PROPOSITION XVIII. THEOREM.
Composition of Reason.
IF Magnitudes divided be proportional, the same also being compounded shall be proportional.
| A, | B, | C, | D. |
| 5. | 3. | 10. | 6. |
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.
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- Subject terms
- Geometry -- Early works to 1800.
- Mathematical analysis.
- Link to this Item
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http://name.umdl.umich.edu/A38722.0001.001
- Cite this Item
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"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 10, 2024.
Pages
Page 238
Demonstration. Seeing it is supposed that there is the same reason of A to B as of C to D, A shall contain an aliquot part whatever of B, as many times as C contains a like aliquot part of D. Now the Magnitude B contains any aliquot part of it self as many times as D con∣tains alike of it self: thence adding B to A, and D to C, AB shall contain an aliquot part of B, as many times as CD contains a like aliquot part of D: there is therefore (by the fifth Definiti∣on) the same reason of AB to B, as of CD to D.
COROLLARY.
Conversion of Reason.
IF there be the same reason of AB to B, as of CD to D, there shall also be the same reason of AB to A, as of CD to C: for (by the foregoing) there will be the same reason of A to B as o C to D: and (by the Coroll. of the 16th.) there will be the same reason of B to A, as of D to C: and by Composition there will be the same reason of AB to A, as of CD to C.
Page 239
USE.
WE make use of this way of Ar∣guing in almost all the Parts of the Mathematicks.