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 39.
Σελίδα 5
... circle def , ae is equal to a d ; but the straight line c is likewise equal d G a e b to ad ; whence ae and c are each of them equal to ad ; therefore the straight line a e is equal ( 1 ax . ) BOOK I. PROPS . II . , III . 5.
... circle def , ae is equal to a d ; but the straight line c is likewise equal d G a e b to ad ; whence ae and c are each of them equal to ad ; therefore the straight line a e is equal ( 1 ax . ) BOOK I. PROPS . II . , III . 5.
Σελίδα 6
... likewise the angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz ...
... likewise the angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz ...
Σελίδα 8
... likewise those which are terminated in the other extremity . d Ir it be possible , let there be two triangles a c b , a d b , upon the same base a b , and upon the same side of it , which have their sides ca , da terminated in the ...
... likewise those which are terminated in the other extremity . d Ir it be possible , let there be two triangles a c b , a d b , upon the same base a b , and upon the same side of it , which have their sides ca , da terminated in the ...
Σελίδα 9
... likewise their sides terminated in the other extremity ; but this is impossible ( i . 7 ) ; therefore , if the base bc coincides with the base ef , the sides ba , a c , cannot but coincide with the sides ed , df ; wherefore likewise the ...
... likewise their sides terminated in the other extremity ; but this is impossible ( i . 7 ) ; therefore , if the base bc coincides with the base ef , the sides ba , a c , cannot but coincide with the sides ed , df ; wherefore likewise the ...
Σελίδα 12
... likewise together equal to two right angles ; therefore the angles c ba , a be are equal to the angles c ba , abd : take away the common angle cba , the remaining angle a be is equal ( 3 ax . ) to the remaining angle a b d , the less to ...
... likewise together equal to two right angles ; therefore the angles c ba , a be are equal to the angles c ba , abd : take away the common angle cba , the remaining angle a be is equal ( 3 ax . ) to the remaining angle a b d , the less to ...
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 perpendicular Q. E. D. PROPOSITION rectangle a b 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 40 - 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 2 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 19 - 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 27 - 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 36 - 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 13 - 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 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 2 - 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 124 - 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.