The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 2
X. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it .
X. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it .
Σελίδα 3
An isosceles triangle is that which has only two sides equal . Isosceles . Scalene . Equilateral . XXVI . A scatene triangle is that which has three unequal sides . XXVII . A right - angled triangle is that which has a right angle .
An isosceles triangle is that which has only two sides equal . Isosceles . Scalene . Equilateral . XXVI . A scatene triangle is that which has three unequal sides . XXVII . A right - angled triangle is that which has a right angle .
Σελίδα 4
Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are ...
Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are ...
Σελίδα 6
a b to de , and a c to df ; and the angle bac equal to the angle edf , the base bc shall be equal to the base ef ; and the triangle a b c to the triangle def ; and the other angles to which the equal b с е sides are opposite , shall be ...
a b to de , and a c to df ; and the angle bac equal to the angle edf , the base bc shall be equal to the base ef ; and the triangle a b c to the triangle def ; and the other angles to which the equal b с е sides are opposite , shall be ...
Σελίδα 7
Because a f is equal to ag , and ab to a c , the two sides fa , a c are equal to the two ga , a b , each to each ; and they contain the angle fag common to the two triangles afc , a gb ; thereа . fore the base fc is equal ( i .
Because a f is equal to ag , and ab to a c , the two sides fa , a c are equal to the two ga , a b , each to each ; and they contain the angle fag common to the two triangles afc , a gb ; thereа . fore the base fc is equal ( i .
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Συχνά εμφανιζόμενοι όροι και φράσεις
abcd angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given rectilineal given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 2 - 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 : XVI.
Σελίδα 42 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 21 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 38 - 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 of...
Σελίδα 15 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Σελίδα 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 126 - 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.