The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Ergebnisse 1-5 von 22
Seite 35
... rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line . LET a and be be two straight lines ; and let bc be divided into any parts in the ...
... rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line . LET a and be be two straight lines ; and let bc be divided into any parts in the ...
Seite 36
Euclides. by a , bc , is equal to the several rectangles contained by a , bd , and by a , de , and also by a , ec ... rectangle contained by ab , bc , together with the rectangle * a b , bac , shall be equal to the square of a b a с C ...
Euclides. by a , bc , is equal to the several rectangles contained by a , bd , and by a , de , and also by a , ec ... rectangle contained by ab , bc , together with the rectangle * a b , bac , shall be equal to the square of a b a с C ...
Seite 37
... rectangle contained by a c , cb , for gc is equal to cb ; therefore ge is also equal to the rectangle a c , cb ; wherefore ag , ge are equal to twice the rectangle ac , cb . And hf , ck are the squares of ac , cb ; wherefore the four ...
... rectangle contained by a c , cb , for gc is equal to cb ; therefore ge is also equal to the rectangle a c , cb ; wherefore ag , ge are equal to twice the rectangle ac , cb . And hf , ck are the squares of ac , cb ; wherefore the four ...
Seite 38
... contained by a d , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomon cmg ; there- fore the gnomon cm8 is equal to the rectangle a d , db : to each of these add 1g , which is equal ( ii . 4. cor . ) to ...
... contained by a d , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomon cmg ; there- fore the gnomon cm8 is equal to the rectangle a d , db : to each of these add 1g , which is equal ( ii . 4. cor . ) to ...
Seite 39
... rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle a b , bc ...
... rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle a b , bc ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
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.