The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 87.
Σελίδα 5
to bg ; and because d is the centre of the circle gkl , dl f is equal to dg , and da , db , parts of them , are equal ; therefore the remainder al is equal to the remainder ( 3 ax . ) bg ; but it has been shewn that bc is equal to bg ...
to bg ; and because d is the centre of the circle gkl , dl f is equal to dg , and da , db , parts of them , are equal ; therefore the remainder al is equal to the remainder ( 3 ax . ) bg ; but it has been shewn that bc is equal to bg ...
Σελίδα 6
to c , and from a b , the greater of two straight lines , a part a e bas been cut off equal to c the less . ... Wherefore the whole triangle a b c shall coincide with the whole triangle de f , and be equal to it ; and the other angles ...
to c , and from a b , the greater of two straight lines , a part a e bas been cut off equal to c the less . ... Wherefore the whole triangle a b c shall coincide with the whole triangle de f , and be equal to it ; and the other angles ...
Σελίδα 7
g In bd take any point f , and from a e the greater , cut off ag equal ( i . 3 ) to a f , the less , and join fc , g b . Because a f is equal to ag , and ab to a c , the two sides fa , a c are equal to the two ga , a b , each to each ...
g In bd take any point f , and from a e the greater , cut off ag equal ( i . 3 ) to a f , the less , and join fc , g b . Because a f is equal to ag , and ab to a c , the two sides fa , a c are equal to the two ga , a b , each to each ...
Σελίδα 8
But if one of the vertices , as d , be within the other triangle a cb ; produce a c , ad to e , f ; therefore , because a c is equal to ad in the triangle ac d , the angles ecd , fdc upon the other side of the base cd are equal ( i .
But if one of the vertices , as d , be within the other triangle a cb ; produce a c , ad to e , f ; therefore , because a c is equal to ad in the triangle ac d , the angles ecd , fdc upon the other side of the base cd are equal ( i .
Σελίδα 9
a b to d e , and a c to df ; and also the base b c equal to the base e f . The angle bac is a d 8 equal to the angle ed f . For , if the triangle a b c be applied to def , so that the pcint b be on e , and the straight line bc upon ef ...
a b to d e , and a c to df ; and also the base b c equal to the base e f . The angle bac is a d 8 equal to the angle ed f . For , if the triangle a b c be applied to def , so that the pcint b be on e , and the straight line bc upon ef ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
abcd angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given rectilineal given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole
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.