The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 11 - 15 από τα 27.
Σελίδα 30
Euclides. produced ; let them meet in k , and through k draw kl , parallel to ea or fh , and produce ha , gb to the ... meets the parallels km , fg , the alternate angles mhg , hgf are equal ( i . 29 ) : add to each of these the angle hg1 ...
Euclides. produced ; let them meet in k , and through k draw kl , parallel to ea or fh , and produce ha , gb to the ... meets the parallels km , fg , the alternate angles mhg , hgf are equal ( i . 29 ) : add to each of these the angle hg1 ...
Σελίδα 37
... meets them ; the angles d kbc , gcb are therefore equal to two right angles ; and kbc is a right angle ; wherefore gcb is a right angle : and therefore also the angles ( i . 34 ) cgk , gkb , opposite to these , are right angles , and ...
... meets them ; the angles d kbc , gcb are therefore equal to two right angles ; and kbc is a right angle ; wherefore gcb is a right angle : and therefore also the angles ( i . 34 ) cgk , gkb , opposite to these , are right angles , and ...
Σελίδα 41
... meet if produced towards b , d : let them meet in g , and join a g : then , b Pi g because ac is equal to ce , the angle cea BOOK II . PROP . X. 41.
... meet if produced towards b , d : let them meet in g , and join a g : then , b Pi g because ac is equal to ce , the angle cea BOOK II . PROP . X. 41.
Σελίδα 47
... meets the circle , and being produced does not cut it . III . Circles are said to touch one another , which meet but do not cut one another . Definitions II . and III . IV . Straight lines are said to be equally distant from the centre ...
... meets the circle , and being produced does not cut it . III . Circles are said to touch one another , which meet but do not cut one another . Definitions II . and III . IV . Straight lines are said to be equally distant from the centre ...
Σελίδα 58
... meets the circumference . And because da is equal to dc , the angle dac is equal ( i . 5 ) to the angle acd ; but ... meet the circumference in h ; and because a gd is a right angle , and dag less ( i . 17 ) than a right angle , da is ...
... meets the circumference . And because da is equal to dc , the angle dac is equal ( i . 5 ) to the angle acd ; but ... meet the circumference in h ; and because a gd is a right angle , and dag less ( i . 17 ) than a right angle , da is ...
Άλλες εκδόσεις - Προβολή όλων
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 pentagon perpendicular Q. E. D. PROPOSITION rectangle a d 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 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.