The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 15
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . LET the two straight lines bd , cd be drawn from b , c , the ends of the side ...
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . LET the two straight lines bd , cd be drawn from b , c , the ends of the side ...
Σελίδα 21
... equal to gkd ; and they are alternate angles ; therefore ab is parallel ( i . 27 ) to cd ; Wherefore , straight lines , & c . Q. E. D. k g b h f d PROPOSITION XXXI . — PROBLEM . To draw a straight BOOK I. PROPS . XXIX . , XXX . 21.
... equal to gkd ; and they are alternate angles ; therefore ab is parallel ( i . 27 ) to cd ; Wherefore , straight lines , & c . Q. E. D. k g b h f d PROPOSITION XXXI . — PROBLEM . To draw a straight BOOK I. PROPS . XXIX . , XXX . 21.
Σελίδα 22
Euclides. PROPOSITION XXXI . — PROBLEM . To draw a straight line through a given point parallel to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw a straight line through the ...
Euclides. PROPOSITION XXXI . — PROBLEM . To draw a straight line through a given point parallel to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw a straight line through the ...
Σελίδα 23
... drawing straight lines from a point f within the figure to each of its angles . And , by the preceding proposition , all the angles of these triangles are equal to twice as many right angles as there are triangles , that is , as there ...
... drawing straight lines from a point f within the figure to each of its angles . And , by the preceding proposition , all the angles of these triangles are equal to twice as many right angles as there are triangles , that is , as there ...
Σελίδα 26
... draw ( i . 31 ) be parallel to ca ; and through c draw cf parallel to bd ; therefore each of the figures ebca , dbcf is a paral- lelogram ; and ebca is equal ( i . 35 ) to dbcf , because they are upon the same base bc , and between the ...
... draw ( i . 31 ) be parallel to ca ; and through c draw cf parallel to bd ; therefore each of the figures ebca , dbcf is a paral- lelogram ; and ebca is equal ( i . 35 ) to dbcf , because they are upon the same base bc , and between the ...
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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