The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 7
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to af , the less , and join ... than the other : let ab be the greater ; and from it cut ( i . 3 ) off db equal to a c , the less , and join dc ...
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to af , the less , and join ... than the other : let ab be the greater ; and from it cut ( i . 3 ) off db equal to a c , the less , and join dc ...
Σελίδα 8
... greater than it ; which is impossible . But if one of the produce a c , ad to e , a f : vertices , as d , be within the other triangle acb ; f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the ...
... greater than it ; which is impossible . But if one of the produce a c , ad to e , a f : vertices , as d , be within the other triangle acb ; f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the ...
Σελίδα 13
... greater than either of the interior opposite angles . LET a b c be a triangle , and let its side b c be produced to ... f , and make e f equal to be ; join also fc , and produce a c to g . Because ae is equal to ec , and be to ef ; a e ...
... greater than either of the interior opposite angles . LET a b c be a triangle , and let its side b c be produced to ... f , and make e f equal to be ; join also fc , and produce a c to g . Because ae is equal to ec , and be to ef ; a e ...
Σελίδα 18
... greater than the base ef ; the angle bac is likewise greater than the angle ed f . For , if it be not greater , it must either be equal to it , or less ; but the angle bac is not equal to the angle e df ; because then the base bc would ...
... greater than the base ef ; the angle bac is likewise greater than the angle ed f . For , if it be not greater , it must either be equal to it , or less ; but the angle bac is not equal to the angle e df ; because then the base bc would ...
Σελίδα 49
... greater to the less , which is impossible : therefore g is not the centre of the circle a bc . In the same manner it can be shewn , that no other point but fis the centre ; that is , f ... than the angle dae ; but dae is equal to the angle ...
... greater to the less , which is impossible : therefore g is not the centre of the circle a bc . In the same manner it can be shewn , that no other point but fis the centre ; that is , f ... than the angle dae ; but dae is equal to the angle ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
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.