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Page 17
... the horizontal thrust on the walls . B. MR . WILLIAMSON . 1. Find the value of the radius of curvature at the origin of the spiral of Archimedes r = a0 . 2. Find the whole area of the curve a2 y2 c 2 JUNIOR SOPHISTERS -- MATHEMATICS . 17.
... the horizontal thrust on the walls . B. MR . WILLIAMSON . 1. Find the value of the radius of curvature at the origin of the spiral of Archimedes r = a0 . 2. Find the whole area of the curve a2 y2 c 2 JUNIOR SOPHISTERS -- MATHEMATICS . 17.
Page 18
... radius is half that of the given circle . 4. Find the time of a small oscillation in a simple pendulum , and show how to determine the corrections due to a change of place , and of length , respectively . 5. A square board ABCD , whose ...
... radius is half that of the given circle . 4. Find the time of a small oscillation in a simple pendulum , and show how to determine the corrections due to a change of place , and of length , respectively . 5. A square board ABCD , whose ...
Page 20
... radius vector and tangent varies inversely as the square of the radius vector ? 15. A particle revolves in a central ellipse ; if t be the time of de- scribing an angle a show that sin ( Vμt ) = rr sin a ab Classics . TACITUS . N.B. ...
... radius vector and tangent varies inversely as the square of the radius vector ? 15. A particle revolves in a central ellipse ; if t be the time of de- scribing an angle a show that sin ( Vμt ) = rr sin a ab Classics . TACITUS . N.B. ...
Page 46
... radius bears a constant ratio to the distance of its centre from the radical axis of the given circles . 2. ABC is an equilateral triangle , find the locus of the point P when PA = PB + PC . 3. A right line touches a circle at a point A ...
... radius bears a constant ratio to the distance of its centre from the radical axis of the given circles . 2. ABC is an equilateral triangle , find the locus of the point P when PA = PB + PC . 3. A right line touches a circle at a point A ...
Page 85
... radius of gyration round centre of gravity . 4. Define the centre of gyration of a body with reference to an axis . In the case of a heavy body , what is the measure of the velocity of this point in any position ? 5. State and prove D ...
... radius of gyration round centre of gravity . 4. Define the centre of gyration of a body with reference to an axis . In the case of a heavy body , what is the measure of the velocity of this point in any position ? 5. State and prove D ...
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Common terms and phrases
acid action agus angle Aristotle axis Beginning BURNSIDE Cæsar calculate centre characters Cicero circle coefficient conic curve deduce Describe determine ellipse Ending English Enumerate equation equilibrium Euripides Explain expression feet find the locus Find the value fixed point following passages force formula Give an account Give some account given Greek Hallam Hamilton heat Ibid illustrate inches Julius Cæsar Kant Latin M'CAY Mansel Mention method Mill Molière moment of inertia nature origin parabola plane Polybius principal Propertius prove quadric radical axis radius relation right line Roman Second Punic War sides square symptoms tangent theory Thucydides tion Translate the following triangle velocity vertical WILLIAMSON words Write a note δὲ ἐν ἐπὶ καὶ κατὰ μὲν οἱ τὰ τὴν τῆς τὸ τοῖς τὸν τοῦ τῷ τῶν ὡς
Popular passages
Page 388 - The world's great age begins anew, The golden years return, The earth doth like a snake renew Her winter weeds outworn: Heaven smiles, and faiths and empires gleam Like wrecks of a dissolving dream.
Page 12 - Or hear'st thou rather pure ethereal stream, Whose fountain who shall tell ? before the sun, Before the heavens thou wert, and at the voice Of God, as with a mantle, didst invest The rising world of waters dark and deep, Won from the void and formless infinite.
Page 310 - His breath like caller air ; His very foot has music in't As he comes up the stair — And will I see his face again ? And will I hear him speak? I'm downright dizzy wi...
Page 386 - THE flower that smiles to-day To-morrow dies; All that we wish to stay Tempts and then flies. What is this world's delight? Lightning that mocks the night, Brief even as bright.
Page 311 - Sleepless! and soon the small birds' melodies Must hear, first uttered from my orchard trees; And the first cuckoo's melancholy cry. Even thus last night, and two nights more, I lay, And could not win thee, Sleep! by any stealth: So do not let me wear...
Page 313 - He calls me boy ; and chides, as he had power To beat me out of Egypt ; my messenger He hath whipp'd with rods ; dares me to personal combat Caesar to Antony : — let the old ruffian know I have many other ways to die ; meantime Laugh at his challenge.
Page 311 - Fair are others ; none beholds thee. But thy voice sounds low and tender, Like the fairest, for it folds thee From the sight, that liquid splendour,— And all feel...
Page 124 - IN yonder grave a Druid lies, Where slowly winds the stealing wave ! The year's best sweets shall duteous rise...
Page 70 - And unto Sarah he said, Behold, I have given thy brother a thousand pieces of silver : behold, he is to thee a covering of the eyes, unto all that are with thee, and with all other: thus she was reproved.
Page 214 - For thoughts may past delights recall, And parted lovers meet again. I weep not for the silent dead : Their toils are past, their sorrows o'er ; And those they loved their steps shall tread, And death shall join to part no more.