The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 5
bg ; but it has been shewn that bc is equal to bg ; wherefore al and bc are each of
them equal to bg ; and things that are equal to the same are equal to one another
; therefore the straight line al is equal to bc . Wherefore from the given point a a ...
bg ; but it has been shewn that bc is equal to bg ; wherefore al and bc are each of
them equal to bg ; and things that are equal to the same are equal to one another
; therefore the straight line al is equal to bc . Wherefore from the given point a a ...
Σελίδα 14
18 ) ; but it is not ; therefore the side ac is not less than a b ; and it has been
shewn that it is not equal to a b ; therefore a c is greater than a b . Wherefore the
greater angle , & c . Q . E . D . PROPOSITION XX . — THEOREM . Any two sides
of a ...
18 ) ; but it is not ; therefore the side ac is not less than a b ; and it has been
shewn that it is not equal to a b ; therefore a c is greater than a b . Wherefore the
greater angle , & c . Q . E . D . PROPOSITION XX . — THEOREM . Any two sides
of a ...
Σελίδα 15
Again , because the two sides ce , ed of the triangle ced are greater than cd , add
db to each of these ; therefore the sides ce , eb are greater than cd , db ; but it has
been shewn that ba , a c , are greater than be , e c , much greater then are b ba ...
Again , because the two sides ce , ed of the triangle ced are greater than cd , add
db to each of these ; therefore the sides ce , eb are greater than cd , db ; but it has
been shewn that ba , a c , are greater than be , e c , much greater then are b ba ...
Σελίδα 18
... therefore the angle bac is not less than the angle edf ; > f and it was shewn that
it is not equal to it ; therefore the angle bac is greater than the angle edf .
Wherefore , if two triangles , & c . Q . E . D . 0 PROPOSITION ŠXVI . — THEOREM
.
... therefore the angle bac is not less than the angle edf ; > f and it was shewn that
it is not equal to it ; therefore the angle bac is greater than the angle edf .
Wherefore , if two triangles , & c . Q . E . D . 0 PROPOSITION ŠXVI . — THEOREM
.
Σελίδα 21
Again , because the straight line gk cuts the parallel straight lines ef , cd , the
angle ghf is equal ( i . 29 ) to the angle gkd ; and it was shewn that the angle a gk
is equal to the angle ghf ; therefore also a gk is equal to gk d ; and they are
alternate ...
Again , because the straight line gk cuts the parallel straight lines ef , cd , the
angle ghf is equal ( i . 29 ) to the angle gkd ; and it was shewn that the angle a gk
is equal to the angle ghf ; therefore also a gk is equal to gk d ; and they are
alternate ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a b c d 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 equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given rectilineal given straight line greater half inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle 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.