The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 6 - 10 από τα 47.
Σελίδα 20
... manner it may be demonstrated , that they do not meet towards a , c , but those straight lines which meet neither way , though produced ever so far , are parallel ( 35 def . ) to one another . ab there- fore is parallel to cd ...
... manner it may be demonstrated , that they do not meet towards a , c , but those straight lines which meet neither way , though produced ever so far , are parallel ( 35 def . ) to one another . ab there- fore is parallel to cd ...
Σελίδα 27
... manner , it can be demonstrated , that no b d other line but ad is parallel to be ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. PROPOSITION XL . — THEOREM . Equal triangles upon equal bases , in the same ...
... manner , it can be demonstrated , that no b d other line but ad is parallel to be ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. PROPOSITION XL . — THEOREM . Equal triangles upon equal bases , in the same ...
Σελίδα 32
... manner , by joining a e , bk , it is demonstrated , that the parallelogram c1 is equal to the square hc ; therefore the whole square bdec is equal to the two squares gb , hc ; and the square bdec is described upon the straight line bc ...
... manner , by joining a e , bk , it is demonstrated , that the parallelogram c1 is equal to the square hc ; therefore the whole square bdec is equal to the two squares gb , hc ; and the square bdec is described upon the straight line bc ...
Σελίδα 35
... , because dk , that is ( i . 34 ) bg is equal to a ; and in like manner the rectangle eh is contained by a , e c . Therefore the rectangle contained f by a , bc , is equal to the several BOOK II . PROP . I. 35 Definitions Propositions.
... , because dk , that is ( i . 34 ) bg is equal to a ; and in like manner the rectangle eh is contained by a , e c . Therefore the rectangle contained f by a , bc , is equal to the several BOOK II . PROP . I. 35 Definitions Propositions.
Σελίδα 49
... manner it can be shewn , that no other point but fis the centre ; that is , f is the centre of the circle a b c . Which was to be found . COR . From this it is manifest , that if in a circle a straight line bisect another at right ...
... manner it can be shewn , that no other point but fis the centre ; that is , f is the centre of the circle a b c . Which was to be found . COR . From this it is manifest , that if in a circle a straight line bisect another at right ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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 perpendicular Q. E. D. PROPOSITION rectangle a b 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
Δημοφιλή αποσπάσματα
Σελίδα 40 - 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.
Σελίδα 2 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 19 - 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.
Σελίδα 27 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 36 - 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...
Σελίδα 13 - 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...
Σελίδα 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 2 - 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...
Σελίδα 124 - 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.