The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 18.
Σελίδα 92
If the first magnitude be the same multiple of the second that the third is of the
fourth , and the fifth the same multiple of the second that the sixth is of the fourth ;
then shall the first together with the fifth be the same multiple of the second , that
the ...
If the first magnitude be the same multiple of the second that the third is of the
fourth , and the fifth the same multiple of the second that the sixth is of the fourth ;
then shall the first together with the fifth be the same multiple of the second , that
the ...
Σελίδα 94
For the same reason , mis the same multiple of b , that n is of d : and because , as
a is to b , so is c to d ( hypoth . ) , and of a and c have been taken certain
equimultiples k , 1 : and of b and d have been taken certain equimultiples m , n ; if
...
For the same reason , mis the same multiple of b , that n is of d : and because , as
a is to b , so is c to d ( hypoth . ) , and of a and c have been taken certain
equimultiples k , 1 : and of b and d have been taken certain equimultiples m , n ; if
...
Σελίδα 95
C Make ck equal to f ; and because a g is the same multiple of e , that ch is of f ,
and that gb is equal to e , and ck to f ; therefore a b is the same multiple of e that
kh is of f . But a b , by the hypothesis , is the same multiple of e that cd is of f ...
C Make ck equal to f ; and because a g is the same multiple of e , that ch is of f ,
and that gb is equal to e , and ck to f ; therefore a b is the same multiple of e that
kh is of f . But a b , by the hypothesis , is the same multiple of e that cd is of f ...
Σελίδα 96
If the first be the same multiple of the second , or the same part of it , that the third
is of the fourth , the first is to the second as the third is to the fourth . LET the first a
be the same multiple of b the second , that c the third is of the fourth d : a is to b ...
If the first be the same multiple of the second , or the same part of it , that the third
is of the fourth , the first is to the second as the third is to the fourth . LET the first a
be the same multiple of b the second , that c the third is of the fourth d : a is to b ...
Σελίδα 97
Next , let the first a be the same part of the second b , that the third c is of the
fourth d : a is to b as c is to d : for b is the same multiple of a that d is of c :
wherefore , by the preceding case , b is to a as d is to c ; and inversely ( v . B . ) a
is to b as c ...
Next , let the first a be the same part of the second b , that the third c is of the
fourth d : a is to b as c is to d : for b is the same multiple of a that d is of c :
wherefore , by the preceding case , b is to a as d is to c ; and inversely ( v . B . ) a
is to b as c ...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
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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.