 | Encyclopaedia - 1845 - 920 pages
...first book of Euclid's Elements of Geometry ; namely, that the square described uptm the hypotbenuse is equal to the sum of the squares described upon the other two sides ; a proposition equally curious from the peculiarity of the result, and important for the numerous... | |
 | Euclid - Geometry - 1845 - 218 pages
...Which was to be done. PROPOSITION XXXI. THEOB. — In right-angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle. Draw the perpendicular... | |
 | Great Britain. Council on Education - 1845 - 696 pages
...but shall contain a greater angle. 60.*If the square described upon one of the sides of a trinngle be equal to the sum of the squares described upon the other two sides of it, the angle contained by these two sides is a right angle. 61. If a straight line be divided into... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...ratio in C (def. 3. 6.). E B ,I146 PROP. XXXI. THEOR. In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle. Let ABC be a right... | |
 | Euclides - 1846 - 272 pages
...therefore equal. PROPOSITION XLVII. THEOREM. In any right angled triangle (ABC) the square of the side (AC) opposite to the right angle, is equal to the sum of the squares of the remaining sides (AB and CB.) On the sides AB, AC and BC describe the squares AX, AF... | |
 | Education - 1847 - 508 pages
...same parts, are between the same parallels. 3. If the square described upon one side of a triangle be equal to the sum of the squares described upon the other two sides of it, the angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight... | |
 | William Ellis - Knowledge, Theory of - 1847 - 160 pages
...merest elements of this science, know that the square described on the side of a right angled triangle, opposite to the right angle, is equal to the sum of the squares described on the two sides which contain the right angle. Although that property of a right... | |
 | William Ellis - Knowledge, Theory of - 1847 - 152 pages
...merest elements of this science, know that the square described on the side of a right angled triangle, opposite to the right angle, is equal to the sum of the squares described on the two sides which contain the right angle. Although that property of a right... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...parallel, ' 256. Theorem. The square described upon the hypothenuse of a right triangle is equivalent to the sum of the squares described upon the other two sides. Proof. Let squares be constructed upon the three sides of the right triangle ABC (fig. 130), right-angled... | |
 | Euclides - 1848 - 52 pages
...given. . PROP. XXX. PROBLEM. PROP. XXXI. THEOREM. In right-angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle. PROP. XXXII. THEOREM.... | |
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In right angled triangles, the' rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle. 
