The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 14.
Σελίδα 13
And consequently that all the angles made by any number of lines meeting in
one point , are together equal to four right angles . PROPOSITION XVI . —
THEOREM . If one side of a triangle be produced , the exterior angle is greater
than either ...
And consequently that all the angles made by any number of lines meeting in
one point , are together equal to four right angles . PROPOSITION XVI . —
THEOREM . If one side of a triangle be produced , the exterior angle is greater
than either ...
Σελίδα 14
In like manner it may be demonstrated , that bac , a cb , as also ca b , a b c , are
less than two right angles . Therefore ... 3 ) ad equal to a b , and join bd ; and
because adb is the exterior angle of the triangle bdc , it is greater ( i . 16 ) than the
...
In like manner it may be demonstrated , that bac , a cb , as also ca b , a b c , are
less than two right angles . Therefore ... 3 ) ad equal to a b , and join bd ; and
because adb is the exterior angle of the triangle bdc , it is greater ( i . 16 ) than the
...
Σελίδα 15
Again , because the exterior angle of a triangle is greater than the interior and
opposite angle , the exterior angle bd c of the triangle cde is greater than ced ; for
the same reason , the exterior angle ceb of the triangle a be is greater than bac ...
Again , because the exterior angle of a triangle is greater than the interior and
opposite angle , the exterior angle bd c of the triangle cde is greater than ced ; for
the same reason , the exterior angle ceb of the triangle a be is greater than bac ...
Σελίδα 19
triangle gb c to the triangle def , and the other angles to the other angles , each to
each , to which the equal sides åre ... that is the exterior angle bha of the triangle
a hc is equal to its interior and opposite angle b ca ; which is impossible ( i .
triangle gb c to the triangle def , and the other angles to the other angles , each to
each , to which the equal sides åre ... that is the exterior angle bha of the triangle
a hc is equal to its interior and opposite angle b ca ; which is impossible ( i .
Σελίδα 20
For , if it be not parallel , a b and cd being produced shall meet either towards b ,
d , or towards a , c : let them be produced and meet towards b , d in the point g ;
therefore gef is a triangle , and its exterior angle a ef is greater ( i . 16 ) than the ...
For , if it be not parallel , a b and cd being produced shall meet either towards b ,
d , or towards a , c : let them be produced and meet towards b , d in the point g ;
therefore gef is a triangle , and its exterior angle a ef is greater ( i . 16 ) than the ...
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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.