PROPOSITION V. THEOREM.
TRiangles whose sides are proportional, are equianguler.
If the Triangles ABC, DEF, have their sides proportional, that is to say, if there be the same reason of AB to
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 4, 2024.
Pages
Page 270
BC, as of DE to EF; as also if there be the same reason of AB to AC, as of DE to DF, the Angles ABC, DEF, A and D; C and F shall be equal. Make the Angle FEG equal to the Angle B; and EFG equal to the Angle C.
Demonstration. The Triangles ABC, EFG, have two Angles equal; they are thence equiangled (by the Cor. of the 32d. of the 1st.) and (by the 4th.) there is the same reason of DE to EF, as of EG to EF. Now it is supposed that there is the same reason of DE to EF, as of EG to EF. Thence (by the 7th. of the 5th.) DE, EG, are equal. In like manner DF, FG, are also equal, and (by the 8th. of the 1st.) the Triangles DEF, GEF, are equiangular. Now the Angle GEF was made equal to the Angle B: thence DEF is equal to the Angle B; and the Angle DFE, to the Angle C. So that the Triangles ABC, DEF, are equiangular.