The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 9
... sides ba , ca do not coincide with the sides ed , fd , but have a different situation , as eg , fg , then upon the same base ef , and upon the same side of it , there can be two triangles that have their sides which are terminated in ...
... sides ba , ca do not coincide with the sides ed , fd , but have a different situation , as eg , fg , then upon the same base ef , and upon the same side of it , there can be two triangles that have their sides which are terminated in ...
Σελίδα 10
... sides a c , cd are equal to 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 ...
... sides a c , cd are equal to 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 ...
Σελίδα 11
... side of a b , and from the centre c , at the distance cd , describe ( 3 post . ) the circle egf meet- ing a b in f , g ... sides fh , hc are equal to the two gh , hc , each to each ; and the base c f is equal ( 15 def . ) to the base cg ...
... side of a b , and from the centre c , at the distance cd , describe ( 3 post . ) the circle egf meet- ing a b in f , g ... sides fh , hc are equal to the two gh , hc , each to each ; and the base c f is equal ( 15 def . ) to the base cg ...
Σελίδα 12
... sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the same straight line . At the point b in the straight line a b , let the two straight lines bc , bd с b a e d ...
... sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the same straight line . At the point b in the straight line a b , let the two straight lines bc , bd с b a e d ...
Σελίδα 13
... sides are opposite ; wherefore the angle bae is equal to the angle ecf ; but the angle ecd is greater than the angle e cf ; therefore the angle a cd is greater than b a d g bae . In the same manner , if the side b c be bisected , it may ...
... sides are opposite ; wherefore the angle bae is equal to the angle ecf ; but the angle ecd is greater than the angle e cf ; therefore the angle a cd is greater than b a d g bae . In the same manner , if the side b c be bisected , it may ...
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.