The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 31.
Σελίδα 6
If two triangles have two sides of the one equal to two sides of the other , each to
each ; and have likewise the angles contained by those sides equal to one
another ; they shall likewise have their bases , or third sides , equal ; and the two
...
If two triangles have two sides of the one equal to two sides of the other , each to
each ; and have likewise the angles contained by those sides equal to one
another ; they shall likewise have their bases , or third sides , equal ; and the two
...
Σελίδα 14
LET a b c be a triangle ; any two sides of it together are greater than the third side
, viz . the sides ba , ac greater than the side bc ; and a b , b c greater than ac ; and
b c , ca greater than a b . Produce ba to the point d , and make ( i . 3 ) ad equal ...
LET a b c be a triangle ; any two sides of it together are greater than the third side
, viz . the sides ba , ac greater than the side bc ; and a b , b c greater than ac ; and
b c , ca greater than a b . Produce ba to the point d , and make ( i . 3 ) ad equal ...
Σελίδα 15
To make a triangle of which the sides shall be equal to three given straight lines ,
but any two whatever of these must be greater than the third ( i . 20 . ) . LET a , b ,
c be the three given straight lines , of which any two whatever are greater than ...
To make a triangle of which the sides shall be equal to three given straight lines ,
but any two whatever of these must be greater than the third ( i . 20 . ) . LET a , b ,
c be the three given straight lines , of which any two whatever are greater than ...
Σελίδα 18
a b to de , and ac to df , and the third angle bac to the third angle e df . For , if a b
be not equal to de , one of them must be the greater . Let a b be the greater of the
two , and make bg equal to d ' e , and join gc ; therefore , because bg is equal to ...
a b to de , and ac to df , and the third angle bac to the third angle e df . For , if a b
be not equal to de , one of them must be the greater . Let a b be the greater of the
two , and make bg equal to d ' e , and join gc ; therefore , because bg is equal to ...
Σελίδα 19
4 ) to the base d f , and the third angle bac to the third angle edf . Next , let the
sides which are opposite to equal angles in each triangle be equal to one
another , viz . ab to de ; likewise in this case , the other sides shall be equal , a c
to df and ...
4 ) to the base d f , and the third angle bac to the third angle edf . Next , let the
sides which are opposite to equal angles in each triangle be equal to one
another , viz . ab to de ; likewise in this case , the other sides shall be equal , a c
to df and ...
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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.