The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 91
... tiple of a less . IV . That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. - THEOREM . If any number of magnitudes be equimultiples of as many others ...
... tiple of a less . IV . That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. - THEOREM . If any number of magnitudes be equimultiples of as many others ...
Página 95
... tiple of e that ch is of f ; and gb the same mul- tiple of e that ck is of f ; therefore ab is the same multiple of e that kh is of f ( v . 2 ) . But ab is the same multiple of e that cd is of f ; therefore kh is the same multiple of f ...
... tiple of e that ch is of f ; and gb the same mul- tiple of e that ck is of f ; therefore ab is the same multiple of e that kh is of f ( v . 2 ) . But ab is the same multiple of e that cd is of f ; therefore kh is the same multiple of f ...
Página 96
... tiple of b that c is of d ; and that e is the same multiple of a that f is of e g f h a b c d a b c d ce is the same multiple of b that f is of d ( v . 3 ) ; therefore e and f are the same multiples of b and d . But g and h are ...
... tiple of b that c is of d ; and that e is the same multiple of a that f is of e g f h a b c d a b c d ce is the same multiple of b that f is of d ( v . 3 ) ; therefore e and f are the same multiples of b and d . But g and h are ...
Página 99
... tiple of d ; and fg , eg are equi- g 1 f k h d g b 1 k d fig . 2 . fig . 3 . multiples of cb , ab ; therefore d has to cb a greater ratio ( v . def . 7 ) than it has to a b . Wherefore , of unequal magnitudes , & c . Q. E. D. ...
... tiple of d ; and fg , eg are equi- g 1 f k h d g b 1 k d fig . 2 . fig . 3 . multiples of cb , ab ; therefore d has to cb a greater ratio ( v . def . 7 ) than it has to a b . Wherefore , of unequal magnitudes , & c . Q. E. D. ...
Página 104
... tiple of a that fis of b , and that magnitudes have the same ratio to one another which their equimultiples have ( v . 15 ) ; therefore a is to b , as e e b 3 14 f g- C d h is to f ; but as a is to b , so is c to d ; wherefore as c is ...
... tiple of a that fis of b , and that magnitudes have the same ratio to one another which their equimultiples have ( v . 15 ) ; therefore a is to b , as e e b 3 14 f g- C d h is to f ; but as a is to b , so is c to d ; wherefore as c is ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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.
Página 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...
Página 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...
Página 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 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...
Página 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.