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 47.
Σελίδα 3
... these are called trape- ziums . XXXV . Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS .
... these are called trape- ziums . XXXV . Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS .
Σελίδα 4
... produced to any length in a straight line . III . And that a circle may be described from any centre , at any dis- tance from that centre . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If equals ...
... produced to any length in a straight line . III . And that a circle may be described from any centre , at any dis- tance from that centre . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If equals ...
Σελίδα 5
... produce ( 2 post . ) the straight lines da , db , to e and f ; from the centre b , at the distance bc , describe ( 3 post . ) the circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to ...
... produce ( 2 post . ) the straight lines da , db , to e and f ; from the centre b , at the distance bc , describe ( 3 post . ) the circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to ...
Σελίδα 6
... produced , the angles upon the other side of the base shall also be equal . LET abc be an isosceles triangle , of which the side 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 ...
... produced , the angles upon the other side of the base shall also be equal . LET abc be an isosceles triangle , of which the side 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 ...
Σελίδα 8
... produce a c , ad to e , a vertices , as d , be within the other triangle a cb ; f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base cd are equal ( i . 5 ) to one another ...
... produce a c , ad to e , a vertices , as d , be within the other triangle a cb ; f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base cd are equal ( i . 5 ) to one another ...
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.