Elementary Synthetic Geometry of the Point Line And Circle in the Plane
Elementary Synthetic Geometry of the Point Line And Circle in the Plane
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When N comes to parallelism with L, AX becomes infinite and BY becomes zero.
. -. Co. O is indefinite since U may have any value we please.
2. The motion continuing, let N come into the position N'. Then AX' is opposite in sense to AX, and BY' to BY. But AX increased to 00, changed sign and then decreased ab- solutely, until it reached its present value AX', while BY decreased to zero and then changed sign.
. •. A magnitude changes sign when it passes through zero or infinity.
3. It is readily ...seen that, as the rotation continues, BY' in- creases negatively and AX' decreases, as represented in one of the stages of change at X" and Y". After this Y" goes ofi" to 00 as X" comes to A. Both magnitudes then change sign again, this time BY" by passing through 00 and AX''' by pass- ing through zero.
Since both segments change sign together the product or rectangle remains always positive and always equal to the constant area U.
l8o SYNTHETIC GEOMETRY.
222°. A line in the plane admits of one kind of varia- tion, rotation.
What to read after Elementary Synthetic Geometry of the Point Line And Circle in the Plane?
You can find similar books in the "Read Also" column, or choose other free books by N F Nathan Fellowes Dupuis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
When N comes to parallelism with L, AX becomes infinite and BY becomes zero.
. -. Co. O is indefinite since U may have any value we please.
2. The motion continuing, let N come into the position N'. Then AX' is opposite in sense to AX, and BY' to BY. But AX increased to 00, changed sign and then decreased ab- solutely, until it reached its present value AX', while BY decreased to zero and then changed sign.
. •. A magnitude changes sign when it passes through zero or infinity.
3. It is readily ...seen that, as the rotation continues, BY' in- creases negatively and AX' decreases, as represented in one of the stages of change at X" and Y". After this Y" goes ofi" to 00 as X" comes to A. Both magnitudes then change sign again, this time BY" by passing through 00 and AX''' by pass- ing through zero.
Since both segments change sign together the product or rectangle remains always positive and always equal to the constant area U.
l8o SYNTHETIC GEOMETRY.
222°. A line in the plane admits of one kind of varia- tion, rotation.
What to read after Elementary Synthetic Geometry of the Point Line And Circle in the Plane?
You can find similar books in the "Read Also" column, or choose other free books by N F Nathan Fellowes Dupuis to read onlineMoreLess
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