The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 24.
Σελίδα 29
LET abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pa a
_ b rallelograms about a c , that is , through which a c passes , and bk , kd , the
other parallelograms which make up the whole figure abcd , which are therefore
...
LET abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pa a
_ b rallelograms about a c , that is , through which a c passes , and bk , kd , the
other parallelograms which make up the whole figure abcd , which are therefore
...
Σελίδα 50
If a straight line drawn through the centre of a circle bisect a straight line in it
which does not pass through the centre , it shall cut it at right angles ; and if it cuts
it at right angles , it shall bisect it . LET abc be a circle ; and let cd , a straight line ...
If a straight line drawn through the centre of a circle bisect a straight line in it
which does not pass through the centre , it shall cut it at right angles ; and if it cuts
it at right angles , it shall bisect it . LET abc be a circle ; and let cd , a straight line ...
Σελίδα 51
Again , because the straight line fe bisects the straight line bd , which does not
pass through the centre , it shall cut it at right angles ( iii . 3 ) : wherefore feb is a
right angle : and fea was shewn to be a right angle ; therefore fea is equal to the ...
Again , because the straight line fe bisects the straight line bd , which does not
pass through the centre , it shall cut it at right angles ( iii . 3 ) : wherefore feb is a
right angle : and fea was shewn to be a right angle ; therefore fea is equal to the ...
Σελίδα 52
ha passes through the centre is always greater than one more remote . And from
the same point there can be drawn only two straight lines that are equal to one
another , one upon each side of the shortest line . LET a b c d be a circle , and a d
...
ha passes through the centre is always greater than one more remote . And from
the same point there can be drawn only two straight lines that are equal to one
another , one upon each side of the shortest line . LET a b c d be a circle , and a d
...
Σελίδα 53
LET a b c be a circle , and d any point without it , from which let the straight lines
da , de , df , dc be drawn to the circumference , whereof da passes through the
centre . Of those which fall upon the concave part of the circumference a e fc , the
...
LET a b c be a circle , and d any point without it , from which let the straight lines
da , de , df , dc be drawn to the circumference , whereof da passes through the
centre . Of those which fall upon the concave part of the circumference a e fc , the
...
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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.