Elements of Geometry |
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Page vi
... four of solid geometry . The first section , entitled first principles , & c . contains the prop- erties of straight lines which meet those of perpendiculars , the theorem upon the sum of the angles ... right - angled triangle , those of ...
... four of solid geometry . The first section , entitled first principles , & c . contains the prop- erties of straight lines which meet those of perpendiculars , the theorem upon the sum of the angles ... right - angled triangle , those of ...
Page 2
... angles DCB , BCE , and the angle DCB is the difference between the two angles DCE , BCE . Fig . 3 . Fig . 4 . Fig . 5 ... right angle . The side opposite to the right angle is called the hypothenuse . Fig . 10. Thus ABC ( fig . 10 ) is a ...
... angles DCB , BCE , and the angle DCB is the difference between the two angles DCE , BCE . Fig . 3 . Fig . 4 . Fig . 5 ... right angle . The side opposite to the right angle is called the hypothenuse . Fig . 10. Thus ABC ( fig . 10 ) is a ...
Page 4
... right angles are equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB , GE , GF , equal to each other ...
... right angles are equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB , GE , GF , equal to each other ...
Page 6
... right angles . In general , if any number of straight lines , as CA , CB ( fig . 22 ) , & c . , meet in the same point C , the sum of all the successive an- gles , ACB , BCD , DCE , ECF , FCA , will be equal to four right angles . For ...
... right angles . In general , if any number of straight lines , as CA , CB ( fig . 22 ) , & c . , meet in the same point C , the sum of all the successive an- gles , ACB , BCD , DCE , ECF , FCA , will be equal to four right angles . For ...
Page 16
... angles equal to a third of two right angles ; so that , if a right angle be expressed by unity , the angle of an ... four right angles ; therefore , if all the angles of a quadrilateral are equal , each of them will be a right angle ...
... angles equal to a third of two right angles ; so that , if a right angle be expressed by unity , the angle of an ... four right angles ; therefore , if all the angles of a quadrilateral are equal , each of them will be a right angle ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence