURSER Latin MAHAFFY means Mention method Mill's Name nature PANTON parabola particle perpendiculars plane position principal PROFESSOR prove PURSER quadric quod radius relation respect right line Roman roots sides sphere surface syllogism tangent theory Thucydides tion Translate into Greek triangle Trinity College University of Dublin velocity Verse vertical W. R. ROBERTS WALTER SMITH words Write a note Write a short αὐτοῦ γὰρ δὲ εἰς ἐν καὶ μὲν τὰ τε τὴν τῆς τὸ τὸν τοῦ τοὺς τῶν ὡς
Pasajes populares
Página 146 - Yet a few days, and thee The all-beholding sun shall see no more In all his course; nor yet in the cold ground, Where thy pale form was laid, with many tears, Nor in the embrace of ocean, shall exist Thy image.
Página 68 - In Xanadu did Kubla Khan A stately pleasure-dome decree: Where Alph, the sacred river, ran Through caverns measureless to man Down to a sunless sea.
Página 221 - Now, when they saw the boldness of Peter and John, and perceived that they were unlearned and ignorant men, they marvelled ; and they took knowledge of them, that they had been with Jesus.
Página 104 - KEEP thy foot when thou goest to the house of God, and be more ready to hear, than to give the sacrifice of fools : for they consider not that they do evil.
Página 232 - Wherefore, the grant of repentance is not to be denied to such as fall into sin after justification: After we have received the Holy Ghost, we may depart from grace given, and fall into sin, and by the grace of God, rise again, and amend our lives.
Página 221 - Again the next day after, John stood, and two of his disciples : And looking upon Jesus as he walked, he saith, Behold the Lamb of God ! And the two disciples heard him speak, and they followed Jesus.
Página 277 - The breezy call of incense-breathing morn, The swallow twittering from the straw-built shed, The cock's shrill clarion, or the echoing horn, No more shall rouse them from their lowly bed. For them no more the blazing hearth shall burn, Or busy housewife ply her evening care: No children run to lisp their sire's return, Or climb his knees the envied kiss to share.
Página 277 - How bowed the woods beneath their sturdy stroke! Let not Ambition mock their useful toil, Their homely joys, and destiny obscure; Nor Grandeur hear with a disdainful smile The short and simple annals of the poor. The boast of heraldry, the pomp of power, And all that beauty, all that wealth e'er gave, Awaits alike the inevitable hour: — The paths of glory lead but to the grave.
Página 274 - Shepherds, weep no more ! For Lycidas, your sorrow, is not dead, Sunk though he be beneath the watery floor. So sinks the day-star in the ocean bed, And yet anon repairs his drooping head, And tricks his beams, and with new-spangled ore Flames in the forehead of the morning sky...
Página 232 - Remember now thy Creator in the days of thy youth, while the evil days come not, nor the years draw nigh, when thou shall say, I have no pleasure in them...