The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 76.
Σελίδα 5
ab ; and because the point b is the centre of the circle acé , bc is equal to ba : but
it has been proved that ca is equal to ab ; therefore ca , cb , are each of them
equal to ab ; but things which are equal to the same are equal to one another ( 1
ax . ) ...
ab ; and because the point b is the centre of the circle acé , bc is equal to ba : but
it has been proved that ca is equal to ab ; therefore ca , cb , are each of them
equal to ab ; but things which are equal to the same are equal to one another ( 1
ax . ) ...
Σελίδα 6
LET a b c d e f be two triangles , which have the two sides a b , ac equal to the
two sides d e , df , each to each , viz . a b to de , and a c to df ; and the angle bac
equal to the angle e df , the base b c shall be equal to the base ef ; and the
triangle ...
LET a b c d e f be two triangles , which have the two sides a b , ac equal to the
two sides d e , df , each to each , viz . a b to de , and a c to df ; and the angle bac
equal to the angle e df , the base b c shall be equal to the base ef ; and the
triangle ...
Σελίδα 7
Because a f is equal to a g , and a b to a c , the two sides fa , a c are equal to the
two ga , a b , each to each ; and they ... it has also been proved that the angle f bc
is equal to the angle gcb , which are the angles upon the other side of the base .
Because a f is equal to a g , and a b to a c , the two sides fa , a c are equal to the
two ga , a b , each to each ; and they ... it has also been proved that the angle f bc
is equal to the angle gcb , which are the angles upon the other side of the base .
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 ... be two triangles , having the two
sides a b , a c , equal to f For , if bc be not equal to ef 8 THE ELEMENTS OF
EUCLID .
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 ... be two triangles , having the two
sides a b , a c , equal to f For , if bc be not equal to ef 8 THE ELEMENTS OF
EUCLID .
Σελίδα 9
a b to d e , and a c to df ; and also the base b c equal to the base e f . The angle
bac is d 8 equal to the angle ed f . For , if the triangle a b c be applied to def , so
that the point b be on e , and the straight line bc upon ef ; the point c shall also ...
a b to d e , and a c to df ; and also the base b c equal to the base e f . The angle
bac is d 8 equal to the angle ed f . For , if the triangle a b c be applied to def , so
that the point b be on e , and the straight line bc upon ef ; the point c shall also ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a b c 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 fourth given rectilineal given straight line greater half inscribed join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle 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.