The first six books of the Elements of Euclid, with numerous exercises |
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Seite 13
Take away the common angle a e d , and the remaining angle ce a is equal ( 3 ax . ) to the remaining angle de b . ... If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles .
Take away the common angle a e d , and the remaining angle ce a is equal ( 3 ax . ) to the remaining angle de b . ... If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles .
Seite 14
In like manner it may be demonstrated , that bac , acb , as also cab , abc , are less than two right angles . ... 3 ) cis a d equal to a b , and join bd ; and because adb is the exterior angle of the triangle bd c , it is greater ( i .
In like manner it may be demonstrated , that bac , acb , as also cab , abc , are less than two right angles . ... 3 ) cis a d equal to a b , and join bd ; and because adb is the exterior angle of the triangle bd c , it is greater ( i .
Seite 15
op- d a bcd is greater than the angle adc ; and because the angle bed of the triangle dcb is greater than its angle ... because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle bdc of ...
op- d a bcd is greater than the angle adc ; and because the angle bed of the triangle dcb is greater than its angle ... because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle bdc of ...
Seite 19
triangle g bc to the triangle def , and the other angles to the other angles , each to each , to which the equal ... the exterior angle bha of the triangle a hc is equal to its interior and opposite angle bca ; which is impossible ( i .
triangle g bc to the triangle def , and the other angles to the other angles , each to each , to which the equal ... the exterior angle bha of the triangle a hc is equal to its interior and opposite angle bca ; which is impossible ( i .
Seite 20
For , if it be not parallel , a b and c d being produced shall meet either towards b , d , or towards a , c : let them be produced and meet towards b , d in the point g ; therefore gef is a triangle , and its exterior angle aefis ...
For , if it be not parallel , a b and c d being produced shall meet either towards b , d , or towards a , c : let them be produced and meet towards b , d in the point g ; therefore gef is a triangle , and its exterior angle aefis ...
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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.