The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 85.
Σελίδα 5
therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and
the triangle abc is therefore equilateral , and it is described upon the given
straight line a b . Which was to be done . PROPOSITION II . PROBLEM . From a
given ...
therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and
the triangle abc is therefore equilateral , and it is described upon the given
straight line a b . Which was to be done . PROPOSITION II . PROBLEM . From a
given ...
Σελίδα 6
Wherefore the whole triangle a b c shall coincide with the whole triangle de f ,
and be equal to it ; and the other angles of the one shall coincide with the
remaining angles of the other , and be equal to them , viz . the angle a b c to the
angle d ef ...
Wherefore the whole triangle a b c shall coincide with the whole triangle de f ,
and be equal to it ; and the other angles of the one shall coincide with the
remaining angles of the other , and be equal to them , viz . the angle a b c to the
angle d ef ...
Σελίδα 7
... and the base bc is common to the two triangles bfc , cgb ; wherefore the
triangles are equal ( i . 4 ) , and their remaining angles , each to each , to which
the equal sides are opposite ; therefore the angle fb c is equal to the angle gcb ,
and the ...
... and the base bc is common to the two triangles bfc , cgb ; wherefore the
triangles are equal ( i . 4 ) , and their remaining angles , each to each , to which
the equal sides are opposite ; therefore the angle fb c is equal to the angle gcb ,
and the ...
Σελίδα 8
another : but the angle ecd is greater than the angle bed : wherefore the angle
fdc is likewise greater than b c d ; much greater then is the angle bd c than the
angle bed . Again , because cb is equal to db , the angle bdc is equal ( i . 5 ) to
the ...
another : but the angle ecd is greater than the angle bed : wherefore the angle
fdc is likewise greater than b c d ; much greater then is the angle bd c than the
angle bed . Again , because cb is equal to db , the angle bdc is equal ( i . 5 ) to
the ...
Σελίδα 9
8 ) to the angle eaf ; wherefore the given rectilineal augle bac is bisected by the
straight line af . Which was to be done . PROPOSITION X . - PROBLEM . To bisect
a given finite straight line , that is , to divide it into two equal parts . LET a b be ...
8 ) to the angle eaf ; wherefore the given rectilineal augle bac is bisected by the
straight line af . Which was to be done . PROPOSITION X . - PROBLEM . To bisect
a given finite straight line , that is , to divide it into two equal parts . LET a b be ...
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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.