 | Euclides - 1840 - 192 pages
...XXXI. THEOR. In a right-angled triangle (ACB), the rectilinear figure described upon the side (AB) opposite to the right angle, is equal to the similar and similarly described figures upon the sides (AC, CB) containing the right angle. From the vertex of the right angle draw CD perpendicular to the... | |
 | Euclides - Geometry - 1841 - 378 pages
...mean ratio in C.* Which was to be done. PROP. XXXI. THEOR. In right-angled triangles, the rectilineal figure described upon the side opposite to the right...figures upon the sides containing the right angle. Let ABC be a right-angled triangle, having the right angle BAC: the rectilineal figure described upon... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...and mean ratio in C (def. 3. 6.). 19 PROP. XXXI. THEOR. In right angled triangles, the' rectilineal figure described upon the side opposite to the right...figures upon the sides containing the right angle. Let ABC be a right angled triangle, having the right angle BAC : The rectilineal figure described upon... | |
 | 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...figures upon the sides containing the right angle. Draw the perpendicular AD : Therefore, because in the right-angled triangle ABC, AD is drawn from the... | |
 | Euclides - 1845 - 546 pages
...in C. (vi. def. 3.) QEfPROPOSITION XXXI. THEOREM. In right-angled triangles, the rectilineal Jigure described upon the side opposite to the right angle, is equal to the similar and similarly described fgures upon the sides containing the right angle. Let ABC be a right-angled triangle, having the right... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...mean 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...figures upon the sides containing the right angle. Let ABC be a right angled triangle, having the right angle BAC : The rectilineal figure described upon... | |
 | Euclides - 1848 - 52 pages
...another given. . PROP. XXX. PROBLEM. PROP. XXXI. THEOREM. In right-angled triangles, the rectilineal figure described upon the side opposite to the right...the sides containing the right angle. PROP. XXXII. THEOREM. If two triangles which have two sides of the one proportional to two sides of the other, be... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...XXXI. THEOR. In right angled triangles, the rectilineal figure described upon the side opposite to ike right angle, is equal to the similar, and similarly...figures upon the sides containing the right angle. Let ABC be a right angled triangle, having the right angle BAC : The .rectilineal figure described... | |
 | Euclides - 1852 - 48 pages
...be given, the square can be constructed. PBOP. XLVTI. THEOB. In a right-angled triangle, the square described upon the side opposite to the right angle is equal to the squares described upon the sides which contain the right angle. Let ABC be a right-angled triangle,... | |
 | Euclides - Geometry - 1853 - 176 pages
...3). Which was to be done. PROPOSITION XXXI. — THEOREM. In riglit-angled triangles the rectilineal figure described upon the side opposite to the right...figures upon the sides containing the right angle. LET ab С be a right-angled triangle, having the right angle ba (/. The rectilineal figure described... | |
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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... 
