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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 187
av Robert Simson - 1806 - 518 sider
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## The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...and . -jnean ratio. PROP. XXXI. THEOR. In a right-angled triangle, the rectilinear figure described upon the side opposite to the right angle, is equal...figures upon the sides containing the right angle. PROP. XXXII. THEOR. If two triangles, having two sides of the one proportional to two sides of the...
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## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...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...
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## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...Which was to be done. PROP. XXXI. THEOR. 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 BAC: the rectilineal figure described upon BC shall be...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. Let ABC be a right angled triangle having the right angle BAC ; the square described upon the side BC is equal to the squares described upon BA, AC. On BC describe (46....
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## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...to be done. PROPOSITION XXXI. THEOB. — 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. Draw the perpendicular AD : Therefore, because in the right-angled triangle ABC, AD is drawn from the...
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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 sider
...the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. Let ABC be a right angled triangle having the right angle BAC ; the square described upon the side BC is equal to the squares described upon BA, AC. On BC describe (46....
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## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...figure described upon the side subtending the right angle is equal to the similar and similarly situated figures upon the sides containing the right angle. Let ABC be a right-angled triangle, having the right angle BAC, and upon AB, AC, BC let any similar and similarly...
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## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...PROP. XXX. PROBLEM. PROP. XXXI. THEOREM. 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. PROP. XXXII. THEOREM. If two triangles which have two sides of the one proportional to two sides of...
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## The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 sider
...the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. Let ABC be a right angled triangle having the right angle BAC; the square described upon the side BC is equal to the squares described upon BA, AC. On BC describe (i....
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