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Updated: June 12, 2025
And by prolonging the arc KQ till it meets AD at Y, the sum of the consequents is DY. Then KX ought to be to DY as 3 to 2. Whence it would appear that the curve KDE was of such a nature that having drawn from some point which had been assumed, such as K, the straight lines KA, KB, the excess by which AK surpasses AD should be to the excess of DB over KB, as 3 to 2.
"If I only had the toys the Awgwas stole from me," said Claus, sadly, "I could easily fill my sack for the children." "Where are they?" asked the Master. "I do not know," replied Claus, "but the wicked Awgwas probably hid them in the mountains." Ak turned to the Fairy Queen. "Can you find them?" he asked. "I will try," she replied, brightly.
"I am glad you did thus," said the good Queen, beaming upon the Master; and Necile, who had eagerly listened to every word, echoed in a whisper: "I, too, am glad!" "And this very night," continued Ak, "as I came to the edge of Burzee I heard a feeble cry, which I judged came from a human infant.
Jeminy, who was seated on his coat by the side of the road, got up with a smile. "Well, Anna Barly," he said. "Ak," she whispered, clapping both hands to her mouth, "how you scared me." She could feel her heart beating with fright; her lips trembled, her eyes filled with tears. She stood staring at Mr. Jeminy, who stared gravely back at her.
Let LG be a ray falling on the arc AK. Its refraction GV will be given by means of the tangent which will be drawn at the point G. Now in GV the point D must be found such that FD together with 3/2 of DG and the straight line GL, may be equal to FB together with 3/2 of BA and the straight line AL; which, as is clear, make up a given length.
Otherwise would we abandon our happy existence for one of trouble and anxiety. Good night, my nymphs!" Then Ak was gone from their midst, and Necile hurried away to her bower to rejoice over her new-found treasure. Claus Another day found Necile's bower the most popular place in the Forest.
I looked about me and found, close to the forest, a helpless babe, lying quite naked upon the grasses and wailing piteously. Not far away, screened by the forest, crouched Shiegra, the lioness, intent upon devouring the infant for her evening meal." "And what did you do, Ak?" asked the Queen, breathlessly. "Not much, being in a hurry to greet my nymphs.
Ak is the Master Woodsman of the world; he sees everything, and knows more than the sons of men. That night he held the Queen's hand, for he loved the nymphs as a father loves his children; and Necile lay at his feet with many of her sisters and earnestly harkened as he spoke.
The Master turned away and came to his Forest of Burzee, where he called a meeting of the immortals and told them of the defiance of the Awgwas and their purpose to kill Claus within three days. The little folk listened to him quietly. "What shall we do?" asked Ak. "These creatures are of no benefit to the world," said the Prince of the Knooks; "we must destroy them."
Now let us assume that the ray has come from A to C along AK, KC; the point of refraction K being nearer to A than the point B is; and let CN be the perpendicular upon BC, KN parallel to BC: BM perpendicular upon KN, and KL upon BA.
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