The Harpur Euclid: An Edition of Euclid's Elements

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Rivingtons, 1890 - 515 من الصفحات
 

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الصفحة 21 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
الصفحة 369 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
الصفحة 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
الصفحة 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
الصفحة 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
الصفحة 96 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
الصفحة 40 - Any two sides of a triangle are together greater than the third side.
الصفحة 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
الصفحة 407 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
الصفحة 156 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...

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