The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 10
... in the same manner , because a bd is a straight line , d the angle d be is equal
to the angle e ba ; wherefore the angle d be is b C equal to the angle c be , the
less to the greater , which is impossible ; therefore two straight lines cannot have
a ...
... in the same manner , because a bd is a straight line , d the angle d be is equal
to the angle e ba ; wherefore the angle d be is b C equal to the angle c be , the
less to the greater , which is impossible ; therefore two straight lines cannot have
a ...
Σελίδα 12
And in like manner it may be demonstrated , that no other can be in the sanie
straight line with it but b d , which therefore is in the same straight line with cb .
Wherefore , if at a point , & c . Q. E. D. PROPOSITION XV .--- THEOREM . If two
straight ...
And in like manner it may be demonstrated , that no other can be in the sanie
straight line with it but b d , which therefore is in the same straight line with cb .
Wherefore , if at a point , & c . Q. E. D. PROPOSITION XV .--- THEOREM . If two
straight ...
Σελίδα 13
In the same manner it can be demonstrated , that the angles ceb , a ed are equal
. Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that
, if two straight lines cut one another , the angles they make at the point where ...
In the same manner it can be demonstrated , that the angles ceb , a ed are equal
. Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that
, if two straight lines cut one another , the angles they make at the point where ...
Σελίδα 14
In like manner it may be demonstrated , that bac , a cb , as also cab , a b c , are
less than two right angles . Therefore any two angles , & c . Q. E. D.
PROPOSITION XVIII . — THEOREM . The greater side of every triangle is
opposite to the ...
In like manner it may be demonstrated , that bac , a cb , as also cab , a b c , are
less than two right angles . Therefore any two angles , & c . Q. E. D.
PROPOSITION XVIII . — THEOREM . The greater side of every triangle is
opposite to the ...
Σελίδα 15
In the same manner it may be demonstrated , that the sides a b , bc , are greater
than ca , and b b c , ca greater than a b . two sides , & c . Q. E. D. Therefore any a
PROPOSITION XXI . — THEOREM . If from the ends of the side of a triangle there
...
In the same manner it may be demonstrated , that the sides a b , bc , are greater
than ca , and b b c , ca greater than a b . two sides , & c . Q. E. D. Therefore any a
PROPOSITION XXI . — THEOREM . If from the ends of the side of a triangle there
...
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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.