The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 10
... angle dbe is equal to the angle cbe , the less to the greater , which is impossible ; therefore two straight lines cannot have a common segment . a b d с PROPOSITION XII . - PROBLEM . To draw a straight 10 THE ELEMENTS OF EUCLID .
... angle dbe is equal to the angle cbe , the less to the greater , which is impossible ; therefore two straight lines cannot have a common segment . a b d с PROPOSITION XII . - PROBLEM . To draw a straight 10 THE ELEMENTS OF EUCLID .
Σελίδα 12
... less to the greater , which is im- possible ; therefore be is not in the same straight line with bc . And in like manner it may be demonstrated , that no other can be in the same straight line with it but b d , which therefore is in the ...
... less to the greater , which is im- possible ; therefore be is not in the same straight line with bc . And in like manner it may be demonstrated , that no other can be in the same straight line with it but b d , which therefore is in the ...
Σελίδα 13
... less than two right angles . LET abc be any triangle ; any two of its angles together are less than two right angles . Produce bc to d ; and because a cd is the exterior angle of the triangle abc , acd is greater ( i . 16 ) than the ...
... less than two right angles . LET abc be any triangle ; any two of its angles together are less than two right angles . Produce bc to d ; and because a cd is the exterior angle of the triangle abc , acd is greater ( i . 16 ) than the ...
Σελίδα 14
... less than two right angles . fore any two angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side ... less than it ; it is not equal , because then the angle abc would be equal ( i . 5 ) to the angle acb ; but it is not ...
... less than two right angles . fore any two angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side ... less than it ; it is not equal , because then the angle abc would be equal ( i . 5 ) to the angle acb ; but it is not ...
Σελίδα 15
... less than the other two sides of the triangle , but shall contain a greater angle . LET the two straight lines bd , cd be drawn from b , c , the ends of the side bc of the triangle a bc , to the point d within it ; bd and dc are less ...
... less than the other two sides of the triangle , but shall contain a greater angle . LET the two straight lines bd , cd be drawn from b , c , the ends of the side bc of the triangle a bc , to the point d within it ; bd and dc are less ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram pentagon perpendicular Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle
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.