The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 17.
Σελίδα 26
34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the
diameter dc bisects it : but the halves of equal things are equal ( 7 axc . ) ;
therefore the triangle a bç is equal to the triangle dbc . Wherefore triangles , & c .
Q . E . D ...
34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the
diameter dc bisects it : but the halves of equal things are equal ( 7 axc . ) ;
therefore the triangle a bç is equal to the triangle dbc . Wherefore triangles , & c .
Q . E . D ...
Σελίδα 33
Given an angle divided into any number of equal angles , to divide one half of the
angle into the same number of equal angles . 6. Given the base , one of the
angles at the base , and the sum of the other two sides , to construct the triangle .
7.
Given an angle divided into any number of equal angles , to divide one half of the
angle into the same number of equal angles . 6. Given the base , one of the
angles at the base , and the sum of the other two sides , to construct the triangle .
7.
Σελίδα 34
Each angle at the base of an isosceles triangle is equal to , or is less , or is
greater than the half of the vertical angle , according as the triangle is right ,
obtuse , or acute - angled . 22 . If the vertical angle of an isosceles triangle be
bisected , the ...
Each angle at the base of an isosceles triangle is equal to , or is less , or is
greater than the half of the vertical angle , according as the triangle is right ,
obtuse , or acute - angled . 22 . If the vertical angle of an isosceles triangle be
bisected , the ...
Σελίδα 37
If a straight line be divided into two equal parts , and also into two unequal parts ,
the rectangle contained by the unequal parts , together with the square of the line
between the points of section , is equal to the square of half the line . LET the ...
If a straight line be divided into two equal parts , and also into two unequal parts ,
the rectangle contained by the unequal parts , together with the square of the line
between the points of section , is equal to the square of half the line . LET the ...
Σελίδα 38
... any point , the rectangle contained by the whole line thus produced , and the
part of it produced , together with the square of half the line bisected , is equal to
the square of the straight line which is made up of the half and the part produced .
... any point , the rectangle contained by the whole line thus produced , and the
part of it produced , together with the square of half the line bisected , is equal to
the square of the straight line which is made up of the half and the part produced .
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
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.