The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 6
... a b is equal to a c , and let the straight lines a b , a c be produced to d and e , the angle a bc shall be equal to the angle a c b , and the angle cbd to the angle bce . In bd take any point f , and from ae 6 THE ELEMENTS OF EUCLID .
... a b is equal to a c , and let the straight lines a b , a c be produced to d and e , the angle a bc shall be equal to the angle a c b , and the angle cbd to the angle bce . In bd take any point f , and from ae 6 THE ELEMENTS OF EUCLID .
Σελίδα 7
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to af , the less , and join fc , g b . f b a g Because af is equal to a g , and ab to a c , the two sides fa , a c are equal to the two ga , ab ...
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to af , the less , and join fc , g b . f b a g Because af is equal to a g , and ab to a c , the two sides fa , a c are equal to the two ga , ab ...
Σελίδα 9
... Take any point d in a b , and from a c cut ( i . 3 ) off a e equal to a d ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join af ; the straight line af bisects the angle bac Because a d is equal to a e ...
... Take any point d in a b , and from a c cut ( i . 3 ) off a e equal to a d ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join af ; the straight line af bisects the angle bac Because a d is equal to a e ...
Σελίδα 10
... Take any point d in a c , and make ( i . 3 ) ce equal to cd , and upon de a d e b describe ( i . 1 ) the equilateral triangle dfe , and join fc , the straight line fc drawn from the given point c is at right angles to the given straight ...
... Take any point d in a c , and make ( i . 3 ) ce equal to cd , and upon de a d e b describe ( i . 1 ) the equilateral triangle dfe , and join fc , the straight line fc drawn from the given point c is at right angles to the given straight ...
Σελίδα 11
... Take any point d upon the other 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 ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch ...
... Take any point d upon the other 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 ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
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.