The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα
... Propositions Exercises III . Definitions Propositions Exercises IV . Definitions Propositions Exercises 1 4 33 35 35 46 47 48 73 75 . 76 87 V. Definitions 89 Propositions 91 Exercises 115 VI . Definitions 116 Propositions 116 Exercises ...
... Propositions Exercises III . Definitions Propositions Exercises IV . Definitions Propositions Exercises 1 4 33 35 35 46 47 48 73 75 . 76 87 V. Definitions 89 Propositions 91 Exercises 115 VI . Definitions 116 Propositions 116 Exercises ...
Σελίδα 4
... PROPOSITION I. — PROBLEM . To describe an equilateral triangle upon a given finite straight line . LET ab be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre a , at the distance ab ...
... PROPOSITION I. — PROBLEM . To describe an equilateral triangle upon a given finite straight line . LET ab be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre a , at the distance ab ...
Σελίδα 5
... PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and be the given straight line ; it is required to draw from the point a a straight line equal to bc ...
... PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and be 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
... PROPOSITION VI . — THEOREM . e 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 abc be a triangle having the angle abc equal ...
... PROPOSITION VI . — THEOREM . e 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 abc be a triangle having the angle abc equal ...
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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 circumference bc 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 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 tiple touches the circle triangle abc triangle def twice the rectangle