The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 48
Similar segments of a circle are those in which the angles are equal , or which
contain equal angles . Definition XI . PROPOSITION I . — PROBLEM . To find the
centre of a given circle . LET a bc be the given circle ; it is required to find its
centre ...
Similar segments of a circle are those in which the angles are equal , or which
contain equal angles . Definition XI . PROPOSITION I . — PROBLEM . To find the
centre of a given circle . LET a bc be the given circle ; it is required to find its
centre ...
Σελίδα 62
Upon the same straight line and upon the same side of it , there cannot be two
similar segments of circles not coinciding with one another . If it be possible , let
the two similar segments of circles , viz . a cb , a db be upon the same side of the
...
Upon the same straight line and upon the same side of it , there cannot be two
similar segments of circles not coinciding with one another . If it be possible , let
the two similar segments of circles , viz . a cb , a db be upon the same side of the
...
Σελίδα 63
And because the segment a cb is similar to the segment adb , and that similar
segments of circles contain ( iii . def . 11 ) equal angles ; the angle acb is equal to
the angle adb , the exterior to the interior , which is impossible ( i . 16 ) . Therefore
...
And because the segment a cb is similar to the segment adb , and that similar
segments of circles contain ( iii . def . 11 ) equal angles ; the angle acb is equal to
the angle adb , the exterior to the interior , which is impossible ( i . 16 ) . Therefore
...
Σελίδα 64
... the two sides bg , gc , are equal to the two eh , hf , and the angle at g is equal to
the angle at h ; therefore the base bc is equal ( i . 4 ) to the base ef . And because
the angle at a is equal to the angle at d , the segment bac is similar ( iii . def .
... the two sides bg , gc , are equal to the two eh , hf , and the angle at g is equal to
the angle at h ; therefore the base bc is equal ( i . 4 ) to the base ef . And because
the angle at a is equal to the angle at d , the segment bac is similar ( iii . def .
Σελίδα 73
Given the vertical angle , the altitude and the base of a triangle , to construct the
triangle . 8. Given a segment of a circle and a straight line , to describe on the line
another segment of a circle which shall be similar to the given segment . 9.
Given the vertical angle , the altitude and the base of a triangle , to construct the
triangle . 8. Given a segment of a circle and a straight line , to describe on the line
another segment of a circle which shall be similar to the given segment . 9.
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.