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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. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 191
av Robert Simson - 1806 - 518 sider
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The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852
...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,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 317 sider
...PROP. XXXI. THEOR. In right angled triangles, the rectilineal figure described upon the side oppo' site to the right angle, is equal to the similar, and similarly...angled triangle, having the right angle BAC : The lectilineal figure described upon BC is equal to the similar, and similarly described figures upon...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...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...the sides containing the right angle. Let ABC be a right-angled triangle, having the right angle BAG : the rectilineal figure described upon BC is equal...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...be done. PROPOSITION XXXI. — THEOREM. In riglit-angled triangles the rectilineal figure described upon the side opposite to the right angle is equ/al...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 upon...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...XXXI.— THEOREM. In a right angled triangle (ABC) the rectilineal figure described upon the side (BC) opposite to the right angle, is equal to the similar and similarly situated figures described upon the sides (AB, AC) containing the right angle. С В .0 * 20 VI. For...
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 sider
...their sides are equal. 43. PROP. XXI. In the case of any right-angled triangle the square described upon the side opposite to the right angle* is equal to the two squares together described upon the two other sides which form the right, angle. Let ABC be aright-angled...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 sider
...ratio in C (def. 3. G.). PROP. XXXI. THEOR. In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal...similarly described figures upon the sides containing the rig/it angle. Let ABC be a right angled triangle, having the right angle BAC: The rectilineal figure...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...17. (c) VI. Def. 3. THEOREM.—If a triangle (ABC) be right-angled, 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. DEMONSTRATION. Draw the perpendicular...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1856 - 318 sider
...XXXI. THEOR. In right angled triangles, the rectilineal figure described upon the side opposite to ttie right angle, is equal to the similar, and similarly...angled triangle, having the right angle BAC : The lectilineal figure described upon BC is equal to the similar, and similarly described figures upon...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...together greater than the other two. 5. In right-angled triangles, the rectilineal figure described upon the side opposite to the right angle is equal...figures upon the sides containing the right angle. 6. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal...
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