The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 2
X . When a straight line standing on another straight line makes the adjacent
angles equal to one another , each of the angles is called a right angle ; and the
straight line which stands on the other is called a perpendicular to it . XI . An
obtuse ...
X . When a straight line standing on another straight line makes the adjacent
angles equal to one another , each of the angles is called a right angle ; and the
straight line which stands on the other is called a perpendicular to it . XI . An
obtuse ...
Σελίδα 11
To draw a straight line perpendicular to a given straight line of an unlimited
length , from a given point without it . LET a b be the given straight line , which
may be produced to any length both ways , and let c be a point without it . It is
required to ...
To draw a straight line perpendicular to a given straight line of an unlimited
length , from a given point without it . LET a b be the given straight line , which
may be produced to any length both ways , and let c be a point without it . It is
required to ...
Σελίδα 34
The straight line drawn from a given point perpendicular to a given line is the
shortest that can be drawn from the point to the line . 17 . If a triangle have its
exterior angle and one of its opposite interior angles double of those in another
triangle ...
The straight line drawn from a given point perpendicular to a given line is the
shortest that can be drawn from the point to the line . 17 . If a triangle have its
exterior angle and one of its opposite interior angles double of those in another
triangle ...
Σελίδα 43
12 ) perpendicular to be produced . The square of a b is greater than the squares
of a c , cb , by twice the rectangle b c , cd . Because the straight line bd is divided
into two parts in the point c , the square of bd is equal ( ii . 4 ) to the squares of ...
12 ) perpendicular to be produced . The square of a b is greater than the squares
of a c , cb , by twice the rectangle b c , cd . Because the straight line bd is divided
into two parts in the point c , the square of bd is equal ( ii . 4 ) to the squares of ...
Σελίδα 44
LET a b c be any triangle , and the angle at b one of its acute angles , and upon
bc , one of the sides containing it , let fall the perpendicular ( i . 12 ) a d from the
opposite angle : the square of a c , opposite to the angle b , is less than the ...
LET a b c be any triangle , and the angle at b one of its acute angles , and upon
bc , one of the sides containing it , let fall the perpendicular ( i . 12 ) a d from the
opposite angle : the square of a c , opposite to the angle b , is less than the ...
Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a b c d 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 equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given rectilineal given straight line greater half inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle 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.