The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 45
... centre g , at the distance gb or gf , de- scribe the semicircle bhf , and produce de to h , and join gh : therefore because the straight line bf is divided into two equal parts in the point g , and into two unequal a b f g e C d at e ...
... centre g , at the distance gb or gf , de- scribe the semicircle bhf , and produce de to h , and join gh : therefore because the straight line bf is divided into two equal parts in the point g , and into two unequal a b f g e C d at e ...
Página 47
... centre of a circle , when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls is said to be farther from the centre . Definitions IV . and V. VI . A segment ...
... centre of a circle , when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls is said to be farther from the centre . Definitions IV . and V. VI . A segment ...
Página 48
... centre , and the circumference between them . Definition X. XI . Similar segments of a circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a ...
... centre , and the circumference between them . Definition X. XI . Similar segments of a circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a ...
Página 49
... centre g * : therefore the angle adg is equal ( i . 8 ) to the angle gdb . But when a straight line standing upon ... centre of the circle abc . In the same manner it can be shewn , that no other point but fis the centre ; that is ...
... centre g * : therefore the angle adg is equal ( i . 8 ) to the angle gdb . But when a straight line standing upon ... centre of the circle abc . In the same manner it can be shewn , that no other point but fis the centre ; that is ...
Página 50
... centre , bisect any straight line ab , which does not pass through the centre , in the point f ; it cuts it also at right angles . C Take ( i . 3 ) e the centre of the circle , and join ea , eb . Then , because af is equal to fb ...
... centre , bisect any straight line ab , which does not pass through the centre , in the point f ; it cuts it also at right angles . C Take ( i . 3 ) e the centre of the circle , and join ea , eb . Then , because af is equal to fb ...
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Términos y frases comunes
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