The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 80.
Σελίδα 7
3 ) to a f , the less , and join fc , g b . 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 ...
3 ) to a f , the less , and join fc , g b . 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 ...
Σελίδα 8
Join cd ; then , in the case in which the vertex of each of the triangles is without the other triangle , because a c is equal to a d , the angle a cd is equal ( i . 5 ) to the angle a dc : but а . b the angle a cd is greater than the ...
Join cd ; then , in the case in which the vertex of each of the triangles is without the other triangle , because a c is equal to a d , the angle a cd is equal ( i . 5 ) to the angle a dc : but а . b the angle a cd is greater than the ...
Σελίδα 9
3 ) off a e equal to ad ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join a f ; the straight line af a bisects the angle bac . Because a d is equal to a e , and a f is common to the two triangles da f ...
3 ) off a e equal to ad ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join a f ; the straight line af a bisects the angle bac . Because a d is equal to a e , and a f is common to the two triangles da f ...
Σελίδα 10
... it is required to draw a straight line from the point c at right angles to a b . Take any point d in a c , and make ( i . 3 ) ce equal to cd , and upon de describe ( i . 1 ) the equilateral triangle dfe , and join fc , the ...
... it is required to draw a straight line from the point c at right angles to a b . Take any point d in a c , and make ( i . 3 ) ce equal to cd , and upon de describe ( i . 1 ) the equilateral triangle dfe , and join fc , the ...
Σελίδα 11
10 ) fg in h , and join h cf , ch , cg ; the straight a f g b line ch , drawn from the d given point c , is perpendicular to the given straight line a b . Because fh is equal to hg , and hc common to the two triangles fh c , ghc , the ...
10 ) fg in h , and join h cf , ch , cg ; the straight a f g b line ch , drawn from the d given point c , is perpendicular to the given straight line a b . Because fh is equal to hg , and hc common to the two triangles fh c , ghc , the ...
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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.