The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 14
... angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of which the side ac is greater than the side a b ; the angle abc is also greater than ...
... angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of which the side ac is greater than the side a b ; the angle abc is also greater than ...
Seite 15
Euclides. a d bcd is greater than the angle adc ; and because the angle bcd of the triangle dcb is greater than its ... opposite angle , the exterior angle bdc of the triangle cde is greater than ced ; for the same reason , the ...
Euclides. a d bcd is greater than the angle adc ; and because the angle bcd of the triangle dcb is greater than its ... opposite angle , the exterior angle bdc of the triangle cde is greater than ced ; for the same reason , the ...
Seite 17
... angle dce is equal ( i . 8 ) to the angle fag . Therefore , at the given point a in the given straight line a b ... opposite to the greater angle ; the side eg is therefore greater than the side ef ; but eg is equal to bc ; and ...
... angle dce is equal ( i . 8 ) to the angle fag . Therefore , at the given point a in the given straight line a b ... opposite to the greater angle ; the side eg is therefore greater than the side ef ; but eg is equal to bc ; and ...
Seite 18
... angle bac is likewise greater than the angle ed f . For , if it be not greater , it must either be equal to it , or ... opposite to equal angles in each ; then shall the other sides be equal , each to each , and also the third ...
... angle bac is likewise greater than the angle ed f . For , if it be not greater , it must either be equal to it , or ... opposite to equal angles in each ; then shall the other sides be equal , each to each , and also the third ...
Seite 19
... angles , each to each , to which the equal sides are opposite ; therefore the angle gcb is equal to the angle dfe ; but dfe is , by the hypothesis , equal to the angle bca ; wherefore also the angle bcg is equal to the angle boa , the ...
... angles , each to each , to which the equal sides are opposite ; therefore the angle gcb is equal to the angle dfe ; but dfe is , by the hypothesis , equal to the angle bca ; wherefore also the angle bcg is equal to the angle boa , the ...
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Häufige Begriffe und Wortgruppen
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
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.