## Famous Geometrical Theorems and Problems, with Their History, Teil 1 |

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Archimedes attempt beautiful believe called centre CHAPTER circle circumference cissoid conclusion construction contain cube curve cylinder definition demonstration described diameter discovered double draw drawn equal equation evident fact famous figure fixed four geometricians geometry give given greater Greek half HEATH Hence hexagon History inscribed knowledge less manner mathematician Mathematics means meet method mind Morgan obtain opposite original parabola parallel parallelogram perpendicular plane polygon position premise present problem produced Professor PROOF NUMBER proportion proposition proved pupil radius reach reason rectangle right angles right-angled triangle says School semicircle sides solution solve sphere square statement straight line studied surface teacher teaching Thales theorem things tion triangle ABC trisection truth whole

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Seite 10 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.

Seite 77 - Philoponus.t it is asserted that the Athenians in 430 BC when suffering from the plague of eruptive typhoid fever, consulted the oracle at Delos as to how they could stop it. Apollo replied that they must double the size of his altar, which was in the form of a cube. To the unlearned suppliants nothing seemed more easy, and a new altar was constructed either having each of its edges double that of the old one...

Seite 70 - RULE. — From half the sum of the three sides subtract each side separately ; multiply the half -sum and the three remainders together ; the square root of the product is the area.

Seite 10 - ... and the three interior angles of every triangle are equal to two right angles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC ; and the three interior angles of the triangle, viz. ABC, BCA, CAB, are together equal to two right angles. Through the point C draw CE parallel (31.

Seite 5 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.

Seite 107 - Several men, being sent in with scythes, cleared the way, and made an opening for us. When we could get at it, and were come near to the front of the pedestal, I found the inscription, though the latter parts of all the verses were effaced almost half away. Thus one of the noblest cities of Greece, and one which at one time likewise had been very celebrated for learning, had known nothing of the monument of its greatest genius, if it had not been discovered to them by a native of Arpinum.

Seite 54 - XY for the discovery he has made if so what a reflection upon Old england the boasted land of freedom the nursery of the arts and sciences that her sons are obliged to go to a foreign country to obtain that recompense to which they are justly entitled.

Seite 56 - A great many people are staggered to this extent, that they imagine there must be the indefinite something in the mysterious all this. They are brought to the point of suspicion that the mathematicians ought not to treat "all this" with such undisguised contempt, at least.

Seite 55 - When my work appeared in numbers, I had not anything like an adequate idea of Mr. James Smith's superiority to the rest of the world in the points in which he is superior. He is beyond a doubt the ablest head at unreasoning, and the greatest hand at writing it, of all who have tried in our day to attach their names to an error. Common cyclometers sink into puny orthodoxy by his side. The behavior of this singular character induces me to pay him the compliment which Achilles paid Hector, to drag him...

Seite 53 - And what is the reason that you will not candidly acknowledge to him . . . that he has squared the circle shall I tell you ? it is because he has performed the feat to obtain the glory of which mathematicians have battled from time immemorial that they might encircle their brows with a wreath of laurels far more glorious than ever conqueror won it is simply this that it is a poor man a humble artisan who has gained that victory that you don't like to acknowledge it you don't like to be beaten and...