The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...
About this Item
Title
The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...
Author
Dechales, Claude-François Milliet, 1621-1678.
Publication
London :: Printed for Philip Lea ...,
1685.
Rights/Permissions
To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
Subject terms
Geometry -- Early works to 1800.
Mathematical analysis.
Link to this Item
http://name.umdl.umich.edu/A38722.0001.001
Cite this Item
"The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ..." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A38722.0001.001. University of Michigan Library Digital Collections. Accessed June 11, 2024.
Pages
descriptionPage 379
PROPOSITION XI. THEOREM.
CYlinders and Cones of the same height, are in the same Ratio as are their Bases.
There is proposed two Cylinders or two Cones of the same height, which have the Circles A and B for their Bases: I say they are in the same Ratio as are their Bases. For if they are not in the same Ratio; one of them, for example A, shall have a greater Ratio to the Cylinder B, than the Base A to the Base B; so that a quantity L, less than the Cylinder A, would have the same Ratio to the Cylinder B, as hath the Base A to the Base B. There may then be in∣scribed a Polygon Prism in the Cylinder A, greater than the quantity L. Let it be that which hath for Base the Polygon CDEF; and let there be inscribed a like Polygon GHIK, in the Base B, which serveth for Base to the Cylinder of the same height.
descriptionPage 380
Demonstration. The Prisms A and B are in the same Ratio as are their Polygon Bases (by the Coroll. 4. of the 39th. of the 11th.) and the Polygons are in the same Ratio as are the Circles (by the Coroll. of the 2d.) so then the Prism A shall be in the same Ratio to the Prism B, as the Circle A to the Circle B. Now as the Circle A is to the Cirle B, so is the quan∣tity L to the Cylinder B; therefore as the Prism A is to the Prism B, so is the quantity L to the Cylinder B. The Prism A is greater than the quantity L; by consequence (according to the 14th. of the 5th.) the Prism B inscribed in the Cylinder B, would be greater than it, which cannot be. Therefore neither Cylinder hath greater Ratio to the other, than that of its Base to the Base of the other.
Coroll. Cylinders are triple to Cones of the same height, therefore Cones of the same height, are in the same Ratio as are their Bases.
email
Do you have questions about this content? Need to report a problem?
Please contact us.