The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα
Propositions Exercises II . Definitions . Propositions Exercises 35 35 46 47 III . Definitions Propositions Exercises 48 73 IV . Definitions 75 76 87 89 Propositions Exercises V. Definitions Propositions Exercises VI . Definitions 91 .
Propositions Exercises II . Definitions . Propositions Exercises 35 35 46 47 III . Definitions Propositions Exercises 48 73 IV . Definitions 75 76 87 89 Propositions Exercises V. Definitions Propositions Exercises VI . Definitions 91 .
Σελίδα 4
ز PROPOSITION I. PROBLEM . To describe an equilateral triangle upon a ... Because the point a is the centre of the circle bed , ac is equal ( 15 def . ) to ab ; and because the point b is the centre 4 THE ELEMENTS OF EUCLID . Propositions.
ز PROPOSITION I. PROBLEM . To describe an equilateral triangle upon a ... Because the point a is the centre of the circle bed , ac is equal ( 15 def . ) to ab ; and because the point b is the centre 4 THE ELEMENTS OF EUCLID . Propositions.
Σελίδα 5
PROPOSITION II . — PROBLEM . a From a given point to draw a straight line equal to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw from the point a a straight line equal to bc .
PROPOSITION II . — PROBLEM . a From a given point to draw a straight line equal to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw from the point a a straight line equal to bc .
Σελίδα 6
PROPOSITION IV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another , they shall likewise have their bases ...
PROPOSITION IV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another , they shall likewise have their bases ...
Σελίδα 7
9 PROPOSITION VI . - THEOREM . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall also be equal to one another . LET a b c be a triangle having the angle a b c ...
9 PROPOSITION VI . - THEOREM . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall also be equal to one another . LET a b c be a triangle having the angle a b c ...
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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