The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 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.
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ab . 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 ab . Which was to be done . PROPOSITION II . — PROBLEM . From a given ...
Σελίδα 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 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 the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one ...
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ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle