Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids ; to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1839 - 318 páginas |
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Página 17
... straight " line . " " COR . Hence two straight lines cannot inclose a space . Neither can " two straight lines have a common segment ; that is , they cannot " coincide in part , without coinciding altogether . " IV . A superficies is ...
... straight " line . " " COR . Hence two straight lines cannot inclose a space . Neither can " two straight lines have a common segment ; that is , they cannot " coincide in part , without coinciding altogether . " IV . A superficies is ...
Página 18
... straight lines that ' contain the angle meet one another , is put between the other two ' letters , and one of these two is somewhere upon one of those straight ' lines , and the other upon the other line : Thus the angle which ' is ...
... straight lines that ' contain the angle meet one another , is put between the other two ' letters , and one of these two is somewhere upon one of those straight ' lines , and the other upon the other line : Thus the angle which ' is ...
Página 19
... line , which is called the circumference , and is such that all straight lines drawn from a cer- tain point within the figure to the circumference , are equal to one another . XII . And this point is called the centre of the circle ...
... line , which is called the circumference , and is such that all straight lines drawn from a cer- tain point within the figure to the circumference , are equal to one another . XII . And this point is called the centre of the circle ...
Página 22
... 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 , describe ( 3 Pos- tulate ) the circle BCD , and from the center B , at the dis ...
... 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 , describe ( 3 Pos- tulate ) the circle BCD , and from the center B , at the dis ...
Página 23
... straight line AL is equal to BC . Where- fore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given straight lines to ...
... straight line AL is equal to BC . Where- fore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . From the greater of two given straight lines to ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB produced proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore