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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 Book of Euclid's Elements, Simplified, Explained, and Illustrated ... - Page 104
by Euclides - 1847

## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...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...

## The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...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...

## Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...parallelogram that has one right angle has all its angles right angles. PROPOSITION XL VII. THEOREM. In any right-angled triangle, the square which is...described upon the sides which contain the right angle. Let ABC be a right-angled triangle having the right angle BAG ; the square described upon the side...

## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...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...

## Remarks on Mathematical Or Demonstrative Reasoning

Edward Tagart - Logic - 1837 - 156 pages
...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...

## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...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...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 hypotenuse...

## An Essay on the Use of the Spirit Level: As Applied to Engineering and Other ...

Thomas Oswald Blackett - Leveling - 1838 - 136 pages
...between the true and apparent level may also be found according to the (Prop. 47, 1st. Book EuclidJ. In any rightangled triangle, the square which is described...described upon the sides which contain the right angle, or, in other words, in all right angled plain triangles, the sum of the squares of the two short sides...

## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...angles right angles. PROP. XLVII. THEOR. IN any right angled triangle, the square which is described ' G upon the side subtending the right angle, is equal...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...