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
PROPOSITION XV. THEOREM.
EQual Cylinders and Cones, have their Bases and height reciprocal, and those which have their Bases and heights reciprocal, are equal.
If the Cylinders AB, CD, are equal; there shall be the same Ratio of the Base B to the Base D, as of the height CD to the height AB. Let the height DE be equal to the height AB.
Demonstration. There is the same Ratio of the Cylinder AB to the Cylin∣der DE, of the same height, as of the Base B to the Base D (by the 14th.) Now as the Cylinder AB is to the Cy∣linder DE; so is the Cylinder CD
descriptionPage 386
equal to AB, to the Cylinder DE; that is to say, so is the height CD to the height AB or DE. Therefore as the Base B is to the Base D, so is the height CD to the height AB.
Secondly, If there be the same Ratio of the Base B to the Base D, as of the height CD to the height AB; the Cylinders AB, CD, shall be equal. For the Cylinder AB is to the Cylin∣der DE, as is the Base B to the Base D, and the Cylinder CD shall have the same Ratio to the Cylinder DE, as CD to DE; there shall thence be the same Ratio of AB to DE, as of CD to DE; and (by the 8th. of the 5th.) the Cylinders AB, and CD, shall be equal.
The Propositions 16 and 17 are very difficult, and are only of use in the 18th. which I will Demonstrate after a more easie method by the Two following Lemma's.
email
Do you have questions about this content? Need to report a problem?
Please contact us.