The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 6 - 10 από τα 19.
Σελίδα 98
Take of a and b any equimultiples whatever d and e , and of c any multiple
whatever f . Then , because d is the same multiple of a that e is of b , and that a is
equal to b ; d is ( v . ax . 1 ) equal to e . Therefore , if d be greater than f , e is
greater ...
Take of a and b any equimultiples whatever d and e , and of c any multiple
whatever f . Then , because d is the same multiple of a that e is of b , and that a is
equal to b ; d is ( v . ax . 1 ) equal to e . Therefore , if d be greater than f , e is
greater ...
Σελίδα 100
8th , there is some multiple f of c , and some equimultiples e and d , of b and a
such , that f is greater than e , and not greater than d ; but because o is to b as c is
to a , and that f , the multiple of the first , is greater than e , the multiple of the ...
8th , there is some multiple f of c , and some equimultiples e and d , of b and a
such , that f is greater than e , and not greater than d ; but because o is to b as c is
to a , and that f , the multiple of the first , is greater than e , the multiple of the ...
Σελίδα 101
And g , and g , h , k , to8 h k a b df m 1 gether are any equimultiples of a , and a , c
, e together ; because if there be any number of magnitudes equimultiples of as
many , each of each , whatever multiple one of them is of its part , the same ...
And g , and g , h , k , to8 h k a b df m 1 gether are any equimultiples of a , and a , c
, e together ; because if there be any number of magnitudes equimultiples of as
many , each of each , whatever multiple one of them is of its part , the same ...
Σελίδα 102
Because c has a greater ratio to d , than e to f , there are some equimultiples of c
and e , and some of d and f , such that the multiple of c is greater than the multiple
of d , but the multiple of e is not greater than the multiple of f ( v . def .
Because c has a greater ratio to d , than e to f , there are some equimultiples of c
and e , and some of d and f , such that the multiple of c is greater than the multiple
of d , but the multiple of e is not greater than the multiple of f ( v . def .
Σελίδα 103
Q. E. D. PROPOSITION XV . — THEOREM , Magnitudes have the same ratio to
one another which their equimultiples have . LET a b be the same multiple of c
that de is of f ; c is to f as a b to de Because a b is the same multiple of c that de is
of ...
Q. E. D. PROPOSITION XV . — THEOREM , Magnitudes have the same ratio to
one another which their equimultiples have . LET a b be the same multiple of c
that de is of f ; c is to f as a b to de Because a b is the same multiple of c that de is
of ...
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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.