The first six books of the Elements of Euclid, with numerous exercises |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 66.
Σελίδα 2
An obtuse angle is that which is greater than a right angle . XII . An acute angle is
that which is less than a right angle . Acute . Obtuse . XIII . A term or boundary is
the extremity of any thing . XIV . A figure is that which is enclosed by one or more
...
An obtuse angle is that which is greater than a right angle . XII . An acute angle is
that which is less than a right angle . Acute . Obtuse . XIII . A term or boundary is
the extremity of any thing . XIV . A figure is that which is enclosed by one or more
...
Σελίδα 4
The whole is greater than its part . X. Two straight lines cannot enclose a space .
XI . All right angles ... centre of the circle bod , ac is equal ( 15 def . ) to another :
but the angle ecd is greater than the 4 THE ELEMENTS OF EUCLID .
Propositions.
The whole is greater than its part . X. Two straight lines cannot enclose a space .
XI . All right angles ... centre of the circle bod , ac is equal ( 15 def . ) to another :
but the angle ecd is greater than the 4 THE ELEMENTS OF EUCLID .
Propositions.
Σελίδα 5
From the greater of two given straight lines to cut off a part equal to the less . LET
ab and c be the two given straight lines , whereof a b is the greater . It is required
to cut off from a b , the greater , a part equal to C , the less . From the point a ...
From the greater of two given straight lines to cut off a part equal to the less . LET
ab and c be the two given straight lines , whereof a b is the greater . It is required
to cut off from a b , the greater , a part equal to C , the less . From the point a ...
Σελίδα 6
to c , and from a b , the greater of two straight lines , a part a e has been cut off
equal to c the less . Which was to be done . PROPOSITION IV . — THEOREM . If
two triangles have two sides of the one equal to two sides of the other , each to ...
to c , and from a b , the greater of two straight lines , a part a e has been cut off
equal to c the less . Which was to be done . PROPOSITION IV . — THEOREM . If
two triangles have two sides of the one equal to two sides of the other , each to ...
Σελίδα 7
In bd take any point f , and from a e the greater , cut off ag equal ( i . 3 ) to a f , the
less , and join fc , gb . Because a f is equal to a g , and a b to a c , the two sides fa
, a c are equal to the two ga , a b , each to each ; and they contain the angle fag ...
In bd take any point f , and from a e the greater , cut off ag equal ( i . 3 ) to a f , the
less , and join fc , gb . Because a f is equal to a g , and a b to a c , the two sides fa
, a c are equal to the two ga , a b , each to each ; and they contain the angle fag ...
Τι λένε οι χρήστες - Σύνταξη κριτικής
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.