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" In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. "
The first two books of the Elements of Euclid, with additional figures ... - Pagina 76
door Euclides - 1852
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pagina’s
...parallelogram that has one right angle has all its angles right angles. PROP. XLVII. THEOR. In any right angled triangle, the square which is described upon the side...sides which contain the right angle. Let ABC be a right angled triangle having the right angle BAG ; the square described upon the side BC is equal to...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 pagina’s
...remaining complement BK is equal to the remaining complement KD. PROP. XXXVII. THEOR. In any right angled triangle, the square which is described upon the side subtending the right angle, is equivalent to the squares described upon the sides which contain the right angle. Let ABC be a right...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...to the sum of the squares of the other two sides, the angle contained by those two sides shall be a right angle. Let ABC be a right-angled triangle, having the right angle, В AC : the square of В С shall be equal to the sum of the squares of В A, AC. Upon В С, В A,...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 pagina’s
...which are about the diameter of any parallelogram, are equal to one another. XLVII. In any right angled triangle, the square which is described upon the side...described upon the sides which contain the right angle. XLVIII. If the square described upon one of the sides of a triangle, be equal to the squares described...
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The Element of Geometry

John Playfair - 1836 - 114 pagina’s
...square upon the side BC,. is equal to the squares upon the sides AB, AC. Therefore, in any right angled triangle, the square which is described upon the side...described upon the sides which contain the right angle. Which was to be proved. PROP. XVIIL THEOR. If the square described upon one of the sides of a triangle...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 pagina’s
...that has one right angle has all its angles right angles. ', PROP. XLVII. THEOR. In any right angled triangle, the square which is described upon the side...sides which contain the right angle. . ( Let ABC be a right angled triangle having the right angle BAG ; the square described upon the side BC is equal to...
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Remarks on Mathematical Or Demonstrative Reasoning

Edward Tagart - 1837 - 135 pagina’s
...of the term straight, the less likely they were to enclose a space. If I were asked how I know that in any rightangled triangle the square which is described...described upon the sides which contain the right angle, my first answer might be, that I knew it by studying the 47th of the first book of Euclid. But the...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 pagina’s
...I. THEOR. IN any right-angled triangle, the square which is described upon the hypotenuse, that is, the side subtending the right angle, is equal to the...be a right-angled triangle, having the right angle BAC; the square described upon the hypotenuse BC is equal to the squares described upon ISA, AC. On...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 pagina’s
...ADE = 2 right Zs, 5. that the fig. is rectangular (and :. a square.) PROPOSITION XLVII. ii Theorem. In any right-angled triangle, the square which is...described upon the sides which contain the right angle. In the construction of the figure it is necessary to show that GA is on the same right line with AC...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 pagina’s
...the right angle, is equal to the similar and similarly described figures upon 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 to the similar and similarly described figures upon BA,...
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