The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 8
PROPOSITION VII . — THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another , and likewise those which are ...
PROPOSITION VII . — THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another , and likewise those which are ...
Σελίδα 9
Q.E.D. eg fg upon PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle , it is required to bisect it .
Q.E.D. eg fg upon PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle , it is required to bisect it .
Σελίδα 10
d b PROPOSITION XI . — PROBLEM . a To draw a straight line at right angles to a given straight line , from a given point in the same . LET a b be a given straight line , and c a point given in it ; it is required to draw a straight line ...
d b PROPOSITION XI . — PROBLEM . a To draw a straight line at right angles to a given straight line , from a given point in the same . LET a b be a given straight line , and c a point given in it ; it is required to draw a straight line ...
Σελίδα 11
PROPOSITION XII . — PROBLEM . To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . LET a b be the given straight line , which may be produced to any length both ways ...
PROPOSITION XII . — PROBLEM . To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . LET a b be the given straight line , which may be produced to any length both ways ...
Σελίδα 12
Q. E. D. PROPOSITION XIV . — THEOREM . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in ...
Q. E. D. PROPOSITION XIV . — THEOREM . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in ...
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a b c angle a b c angle bac 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 join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole