The first six books of the Elements of Euclid, with numerous exercises |
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Seite 5
therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and the tri- angle abc is therefore equilateral , and it is described upon the given straight line ab . Which was to be done . PROPOSITION II . - PROBLEM .
therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and the tri- angle abc is therefore equilateral , and it is described upon the given straight line ab . Which was to be done . PROPOSITION II . - PROBLEM .
Seite 6
Wherefore the whole triangle a b c shall coincide with the whole triangle def , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a bc to ...
Wherefore the whole triangle a b c shall coincide with the whole triangle def , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a bc to ...
Seite 7
... and the base bc is common to the two triangles bfc , cgb ; wherefore the tri- angles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle fbc is equal to the ...
... and the base bc is common to the two triangles bfc , cgb ; wherefore the tri- angles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle fbc is equal to the ...
Seite 8
5 ) to one another but the angle ecd is greater than the angle bed wherefore the angle fdc is like- wise greater than bcd ; much greater then is the angle bd c than the angle bcd . Again , because cb is equal to db , the angle bdc is ...
5 ) to one another but the angle ecd is greater than the angle bed wherefore the angle fdc is like- wise greater than bcd ; much greater then is the angle bd c than the angle bcd . Again , because cb is equal to db , the angle bdc is ...
Seite 9
8 ) to the angle eaf ; wherefore the given rectilineal angle bac is bisected b by the straight line af . Which was to be done . f 44 a PROPOSITION X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two ...
8 ) to the angle eaf ; wherefore the given rectilineal angle bac is bisected b by the straight line af . Which was to be done . f 44 a PROPOSITION X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two ...
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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.