The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 30.
Σελίδα 3
Of four - sided figures , a square is that which has all its sides equal , and all its angles right angles . Square . Oblong . XXXI . An oblong is that which has all its angles right anglės , but has not all its sides equal . XXXII .
Of four - sided figures , a square is that which has all its sides equal , and all its angles right angles . Square . Oblong . XXXI . An oblong is that which has all its angles right anglės , but has not all its sides equal . XXXII .
Σελίδα 31
To describe a square upon a given straight line . LËT a b be the given straight line ; it is required to describe a square upon a b From the point a draw ( i . 11 ) a c at right angles to a b ; and make ( i .
To describe a square upon a given straight line . LËT a b be the given straight line ; it is required to describe a square upon a b From the point a draw ( i . 11 ) a c at right angles to a b ; and make ( i .
Σελίδα 32
41 ) of the triangle a bd , because they are upon the same base bd , and between the same parallels bd , al ; and bi the square gb is double of the triangle fb c , because these also are upon the same base fb , and between the same ...
41 ) of the triangle a bd , because they are upon the same base bd , and between the same parallels bd , al ; and bi the square gb is double of the triangle fb c , because these also are upon the same base fb , and between the same ...
Σελίδα 33
To find a point in a triangle equidistant from the three angular points of the triangle . 8. Given the three angles of a triangle and the sum of its three sides to construct the triangle . 9. To find a square which shall be equal to any ...
To find a point in a triangle equidistant from the three angular points of the triangle . 8. Given the three angles of a triangle and the sum of its three sides to construct the triangle . 9. To find a square which shall be equal to any ...
Σελίδα 36
If a straight line be divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the square of the whole line . LET the straight line ab be divided into any two parts in the point c ...
If a straight line be divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the square of the whole line . LET the straight line ab be divided into any two parts in the point c ...
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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.