The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 1
... same direction . IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... straight lines Definitions, &c.
... same direction . IX . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... straight lines Definitions, &c.
Seite 2
... the angle dbc , or cbd ; but if there be only one angle at a point , it may be expressed by a letter placed at that point ; as the angle at e . X. When a straight line standing on another straight line makes the adjacent angles equal to ...
... the angle dbc , or cbd ; but if there be only one angle at a point , it may be expressed by a letter placed at that point ; as the angle at e . X. When a straight line standing on another straight line makes the adjacent angles equal to ...
Seite 4
... 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 dis- tance from that centre . AXIOMS . I. Things which are equal ... lines cannot enclose a space . XI . All ...
... 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 dis- tance from that centre . AXIOMS . I. Things which are equal ... lines cannot enclose a space . XI . All ...
Seite 5
... equal to cb ; wherefore ca , ab , bc are equal to one another ; and the tri- angle abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given ...
... equal to cb ; wherefore ca , ab , bc are equal to one another ; and the tri- angle abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given ...
Seite 6
Euclides. line a e is equal ( 1 ax . ) to c , and from a b , the greater of two straight lines , a part ae has been cut off equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one ...
Euclides. line a e is equal ( 1 ax . ) to c , and from a b , the greater of two straight lines , a part ae has been cut off equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one ...
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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