Elements of Geometry |
From inside the book
Results 1-5 of 93
Page v
... given points . For , from this essential property we can deduce all the other properties of a straight line , and particularly that of its being the shortest be- tween two given points . But in order to this it would have been necessary ...
... given points . For , from this essential property we can deduce all the other properties of a straight line , and particularly that of its being the shortest be- tween two given points . But in order to this it would have been necessary ...
Page vii
... given two methods of approximation for squaring the circle , one of which is that of James Gregory . This section is followed by an appendix , in which we have de- monstrated that the circle is greater than any rectilineal figure of the ...
... given two methods of approximation for squaring the circle , one of which is that of James Gregory . This section is followed by an appendix , in which we have de- monstrated that the circle is greater than any rectilineal figure of the ...
Page 3
... given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show ...
... given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show ...
Page 11
... given point A ( fig . 31 ) , without a straight line DE , Fig 31 . only one perpendicular can be drawn to that line . Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that BF AB , and join CF ...
... given point A ( fig . 31 ) , without a straight line DE , Fig 31 . only one perpendicular can be drawn to that line . Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that BF AB , and join CF ...
Page 12
... given straight line ; for , if this could be done , there would be on the same side of the perpendicular two equal oblique lines , which is impossible . Fig . 32 THEOREM . 55. If from the point C ( fig . 32 ) , the middle of the ...
... given straight line ; for , if this could be done , there would be on the same side of the perpendicular two equal oblique lines , which is impossible . Fig . 32 THEOREM . 55. If from the point C ( fig . 32 ) , the middle of the ...
Other editions - View all
Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence