The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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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 abc 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 abc be the given circle ; it is required to ...
Σελίδα 62
... similar segments of circles not coinciding with one another . d b Ir it be possible , let the two similar segments of circles , viz . a cb , adb be upon the same side of the same straight line a b , not coinciding with one an- other ...
... similar segments of circles not coinciding with one another . d b Ir it be possible , let the two similar segments of circles , viz . a cb , adb be upon the same side of the same straight line a b , not coinciding with one an- other ...
Σελίδα 63
... 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 adb , the exterior to the interior , which is im- possible ( i . 16 ) . Therefore there ...
... 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 adb , the exterior to the interior , which is im- possible ( i . 16 ) . Therefore there ...
Σελίδα 64
... similar ( iii . def . 11 ) to the segment edf ; and they are upon equal straight lines bc , ef . But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the ...
... similar ( iii . def . 11 ) to the segment edf ; and they are upon equal straight lines bc , ef . But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the ...
Σελίδα 73
... similar to the given segment . 9. Given a point , a straight line , and a point in the line , to describe a circle which shall pass through the first point , and touch the straight line in the other point . SECT . II . THEOREMS . 10 ...
... similar to the given segment . 9. Given a point , a straight line , and a point in the line , to describe a circle which shall pass through the first point , and touch the straight line in the other point . SECT . II . THEOREMS . 10 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular Q. E. D. PROPOSITION rectangle a b rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 40 - 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 2 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 19 - 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 27 - 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 36 - 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 13 - 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 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 2 - 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 124 - 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.