The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 41.
Σελίδα 7
Because a f is equal to a g , and a b to a c , the two sides fa , a c are equal to the
two ga , a b , each to each ; and they contain the angle fag common to the two
triangles afc , a gb ; therefore the base fc is equal ( i . 4 ) to the base gb , and the ...
Because a f is equal to a g , and a b to a c , the two sides fa , a c are equal to the
two ga , a b , each to each ; and they contain the angle fag common to the two
triangles afc , a gb ; therefore the base fc is equal ( i . 4 ) to the base gb , and the ...
Σελίδα 9
Because a d is equal to a e , and a f is common to the two triangles da f , eaf ; the
two sides da , af , are equal to the two sides e a , a f , each to each ; and the base
df is equal to the base ef ; therefore the angle daf is equal ( i . 8 ) to the angle ...
Because a d is equal to a e , and a f is common to the two triangles da f , eaf ; the
two sides da , af , are equal to the two sides e a , a f , each to each ; and the base
df is equal to the base ef ; therefore the angle daf is equal ( i . 8 ) to the angle ...
Σελίδα 10
Because a c is equal to cb , and cd common to the two triangles a cd , bcd ; the
two sides a c , cd are equal to bc , cd , each to each ; and the angle a cd is equal
to the angle bed ; therefore the base ad is equal to the base ( i . 4 ) d b , and the ...
Because a c is equal to cb , and cd common to the two triangles a cd , bcd ; the
two sides a c , cd are equal to bc , cd , each to each ; and the angle a cd is equal
to the angle bed ; therefore the base ad is equal to the base ( i . 4 ) d b , and the ...
Σελίδα 11
Because fh is equal to hg , and h c common to the two triangles fhc , ghc , the two
sides fh , h c are equal to the two gh , hc , each to each ; and the base cf is equal (
15 def . ) to the base cg ; therefore the angle chf is equal ( i . 8 ) to the angle ...
Because fh is equal to hg , and h c common to the two triangles fhc , ghc , the two
sides fh , h c are equal to the two gh , hc , each to each ; and the base cf is equal (
15 def . ) to the base cg ; therefore the angle chf is equal ( i . 8 ) to the angle ...
Σελίδα 12
13 ) to two right angles ; but the angles a b c , abd are likewise together equal to
two right angles ; therefore the angles c ba , a b e are equal to the angles cba , a
bd : take away the common angle cba , the remaining angle a be is equal ( 3 ax .
) ...
13 ) to two right angles ; but the angles a b c , abd are likewise together equal to
two right angles ; therefore the angles c ba , a b e are equal to the angles cba , a
bd : take away the common angle cba , the remaining angle a be is equal ( 3 ax .
) ...
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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.