The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 1 - 5 από τα 45.
Σελίδα 6
... base b c shall coincide with the base ef , because the point b coinciding with e , and c with f , if the base b c does not coincide with the base e f , two straight lines would enclose a space , which is impossible ( 10 ax . ) . Therefore ...
... base b c shall coincide with the base ef , because the point b coinciding with e , and c with f , if the base b c does not coincide with the base e f , two straight lines would enclose a space , which is impossible ( 10 ax . ) . Therefore ...
Σελίδα 7
... base bc is common to the two triangles bfc , cgb ; wherefore the tri- angles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle fbc is equal to the angle gcb ...
... base bc is common to the two triangles bfc , cgb ; wherefore the tri- angles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle fbc is equal to the angle gcb ...
Σελίδα 9
... base bc equal to the base ef . The angle bac is equal to the angle ed f a b с d g f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line bc upon ef ; the point c shall also coin- cide with ...
... base bc equal to the base ef . The angle bac is equal to the angle ed f a b с d g f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line bc upon ef ; the point c shall also coin- cide with ...
Σελίδα 10
... bc , cd , each to each ; and the angle a cd is equal to the angle bcd ; therefore the base ad is equal to the base ( i . 4 ) db , and the b straight line ab is divided into two equal parts in the point d . Which was to be done ...
... bc , cd , each to each ; and the angle a cd is equal to the angle bcd ; therefore the base ad is equal to the base ( i . 4 ) db , and the b straight line ab is divided into two equal parts in the point d . Which was to be done ...
Σελίδα 13
... b c be produced to d , the exterior angle a cd is greater than either of the interior opposite angles cba , bac ... base ab is equal ( i . 4 ) to the base cf , and the triangle aeb to the triangle cef , and the re- maining angles ...
... b c be produced to d , the exterior angle a cd is greater than either of the interior opposite angles cba , bac ... base ab is equal ( i . 4 ) to the base cf , and the triangle aeb to the triangle cef , and the re- maining angles ...
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.