Wentworths Solid Geometry
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In our eReader you can find the full English version of the book. Read Wentworths Solid Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Wentworths Solid Geometry
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This line will cut the arcs DCF and GCE in separate points D and E ; and if we revolve the line A D about A as a fixed point until D coincides with C, we shall have a line from A to C equal to the line AD. In like manner, we can draw a line from J5 to C equal to the line BE. Therefore a line can be drawn from A to B through C that is equal to the sum of the lines AD and BE, and hence is less than the line A DEB by the line DE. Therefore no line which does not pass through C can be the shortest ...line from ^ to j5. Therefore the shortest line from A to B passes through C. But C is any point in the arc AB. Therefore the shortest line from A to B passes through every point of the arc AB, and consequently coincides with the arc AB. Therefore the shortest line from A to B is the great-circle arc ^5. Q. E. D. EXERCISE 106 1. The three medians of a spherical triangle are concurrent. 2. To construct with a given radius a spherical surface that passes through three given points. 3. To construct with a given radius a spherical surface that passes through two given points and is tangent to a given plane.
What to read after Wentworths Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by George Wentworth to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
This line will cut the arcs DCF and GCE in separate points D and E ; and if we revolve the line A D about A as a fixed point until D coincides with C, we shall have a line from A to C equal to the line AD. In like manner, we can draw a line from J5 to C equal to the line BE. Therefore a line can be drawn from A to B through C that is equal to the sum of the lines AD and BE, and hence is less than the line A DEB by the line DE. Therefore no line which does not pass through C can be the shortest ...line from ^ to j5. Therefore the shortest line from A to B passes through C. But C is any point in the arc AB. Therefore the shortest line from A to B passes through every point of the arc AB, and consequently coincides with the arc AB. Therefore the shortest line from A to B is the great-circle arc ^5. Q. E. D. EXERCISE 106 1. The three medians of a spherical triangle are concurrent. 2. To construct with a given radius a spherical surface that passes through three given points. 3. To construct with a given radius a spherical surface that passes through two given points and is tangent to a given plane.
What to read after Wentworths Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by George Wentworth to read onlineMoreLess
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