The first six books of the Elements of Euclid, with numerous exercises |
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An acute angle is that which is less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that which is enclosed by one or more boundaries . XV . A circle is a plain figure ...
An acute angle is that which is less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that which is enclosed by one or more boundaries . XV . A circle is a plain figure ...
Seite 4
And that a circle may be described from any centre , at any dis- tance from that centre . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If equals be added to equals , the wholes are equal . III .
And that a circle may be described from any centre , at any dis- tance from that centre . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If equals be added to equals , the wholes are equal . III .
Seite 5
ab ; and because the point b is the centre of the circle ace , bc is equal to ba but it has been proved that ca is equal to ab ; therefore ca , cb , are each of them equal to ab ; but things which are equal to the same are equal to one ...
ab ; and because the point b is the centre of the circle ace , bc is equal to ba but it has been proved that ca is equal to ab ; therefore ca , cb , are each of them equal to ab ; but things which are equal to the same are equal to one ...
Seite 11
the circle egf meet- ing a b in f , g ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch , drawn from the given point c , is perpendicular to the given straight line a b . a f h d g b Because fh is equal to ...
the circle egf meet- ing a b in f , g ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch , drawn from the given point c , is perpendicular to the given straight line a b . a f h d g b Because fh is equal to ...
Seite 16
the circle dkl ; d f مع g h a b and from the centre g , at the distance gh , describe ( 3 post . ) another circle hlk ; and join kf , kg ; the triangle kfg has its sides equal to the three straight lines a , b , c .
the circle dkl ; d f مع g h a b and from the centre g , at the distance gh , describe ( 3 post . ) another circle hlk ; and join kf , kg ; the triangle kfg has its sides equal to the three straight lines a , b , c .
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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 produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc straight line drawn tiple touches the circle triangle abc triangle def twice the rectangle
Beliebte Passagen
Seite 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.
Seite 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.
Seite 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 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...
Seite 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.