The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 24.
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 b c be the given circle ; it is required to ...
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 b c be the given circle ; it is required to ...
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 . d IF it be possible , let the two similar segments of circles , viz . a cb , a db be the same ...
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 . d IF it be possible , let the two similar segments of circles , viz . a cb , a db be the same ...
Σελίδα 63
And because the segment acb is similar to the segment a db , and that similar segments of circles contain ( iii . def . 11 ) equal angles ; the angle acb is equal to the angle a db , the exterior to the interior , which is impossible ...
And because the segment acb is similar to the segment a db , and that similar segments of circles contain ( iii . def . 11 ) equal angles ; the angle acb is equal to the angle a db , the exterior to the interior , which is impossible ...
Σελίδα 64
But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the segment ed f . But the whole circle abc is equal to the whole def ; therefore the remaining ...
But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the segment ed f . But the whole circle abc is equal to the whole def ; therefore the remaining ...
Σελίδα 73
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 a point , a straight line , and a point in the line , to describe a circle ...
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 a point , a straight line , and a point in the line , to describe a circle ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
abcd 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 four fourth given rectilineal given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION 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.