The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 3
Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . a I. Let it be granted that a DEFINITIONS . 3.
Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . a I. Let it be granted that a DEFINITIONS . 3.
Σελίδα 4
That a terminated straight line may be produced to any length in a straight line . III . And that a circle may be described from any centre , at any distance from that centre . AXIOMS . I. Things which are equal to the same thing are ...
That a terminated straight line may be produced to any length in a straight line . III . And that a circle may be described from any centre , at any distance from that centre . AXIOMS . I. Things which are equal to the same thing are ...
Σελίδα 5
the straight line ab ; and upon it describe ( i . 1 ) the equilateral triangle d a b , and produce ( 2 post . ) the straight lines da , db , to e and h f ; from the centre b , at the distance bc , describe ( 3 post . ) ...
the straight line ab ; and upon it describe ( i . 1 ) the equilateral triangle d a b , and produce ( 2 post . ) the straight lines da , db , to e and h f ; from the centre b , at the distance bc , describe ( 3 post . ) ...
Σελίδα 6
The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . LET a b c be an isosceles triangle , of which the side ab ...
The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . LET a b c be an isosceles triangle , of which the side ab ...
Σελίδα 8
But if one of the vertices , as d , be within the other triangle a cb ; produce a c , ad to e , 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 .
But if one of the vertices , as d , be within the other triangle a cb ; produce a c , ad to e , 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 .
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angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole