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 34.
Σελίδα 37
... reason hf also is a square , and it is upon the side hg , which is equal to a c . Therefore hf , ck are the squares of a c , cb ; and because the complement ag is equal ( i . 43 ) to the complement ge , and that a g is the rectangle ...
... reason hf also is a square , and it is upon the side hg , which is equal to a c . Therefore hf , ck are the squares of a c , cb ; and because the complement ag is equal ( i . 43 ) to the complement ge , and that a g is the rectangle ...
Σελίδα 39
... such as in the preceding . Because cb is equal to bd , and that cb is equal ( i . 34 ) to gk , and bd to kn ; therefore gk is equal to kn for the same reason , pr is equal : C b g H P d r 0 to ro BOOK II . PROPS . VII . , VIII . 39.
... such as in the preceding . Because cb is equal to bd , and that cb is equal ( i . 34 ) to gk , and bd to kn ; therefore gk is equal to kn for the same reason , pr is equal : C b g H P d r 0 to ro BOOK II . PROPS . VII . , VIII . 39.
Σελίδα 41
... reason , each of the angles ceb , ebc is half a right angle ; and therefore the whole a eb is a right angle : and because the angle gef is half a right angle , and eg fa right angle , for it is equal ( i . 29 ) to the interior and ...
... reason , each of the angles ceb , ebc is half a right angle ; and therefore the whole a eb is a right angle : and because the angle gef is half a right angle , and eg fa right angle , for it is equal ( i . 29 ) to the interior and ...
Σελίδα 42
... reason , each of the angles ceb , ebc is half a right angle ; therefore aeb is a right angle and because ebc is half a right angle , dbg is also ( i . 15 ) half a right angle , for they are vertically opposite ; but bdg is a right angle ...
... reason , each of the angles ceb , ebc is half a right angle ; therefore aeb is a right angle and because ebc is half a right angle , dbg is also ( i . 15 ) half a right angle , for they are vertically opposite ; but bdg is a right angle ...
Σελίδα 52
... reason cf is greater than gf . Again , be- cause gf , fe are greater ( i . 20 ) than eg , and eg is equal to ed , gf , fe are greater than ed ; take away the common part fe , and the remainder gf is greater than the remainder fd ...
... reason cf is greater than gf . Again , be- cause gf , fe are greater ( i . 20 ) than eg , and eg is equal to ed , gf , fe are greater than ed ; take away the common part fe , and the remainder gf is greater than the remainder fd ...
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 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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 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...
Σελίδα 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.